From 43bf030295815ed9f6a678b70a847a49b11c7e48 Mon Sep 17 00:00:00 2001
From: Andrey Pokidov <9942846+Morgend@users.noreply.github.com>
Date: Wed, 12 Feb 2025 19:39:28 +0700
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---
 basic-geometry-dev/basic-geometry-dev.cbp     |   3 +-
 basic-geometry-dev/main.c                     |  32 +-
 basic-geometry-test/tests/utilities/is_unit.c |  20 +-
 basic-geometry-test/tests/utilities/is_unit.h |   4 +-
 basic-geometry-test/tests/vector2.c           |   4 +-
 basic-geometry/basic-geometry.cbp             |   6 +
 basic-geometry/matrix2x2.c                    |  44 ++-
 basic-geometry/matrix2x2.h                    | 278 ++++++-------
 basic-geometry/matrix2x3.c                    |  12 +-
 basic-geometry/matrix2x3.h                    | 115 +++---
 basic-geometry/matrix3x2.c                    |  12 +-
 basic-geometry/matrix3x2.h                    | 106 ++---
 basic-geometry/matrix3x3.c                    |  15 +-
 basic-geometry/matrix3x3.h                    | 142 ++++---
 basic-geometry/quaternion.c                   |  53 +--
 basic-geometry/quaternion.h                   | 364 +++++++++---------
 basic-geometry/tangent-pair.c                 |  22 +-
 basic-geometry/tangent-pair.h                 | 184 ++++-----
 basic-geometry/utilities.c                    |   4 +-
 basic-geometry/utilities.h                    |   4 +-
 basic-geometry/vector2.c                      |  71 ++--
 basic-geometry/vector2.h                      | 248 +++++++-----
 basic-geometry/vector3.c                      |  66 ++--
 basic-geometry/vector3.h                      | 268 +++++++------
 basic-geometry/versor.c                       |  69 ++--
 basic-geometry/versor.h                       | 216 +++++------
 26 files changed, 1225 insertions(+), 1137 deletions(-)

diff --git a/basic-geometry-dev/basic-geometry-dev.cbp b/basic-geometry-dev/basic-geometry-dev.cbp
index d894694..5548732 100644
--- a/basic-geometry-dev/basic-geometry-dev.cbp
+++ b/basic-geometry-dev/basic-geometry-dev.cbp
@@ -27,10 +27,11 @@
 				<Option type="1" />
 				<Option compiler="gcc" />
 				<Compiler>
-					<Add option="-O2" />
+					<Add option="-O3" />
 					<Add directory="../basic-geometry" />
 				</Compiler>
 				<Linker>
+					<Add option="-O3" />
 					<Add option="-s" />
 					<Add library="basic-geometry" />
 					<Add library="m" />
diff --git a/basic-geometry-dev/main.c b/basic-geometry-dev/main.c
index b1f5468..0f4ad34 100644
--- a/basic-geometry-dev/main.c
+++ b/basic-geometry-dev/main.c
@@ -1,4 +1,3 @@
-/*
 #include <stdio.h>
 #include <stdlib.h>
 #include <math.h>
@@ -12,8 +11,6 @@
 
 typedef struct {
     BgcVersorFP32 versor1, versor2, result;
-    //BgcMatrix3x3FP32 matrix;
-    //BgcVector3FP32 vector1, vector2;
 } structure_fp32_t;
 
 structure_fp32_t* allocate_structures(const unsigned int amount)
@@ -49,18 +46,6 @@ structure_fp32_t* make_structures(const unsigned int amount)
         );
 
         bgc_versor_reset_fp32(&list[i].result);
-
-        //bgc_matrix3x3_set_to_identity_fp32(&list[i].matrix);
-        /*
-        bgc_vector3_set_values_fp32(
-            rand() * multiplier - 1.0f,
-            rand() * multiplier - 1.0f,
-            rand() * multiplier - 1.0f,
-            &list[i].vector1
-        );
-
-        bgc_vector3_reset_fp32(&list[i].vector2);
-        *//*
     }
 
     return list;
@@ -94,7 +79,7 @@ void list_work(const uint_fast32_t amount, structure_fp32_t* list)
         }
     }
 }
-/*
+
 int main()
 {
     const unsigned int amount = 1000000;
@@ -136,18 +121,3 @@ int main()
 
     return 0;
 }
-*/
-
-#include <stdio.h>
-#include <basic-geometry.h>
-
-int main()
-{
-    BgcVector3FP32 my_vector;
-
-    bgc_vector3_set_values_fp32(-2, 7, 10, &my_vector);
-
-    printf("x1 = %f, x2 = %f, x3 = %f\n", my_vector.x1, my_vector.x2, my_vector.x3);
-
-    return 0;
-}
diff --git a/basic-geometry-test/tests/utilities/is_unit.c b/basic-geometry-test/tests/utilities/is_unit.c
index b6b1f53..5f27e88 100644
--- a/basic-geometry-test/tests/utilities/is_unit.c
+++ b/basic-geometry-test/tests/utilities/is_unit.c
@@ -106,13 +106,13 @@ static const float _TEST_FP32_DATA_SQUARE_NONUNIT[] = {
     1.0f - 2.25f * BGC_EPSYLON_FP32
 };
 
-int test_is_sqare_value_unit_fp32()
+int test_is_sqare_unit_fp32()
 {
-    print_testing_name("bgc_is_sqare_value_unit_fp32");
+    print_testing_name("bgc_is_sqare_unit_fp32");
 
     // Testing unit values:
     for (int i = 0; i < _TEST_FP32_DATA_SQUARE_UNIT_AMOUNT; i++) {
-        if (!bgc_is_sqare_value_unit_fp32(_TEST_FP32_DATA_SQUARE_UNIT[i])) {
+        if (!bgc_is_sqare_unit_fp32(_TEST_FP32_DATA_SQUARE_UNIT[i])) {
             print_testing_failed();
             return TEST_FAILED;
         }
@@ -120,7 +120,7 @@ int test_is_sqare_value_unit_fp32()
 
     // Testing non-unit values:
     for (int i = 0; i < _TEST_FP32_DATA_SQUARE_NONUNIT_AMOUNT; i++) {
-        if (bgc_is_sqare_value_unit_fp32(_TEST_FP32_DATA_SQUARE_NONUNIT[i])) {
+        if (bgc_is_sqare_unit_fp32(_TEST_FP32_DATA_SQUARE_NONUNIT[i])) {
             print_testing_failed();
             return TEST_FAILED;
         }
@@ -149,13 +149,13 @@ static const double _TEST_FP64_DATA_SQUARE_NONUNIT[] = {
     1.0 - 2.25 * BGC_EPSYLON_FP64
 };
 
-int test_is_sqare_value_unit_fp64()
+int test_is_sqare_unit_fp64()
 {
-    print_testing_name("bgc_is_sqare_value_unit_fp64");
+    print_testing_name("bgc_is_sqare_unit_fp64");
 
     // Testing unit values:
     for (int i = 0; i < _TEST_FP64_DATA_SQUARE_UNIT_AMOUNT; i++) {
-        if (!bgc_is_sqare_value_unit_fp64(_TEST_FP64_DATA_SQUARE_UNIT[i])) {
+        if (!bgc_is_sqare_unit_fp64(_TEST_FP64_DATA_SQUARE_UNIT[i])) {
             print_testing_failed();
             return TEST_FAILED;
         }
@@ -163,7 +163,7 @@ int test_is_sqare_value_unit_fp64()
 
     // Testing non-unit values:
     for (int i = 0; i < _TEST_FP64_DATA_SQUARE_NONUNIT_AMOUNT; i++) {
-        if (bgc_is_sqare_value_unit_fp64(_TEST_FP64_DATA_SQUARE_NONUNIT[i])) {
+        if (bgc_is_sqare_unit_fp64(_TEST_FP64_DATA_SQUARE_NONUNIT[i])) {
             print_testing_failed();
             return TEST_FAILED;
         }
@@ -184,11 +184,11 @@ int test_is_unit()
         return TEST_FAILED;
     }
 
-    if (test_is_sqare_value_unit_fp32() != TEST_SUCCES) {
+    if (test_is_sqare_unit_fp32() != TEST_SUCCES) {
         return TEST_FAILED;
     }
 
-    if (test_is_sqare_value_unit_fp64() != TEST_SUCCES) {
+    if (test_is_sqare_unit_fp64() != TEST_SUCCES) {
         return TEST_FAILED;
     }
 
diff --git a/basic-geometry-test/tests/utilities/is_unit.h b/basic-geometry-test/tests/utilities/is_unit.h
index 4f8eb44..90195ce 100644
--- a/basic-geometry-test/tests/utilities/is_unit.h
+++ b/basic-geometry-test/tests/utilities/is_unit.h
@@ -5,9 +5,9 @@ int test_is_unit_fp32();
 
 int test_is_unit_fp64();
 
-int test_is_sqare_value_unit_fp32();
+int test_is_sqare_unit_fp32();
 
-int test_is_sqare_value_unit_fp64();
+int test_is_sqare_unit_fp64();
 
 int test_is_unit();
 
diff --git a/basic-geometry-test/tests/vector2.c b/basic-geometry-test/tests/vector2.c
index ca84171..930c1b0 100644
--- a/basic-geometry-test/tests/vector2.c
+++ b/basic-geometry-test/tests/vector2.c
@@ -73,7 +73,7 @@ int test_vector2_fp32_square_modulus()
     return TEST_SUCCES;
 }
 
-// =================== Module =================== //
+// ================== Modulus =================== //
 
 const float FP32_VECTOR2_MODULUS_1[] = { 5.0f, 5.0f, 22360.68f, 10.0005f, 123.55626338f };
 
@@ -180,4 +180,4 @@ int test_fp32_vector2()
 
     return TEST_SUCCES;
 }
-*/
\ No newline at end of file
+*/
diff --git a/basic-geometry/basic-geometry.cbp b/basic-geometry/basic-geometry.cbp
index c7039a3..3e21644 100644
--- a/basic-geometry/basic-geometry.cbp
+++ b/basic-geometry/basic-geometry.cbp
@@ -52,7 +52,13 @@
 			<Option compilerVar="CC" />
 		</Unit>
 		<Unit filename="matrix2x2.h" />
+		<Unit filename="matrix2x3.c">
+			<Option compilerVar="CC" />
+		</Unit>
 		<Unit filename="matrix2x3.h" />
+		<Unit filename="matrix3x2.c">
+			<Option compilerVar="CC" />
+		</Unit>
 		<Unit filename="matrix3x2.h" />
 		<Unit filename="matrix3x3.c">
 			<Option compilerVar="CC" />
diff --git a/basic-geometry/matrix2x2.c b/basic-geometry/matrix2x2.c
index 23a65b2..9dc6a72 100644
--- a/basic-geometry/matrix2x2.c
+++ b/basic-geometry/matrix2x2.c
@@ -9,8 +9,14 @@ extern inline void bgc_matrix2x2_set_to_identity_fp64(BgcMatrix2x2FP64* matrix);
 extern inline void bgc_matrix2x2_set_to_diagonal_fp32(const float d1, const float d2, BgcMatrix2x2FP32* matrix);
 extern inline void bgc_matrix2x2_set_to_diagonal_fp64(const double d1, const double d2, BgcMatrix2x2FP64* matrix);
 
-extern inline void bgc_matrix2x2_make_rotation_fp32(const float angle, const BgcAngleUnitEnum unit, BgcMatrix2x2FP32* matrix);
-extern inline void bgc_matrix2x2_make_rotation_fp64(const double angle, const BgcAngleUnitEnum unit, BgcMatrix2x2FP64* matrix);
+extern inline void bgc_matrix2x2_set_turn_fp32(const float angle, const BgcAngleUnitEnum unit, BgcMatrix2x2FP32* matrix);
+extern inline void bgc_matrix2x2_set_turn_fp64(const double angle, const BgcAngleUnitEnum unit, BgcMatrix2x2FP64* matrix);
+
+extern inline float bgc_matrix2x2_get_determinant_fp32(const BgcMatrix2x2FP32* matrix);
+extern inline double bgc_matrix2x2_get_determinant_fp64(const BgcMatrix2x2FP64* matrix);
+
+extern inline int bgc_matrix2x2_is_singular_fp32(const BgcMatrix2x2FP32* matrix);
+extern inline int bgc_matrix2x2_is_singular_fp64(const BgcMatrix2x2FP64* matrix);
 
 extern inline void bgc_matrix2x2_copy_fp32(const BgcMatrix2x2FP32* from, BgcMatrix2x2FP32* to);
 extern inline void bgc_matrix2x2_copy_fp64(const BgcMatrix2x2FP64* from, BgcMatrix2x2FP64* to);
@@ -21,23 +27,11 @@ extern inline void bgc_matrix2x2_swap_fp64(BgcMatrix2x2FP64* matrix1, BgcMatrix2
 extern inline void bgc_matrix2x2_convert_fp64_to_fp32(const BgcMatrix2x2FP64* from, BgcMatrix2x2FP32* to);
 extern inline void bgc_matrix2x2_convert_fp32_to_fp64(const BgcMatrix2x2FP32* from, BgcMatrix2x2FP64* to);
 
-extern inline float bgc_matrix2x2_get_determinant_fp32(const BgcMatrix2x2FP32* matrix);
-extern inline double bgc_matrix2x2_get_determinant_fp64(const BgcMatrix2x2FP64* matrix);
-
-extern inline int bgc_matrix2x2_is_singular_fp32(const BgcMatrix2x2FP32* matrix);
-extern inline int bgc_matrix2x2_is_singular_fp64(const BgcMatrix2x2FP64* matrix);
-
-extern inline void bgc_matrix2x2_transpose_fp32(BgcMatrix2x2FP32* matrix);
-extern inline void bgc_matrix2x2_transpose_fp64(BgcMatrix2x2FP64* matrix);
-
 extern inline int bgc_matrix2x2_invert_fp32(BgcMatrix2x2FP32* matrix);
 extern inline int bgc_matrix2x2_invert_fp64(BgcMatrix2x2FP64* matrix);
 
-extern inline void bgc_matrix2x2_set_transposed_fp32(const BgcMatrix2x2FP32* from, BgcMatrix2x2FP32* to);
-extern inline void bgc_matrix2x2_set_transposed_fp64(const BgcMatrix2x2FP64* from, BgcMatrix2x2FP64* to);
-
-extern inline int bgc_matrix2x2_set_inverted_fp32(const BgcMatrix2x2FP32* from, BgcMatrix2x2FP32* to);
-extern inline int bgc_matrix2x2_set_inverted_fp64(const BgcMatrix2x2FP64* from, BgcMatrix2x2FP64* to);
+extern inline void bgc_matrix2x2_transpose_fp32(BgcMatrix2x2FP32* matrix);
+extern inline void bgc_matrix2x2_transpose_fp64(BgcMatrix2x2FP64* matrix);
 
 extern inline void bgc_matrix2x2_set_row1_fp32(const float c1, const float c2, BgcMatrix2x2FP32* matrix);
 extern inline void bgc_matrix2x2_set_row1_fp64(const double c1, const double c2, BgcMatrix2x2FP64* matrix);
@@ -51,6 +45,12 @@ extern inline void bgc_matrix2x2_set_column1_fp64(const double r1, const double
 extern inline void bgc_matrix2x2_set_column2_fp32(const float r1, const float r2, BgcMatrix2x2FP32* matrix);
 extern inline void bgc_matrix2x2_set_column2_fp64(const double r1, const double r2, BgcMatrix2x2FP64* matrix);
 
+extern inline int bgc_matrix2x2_make_inverted_fp32(const BgcMatrix2x2FP32* from, BgcMatrix2x2FP32* to);
+extern inline int bgc_matrix2x2_make_inverted_fp64(const BgcMatrix2x2FP64* from, BgcMatrix2x2FP64* to);
+
+extern inline void bgc_matrix2x2_make_transposed_fp32(const BgcMatrix2x2FP32* from, BgcMatrix2x2FP32* to);
+extern inline void bgc_matrix2x2_make_transposed_fp64(const BgcMatrix2x2FP64* from, BgcMatrix2x2FP64* to);
+
 extern inline void bgc_matrix2x2_add_fp32(const BgcMatrix2x2FP32* matrix1, const BgcMatrix2x2FP32* matrix2, BgcMatrix2x2FP32* sum);
 extern inline void bgc_matrix2x2_add_fp64(const BgcMatrix2x2FP64* matrix1, const BgcMatrix2x2FP64* matrix2, BgcMatrix2x2FP64* sum);
 
@@ -60,14 +60,18 @@ extern inline void bgc_matrix2x2_add_scaled_fp64(const BgcMatrix2x2FP64* basic_m
 extern inline void bgc_matrix2x2_subtract_fp32(const BgcMatrix2x2FP32* minuend, const BgcMatrix2x2FP32* subtrahend, BgcMatrix2x2FP32* difference);
 extern inline void bgc_matrix2x2_subtract_fp64(const BgcMatrix2x2FP64* minuend, const BgcMatrix2x2FP64* subtrahend, BgcMatrix2x2FP64* difference);
 
+extern inline void bgc_matrix2x2_subtract_scaled_fp32(const BgcMatrix2x2FP32* basic_matrix, const BgcMatrix2x2FP32* scalable_matrix, const float scale, BgcMatrix2x2FP32* difference);
+extern inline void bgc_matrix2x2_subtract_scaled_fp64(const BgcMatrix2x2FP64* basic_matrix, const BgcMatrix2x2FP64* scalable_matrix, const double scale, BgcMatrix2x2FP64* difference);
+
 extern inline void bgc_matrix2x2_multiply_fp32(const BgcMatrix2x2FP32* multiplicand, const float multiplier, BgcMatrix2x2FP32* product);
 extern inline void bgc_matrix2x2_multiply_fp64(const BgcMatrix2x2FP64* multiplicand, const double multiplier, BgcMatrix2x2FP64* product);
 
 extern inline void bgc_matrix2x2_divide_fp32(const BgcMatrix2x2FP32* dividend, const float divisor, BgcMatrix2x2FP32* quotient);
 extern inline void bgc_matrix2x2_divide_fp64(const BgcMatrix2x2FP64* dividend, const double divisor, BgcMatrix2x2FP64* quotient);
 
-extern inline void bgc_matrix2x2_left_product_fp32(const BgcVector2FP32* vector, const BgcMatrix2x2FP32* matrix, BgcVector2FP32* result);
-extern inline void bgc_matrix2x2_left_product_fp64(const BgcVector2FP64* vector, const BgcMatrix2x2FP64* matrix, BgcVector2FP64* result);
+extern inline void bgc_matrix2x2_left_product_fp32(const BgcVector2FP32* vector, const BgcMatrix2x2FP32* matrix, BgcVector2FP32* product);
+extern inline void bgc_matrix2x2_left_product_fp64(const BgcVector2FP64* vector, const BgcMatrix2x2FP64* matrix, BgcVector2FP64* product);
+
+extern inline void bgc_matrix2x2_right_product_fp32(const BgcMatrix2x2FP32* matrix, const BgcVector2FP32* vector, BgcVector2FP32* product);
+extern inline void bgc_matrix2x2_right_product_fp64(const BgcMatrix2x2FP64* matrix, const BgcVector2FP64* vector, BgcVector2FP64* product);
 
-extern inline void bgc_matrix2x2_right_product_fp32(const BgcMatrix2x2FP32* matrix, const BgcVector2FP32* vector, BgcVector2FP32* result);
-extern inline void bgc_matrix2x2_right_product_fp64(const BgcMatrix2x2FP64* matrix, const BgcVector2FP64* vector, BgcVector2FP64* result);
diff --git a/basic-geometry/matrix2x2.h b/basic-geometry/matrix2x2.h
index a6f8fce..e421021 100644
--- a/basic-geometry/matrix2x2.h
+++ b/basic-geometry/matrix2x2.h
@@ -61,7 +61,7 @@ inline void bgc_matrix2x2_set_to_diagonal_fp64(const double d1, const double d2,
 
 // ============== Rotation Matrix =============== //
 
-inline void bgc_matrix2x2_make_rotation_fp32(const float angle, const BgcAngleUnitEnum unit, BgcMatrix2x2FP32* matrix)
+inline void bgc_matrix2x2_set_turn_fp32(const float angle, const BgcAngleUnitEnum unit, BgcMatrix2x2FP32* matrix)
 {
     const float radians = bgc_angle_to_radians_fp32(angle, unit);
     const float cosine = cosf(radians);
@@ -73,7 +73,7 @@ inline void bgc_matrix2x2_make_rotation_fp32(const float angle, const BgcAngleUn
     matrix->r2c2 = cosine;
 }
 
-inline void bgc_matrix2x2_make_rotation_fp64(const double angle, const BgcAngleUnitEnum unit, BgcMatrix2x2FP64* matrix)
+inline void bgc_matrix2x2_set_turn_fp64(const double angle, const BgcAngleUnitEnum unit, BgcMatrix2x2FP64* matrix)
 {
     const double radians = bgc_angle_to_radians_fp64(angle, unit);
     const double cosine = cos(radians);
@@ -85,6 +85,30 @@ inline void bgc_matrix2x2_make_rotation_fp64(const double angle, const BgcAngleU
     matrix->r2c2 = cosine;
 }
 
+// ================ Determinant ================= //
+
+inline float bgc_matrix2x2_get_determinant_fp32(const BgcMatrix2x2FP32* matrix)
+{
+    return matrix->r1c1 * matrix->r2c2 - matrix->r1c2 * matrix->r2c1;
+}
+
+inline double bgc_matrix2x2_get_determinant_fp64(const BgcMatrix2x2FP64* matrix)
+{
+    return matrix->r1c1 * matrix->r2c2 - matrix->r1c2 * matrix->r2c1;
+}
+
+// ================== Singular ================== //
+
+inline int bgc_matrix2x2_is_singular_fp32(const BgcMatrix2x2FP32* matrix)
+{
+    return bgc_is_zero_fp32(bgc_matrix2x2_get_determinant_fp32(matrix));
+}
+
+inline int bgc_matrix2x2_is_singular_fp64(const BgcMatrix2x2FP64* matrix)
+{
+    return bgc_is_zero_fp64(bgc_matrix2x2_get_determinant_fp64(matrix));
+}
+
 // ==================== Copy ==================== //
 
 inline void bgc_matrix2x2_copy_fp32(const BgcMatrix2x2FP32* from, BgcMatrix2x2FP32* to)
@@ -149,7 +173,7 @@ inline void bgc_matrix2x2_swap_fp64(BgcMatrix2x2FP64* matrix1, BgcMatrix2x2FP64*
     matrix1->r2c2 = r2c2;
 }
 
-// ============= Copy to twin type ============== //
+// ================== Convert =================== //
 
 inline void bgc_matrix2x2_convert_fp64_to_fp32(const BgcMatrix2x2FP64* from, BgcMatrix2x2FP32* to)
 {
@@ -169,47 +193,7 @@ inline void bgc_matrix2x2_convert_fp32_to_fp64(const BgcMatrix2x2FP32* from, Bgc
     to->r2c2 = from->r2c2;
 }
 
-// ================ Determinant ================= //
-
-inline float bgc_matrix2x2_get_determinant_fp32(const BgcMatrix2x2FP32* matrix)
-{
-    return matrix->r1c1 * matrix->r2c2 - matrix->r1c2 * matrix->r2c1;
-}
-
-inline double bgc_matrix2x2_get_determinant_fp64(const BgcMatrix2x2FP64* matrix)
-{
-    return matrix->r1c1 * matrix->r2c2 - matrix->r1c2 * matrix->r2c1;
-}
-
-// ================== Singular ================== //
-
-inline int bgc_matrix2x2_is_singular_fp32(const BgcMatrix2x2FP32* matrix)
-{
-    return bgc_is_zero_fp32(bgc_matrix2x2_get_determinant_fp32(matrix));
-}
-
-inline int bgc_matrix2x2_is_singular_fp64(const BgcMatrix2x2FP64* matrix)
-{
-    return bgc_is_zero_fp64(bgc_matrix2x2_get_determinant_fp64(matrix));
-}
-
-// =============== Transposition ================ //
-
-inline void bgc_matrix2x2_transpose_fp32(BgcMatrix2x2FP32* matrix)
-{
-    const float tmp = matrix->r1c2;
-    matrix->r1c2 = matrix->r2c1;
-    matrix->r2c1 = tmp;
-}
-
-inline void bgc_matrix2x2_transpose_fp64(BgcMatrix2x2FP64* matrix)
-{
-    const double tmp = matrix->r1c2;
-    matrix->r1c2 = matrix->r2c1;
-    matrix->r2c1 = tmp;
-}
-
-// ================= Inversion ================== //
+// =================== Invert =================== //
 
 inline int bgc_matrix2x2_invert_fp32(BgcMatrix2x2FP32* matrix)
 {
@@ -261,80 +245,20 @@ inline int bgc_matrix2x2_invert_fp64(BgcMatrix2x2FP64* matrix)
     return 1;
 }
 
-// =============== Set Transposed =============== //
+// ================= Transpose ================== //
 
-inline void bgc_matrix2x2_set_transposed_fp32(const BgcMatrix2x2FP32* from, BgcMatrix2x2FP32* to)
+inline void bgc_matrix2x2_transpose_fp32(BgcMatrix2x2FP32* matrix)
 {
-    float tmp = from->r1c2;
-
-    to->r1c1 = from->r1c1;
-    to->r1c2 = from->r2c1;
-
-    to->r2c1 = tmp;
-    to->r2c2 = from->r2c2;
+    const float tmp = matrix->r1c2;
+    matrix->r1c2 = matrix->r2c1;
+    matrix->r2c1 = tmp;
 }
 
-inline void bgc_matrix2x2_set_transposed_fp64(const BgcMatrix2x2FP64* from, BgcMatrix2x2FP64* to)
+inline void bgc_matrix2x2_transpose_fp64(BgcMatrix2x2FP64* matrix)
 {
-    double tmp = from->r1c2;
-
-    to->r1c1 = from->r1c1;
-    to->r1c2 = from->r2c1;
-
-    to->r2c1 = tmp;
-    to->r2c2 = from->r2c2;
-}
-
-// ================ Set Inverted ================ //
-
-inline int bgc_matrix2x2_set_inverted_fp32(const BgcMatrix2x2FP32* from, BgcMatrix2x2FP32* to)
-{
-    const float determinant = bgc_matrix2x2_get_determinant_fp32(from);
-
-    if (bgc_is_zero_fp32(determinant)) {
-        return 0;
-    }
-
-    const float r1c1 = from->r2c2;
-    const float r1c2 = -from->r1c2;
-
-    const float r2c1 = -from->r2c1;
-    const float r2c2 = from->r1c1;
-
-    const float multiplier = 1.0f / determinant;
-
-    to->r1c1 = r1c1 * multiplier;
-    to->r1c2 = r1c2 * multiplier;
-
-    to->r2c1 = r2c1 * multiplier;
-    to->r2c2 = r2c2 * multiplier;
-
-    return 1;
-}
-
-inline int bgc_matrix2x2_set_inverted_fp64(const BgcMatrix2x2FP64* from, BgcMatrix2x2FP64* to)
-{
-    const double determinant = bgc_matrix2x2_get_determinant_fp64(from);
-
-    if (bgc_is_zero_fp64(determinant)) {
-        return 0;
-    }
-
-    const double r1c1 = from->r2c2;
-    const double r1c2 = -from->r1c2;
-
-    const double r2c1 = -from->r2c1;
-    const double r2c2 = from->r1c1;
-
-    const double multiplier = 1.0 / determinant;
-
-    to->r1c1 = r1c1 * multiplier;
-    to->r1c2 = r1c2 * multiplier;
-
-    to->r2c1 = r2c1 * multiplier;
-    to->r2c2 = r2c2 * multiplier;
-
-    return 1;
+    const double tmp = matrix->r1c2;
+    matrix->r1c2 = matrix->r2c1;
+    matrix->r2c1 = tmp;
 }
 
 // ================= Set Row 1 ================== //
@@ -393,7 +317,83 @@ inline void bgc_matrix2x2_set_column2_fp64(const double r1, const double r2, Bgc
     matrix->r2c2 = r2;
 }
 
-// ================== Addition ================== //
+// =============== Make Inverted ================ //
+
+inline int bgc_matrix2x2_make_inverted_fp32(const BgcMatrix2x2FP32* matrix, BgcMatrix2x2FP32* inverted)
+{
+    const float determinant = bgc_matrix2x2_get_determinant_fp32(matrix);
+
+    if (bgc_is_zero_fp32(determinant)) {
+        return 0;
+    }
+
+    const float r1c1 = matrix->r2c2;
+    const float r1c2 = -matrix->r1c2;
+
+    const float r2c1 = -matrix->r2c1;
+    const float r2c2 = matrix->r1c1;
+
+    const float multiplier = 1.0f / determinant;
+
+    inverted->r1c1 = r1c1 * multiplier;
+    inverted->r1c2 = r1c2 * multiplier;
+
+    inverted->r2c1 = r2c1 * multiplier;
+    inverted->r2c2 = r2c2 * multiplier;
+
+    return 1;
+}
+
+inline int bgc_matrix2x2_make_inverted_fp64(const BgcMatrix2x2FP64* matrix, BgcMatrix2x2FP64* inverted)
+{
+    const double determinant = bgc_matrix2x2_get_determinant_fp64(matrix);
+
+    if (bgc_is_zero_fp64(determinant)) {
+        return 0;
+    }
+
+    const double r1c1 = matrix->r2c2;
+    const double r1c2 = -matrix->r1c2;
+
+    const double r2c1 = -matrix->r2c1;
+    const double r2c2 = matrix->r1c1;
+
+    const double multiplier = 1.0 / determinant;
+
+    inverted->r1c1 = r1c1 * multiplier;
+    inverted->r1c2 = r1c2 * multiplier;
+
+    inverted->r2c1 = r2c1 * multiplier;
+    inverted->r2c2 = r2c2 * multiplier;
+
+    return 1;
+}
+
+// ============== Make Transposed =============== //
+
+inline void bgc_matrix2x2_make_transposed_fp32(const BgcMatrix2x2FP32* matrix, BgcMatrix2x2FP32* transposed)
+{
+    float tmp = matrix->r1c2;
+
+    transposed->r1c1 = matrix->r1c1;
+    transposed->r1c2 = matrix->r2c1;
+
+    transposed->r2c1 = tmp;
+    transposed->r2c2 = matrix->r2c2;
+}
+
+inline void bgc_matrix2x2_make_transposed_fp64(const BgcMatrix2x2FP64* matrix, BgcMatrix2x2FP64* transposed)
+{
+    double tmp = matrix->r1c2;
+
+    transposed->r1c1 = matrix->r1c1;
+    transposed->r1c2 = matrix->r2c1;
+
+    transposed->r2c1 = tmp;
+    transposed->r2c2 = matrix->r2c2;
+}
+
+// ==================== Add ===================== //
 
 inline void bgc_matrix2x2_add_fp32(const BgcMatrix2x2FP32* matrix1, const BgcMatrix2x2FP32* matrix2, BgcMatrix2x2FP32* sum)
 {
@@ -433,7 +433,7 @@ inline void bgc_matrix2x2_add_scaled_fp64(const BgcMatrix2x2FP64* basic_matrix,
     sum->r2c2 = basic_matrix->r2c2 + scalable_matrix->r2c2 * scale;
 }
 
-// ================ Subtraction ================= //
+// ================== Subtract ================== //
 
 inline void bgc_matrix2x2_subtract_fp32(const BgcMatrix2x2FP32* minuend, const BgcMatrix2x2FP32* subtrahend, BgcMatrix2x2FP32* difference)
 {
@@ -453,7 +453,27 @@ inline void bgc_matrix2x2_subtract_fp64(const BgcMatrix2x2FP64* minuend, const B
     difference->r2c2 = minuend->r2c2 - subtrahend->r2c2;
 }
 
-// =============== Multiplication =============== //
+// ============== Subtract scaled =============== //
+
+inline void bgc_matrix2x2_subtract_scaled_fp32(const BgcMatrix2x2FP32* basic_matrix, const BgcMatrix2x2FP32* scalable_matrix, const float scale, BgcMatrix2x2FP32* difference)
+{
+    difference->r1c1 = basic_matrix->r1c1 - scalable_matrix->r1c1 * scale;
+    difference->r1c2 = basic_matrix->r1c2 - scalable_matrix->r1c2 * scale;
+
+    difference->r2c1 = basic_matrix->r2c1 - scalable_matrix->r2c1 * scale;
+    difference->r2c2 = basic_matrix->r2c2 - scalable_matrix->r2c2 * scale;
+}
+
+inline void bgc_matrix2x2_subtract_scaled_fp64(const BgcMatrix2x2FP64* basic_matrix, const BgcMatrix2x2FP64* scalable_matrix, const double scale, BgcMatrix2x2FP64* difference)
+{
+    difference->r1c1 = basic_matrix->r1c1 - scalable_matrix->r1c1 * scale;
+    difference->r1c2 = basic_matrix->r1c2 - scalable_matrix->r1c2 * scale;
+
+    difference->r2c1 = basic_matrix->r2c1 - scalable_matrix->r2c1 * scale;
+    difference->r2c2 = basic_matrix->r2c2 - scalable_matrix->r2c2 * scale;
+}
+
+// ================== Multiply ================== //
 
 inline void bgc_matrix2x2_multiply_fp32(const BgcMatrix2x2FP32* multiplicand, const float multiplier, BgcMatrix2x2FP32* product)
 {
@@ -473,7 +493,7 @@ inline void bgc_matrix2x2_multiply_fp64(const BgcMatrix2x2FP64* multiplicand, co
     product->r2c2 = multiplicand->r2c2 * multiplier;
 }
 
-// ================== Division ================== //
+// =================== Divide =================== //
 
 inline void bgc_matrix2x2_divide_fp32(const BgcMatrix2x2FP32* dividend, const float divisor, BgcMatrix2x2FP32* quotient)
 {
@@ -487,42 +507,42 @@ inline void bgc_matrix2x2_divide_fp64(const BgcMatrix2x2FP64* dividend, const do
 
 // ============ Left Vector Product ============= //
 
-inline void bgc_matrix2x2_left_product_fp32(const BgcVector2FP32* vector, const BgcMatrix2x2FP32* matrix, BgcVector2FP32* result)
+inline void bgc_matrix2x2_left_product_fp32(const BgcVector2FP32* vector, const BgcMatrix2x2FP32* matrix, BgcVector2FP32* product)
 {
     const float x1 = vector->x1 * matrix->r1c1 + vector->x2 * matrix->r2c1;
     const float x2 = vector->x1 * matrix->r1c2 + vector->x2 * matrix->r2c2;
 
-    result->x1 = x1;
-    result->x2 = x2;
+    product->x1 = x1;
+    product->x2 = x2;
 }
 
-inline void bgc_matrix2x2_left_product_fp64(const BgcVector2FP64* vector, const BgcMatrix2x2FP64* matrix, BgcVector2FP64* result)
+inline void bgc_matrix2x2_left_product_fp64(const BgcVector2FP64* vector, const BgcMatrix2x2FP64* matrix, BgcVector2FP64* product)
 {
     const double x1 = vector->x1 * matrix->r1c1 + vector->x2 * matrix->r2c1;
     const double x2 = vector->x1 * matrix->r1c2 + vector->x2 * matrix->r2c2;
 
-    result->x1 = x1;
-    result->x2 = x2;
+    product->x1 = x1;
+    product->x2 = x2;
 }
 
 // ============ Right Vector Product ============ //
 
-inline void bgc_matrix2x2_right_product_fp32(const BgcMatrix2x2FP32* matrix, const BgcVector2FP32* vector, BgcVector2FP32* result)
+inline void bgc_matrix2x2_right_product_fp32(const BgcMatrix2x2FP32* matrix, const BgcVector2FP32* vector, BgcVector2FP32* product)
 {
     const float x1 = matrix->r1c1 * vector->x1 + matrix->r1c2 * vector->x2;
     const float x2 = matrix->r2c1 * vector->x1 + matrix->r2c2 * vector->x2;
 
-    result->x1 = x1;
-    result->x2 = x2;
+    product->x1 = x1;
+    product->x2 = x2;
 }
 
-inline void bgc_matrix2x2_right_product_fp64(const BgcMatrix2x2FP64* matrix, const BgcVector2FP64* vector, BgcVector2FP64* result)
+inline void bgc_matrix2x2_right_product_fp64(const BgcMatrix2x2FP64* matrix, const BgcVector2FP64* vector, BgcVector2FP64* product)
 {
     const double x1 = matrix->r1c1 * vector->x1 + matrix->r1c2 * vector->x2;
     const double x2 = matrix->r2c1 * vector->x1 + matrix->r2c2 * vector->x2;
 
-    result->x1 = x1;
-    result->x2 = x2;
+    product->x1 = x1;
+    product->x2 = x2;
 }
 
 #endif
diff --git a/basic-geometry/matrix2x3.c b/basic-geometry/matrix2x3.c
index 939fc72..ab3e953 100644
--- a/basic-geometry/matrix2x3.c
+++ b/basic-geometry/matrix2x3.c
@@ -12,12 +12,6 @@ extern inline void bgc_matrix2x3_swap_fp64(BgcMatrix2x3FP64* matrix1, BgcMatrix2
 extern inline void bgc_matrix2x3_convert_fp64_to_fp32(const BgcMatrix2x3FP64* from, BgcMatrix2x3FP32* to);
 extern inline void bgc_matrix2x3_convert_fp32_to_fp64(const BgcMatrix2x3FP32* from, BgcMatrix2x3FP64* to);
 
-extern inline void bgc_matrix2x3_set_transposed_fp32(const BgcMatrix3x2FP32* from, BgcMatrix2x3FP32* to);
-extern inline void bgc_matrix2x3_set_transposed_fp64(const BgcMatrix3x2FP64* from, BgcMatrix2x3FP64* to);
-
-extern inline void bgc_matrix2x3_set_transposed_fp32_fp64(const BgcMatrix3x2FP64* from, BgcMatrix2x3FP32* to);
-extern inline void bgc_matrix2x3_set_transposed_fp64_fp32(const BgcMatrix3x2FP32* from, BgcMatrix2x3FP64* to);
-
 extern inline void bgc_matrix2x3_set_row1_fp32(const float c1, const float c2, BgcMatrix2x3FP32* matrix);
 extern inline void bgc_matrix2x3_set_row1_fp64(const double c1, const double c2, BgcMatrix2x3FP64* matrix);
 
@@ -33,6 +27,9 @@ extern inline void bgc_matrix2x3_set_column1_fp64(const double r1, const double
 extern inline void bgc_matrix2x3_set_column2_fp32(const float r1, const float r2, const float r3, BgcMatrix2x3FP32* matrix);
 extern inline void bgc_matrix2x3_set_column2_fp64(const double r1, const double r2, const double r3, BgcMatrix2x3FP64* matrix);
 
+extern inline void bgc_matrix2x3_make_transposed_fp32(const BgcMatrix3x2FP32* from, BgcMatrix2x3FP32* to);
+extern inline void bgc_matrix2x3_make_transposed_fp64(const BgcMatrix3x2FP64* from, BgcMatrix2x3FP64* to);
+
 extern inline void bgc_matrix2x3_add_fp32(const BgcMatrix2x3FP32* matrix1, const BgcMatrix2x3FP32* matrix2, BgcMatrix2x3FP32* sum);
 extern inline void bgc_matrix2x3_add_fp64(const BgcMatrix2x3FP64* matrix1, const BgcMatrix2x3FP64* matrix2, BgcMatrix2x3FP64* sum);
 
@@ -42,6 +39,9 @@ extern inline void bgc_matrix2x3_add_scaled_fp64(const BgcMatrix2x3FP64* basic_m
 extern inline void bgc_matrix2x3_subtract_fp32(const BgcMatrix2x3FP32* minuend, const BgcMatrix2x3FP32* subtrahend, BgcMatrix2x3FP32* difference);
 extern inline void bgc_matrix2x3_subtract_fp64(const BgcMatrix2x3FP64* minuend, const BgcMatrix2x3FP64* subtrahend, BgcMatrix2x3FP64* difference);
 
+extern inline void bgc_matrix2x3_subtract_scaled_fp32(const BgcMatrix2x3FP32* basic_matrix, const BgcMatrix2x3FP32* scalable_matrix, const float scale, BgcMatrix2x3FP32* difference);
+extern inline void bgc_matrix2x3_subtract_scaled_fp64(const BgcMatrix2x3FP64* basic_matrix, const BgcMatrix2x3FP64* scalable_matrix, const double scale, BgcMatrix2x3FP64* difference);
+
 extern inline void bgc_matrix2x3_multiply_fp32(const BgcMatrix2x3FP32* multiplicand, const float multiplier, BgcMatrix2x3FP32* product);
 extern inline void bgc_matrix2x3_multiply_fp64(const BgcMatrix2x3FP64* multiplicand, const double multiplier, BgcMatrix2x3FP64* product);
 
diff --git a/basic-geometry/matrix2x3.h b/basic-geometry/matrix2x3.h
index 73e8e97..27002d4 100644
--- a/basic-geometry/matrix2x3.h
+++ b/basic-geometry/matrix2x3.h
@@ -119,7 +119,7 @@ inline void bgc_matrix2x3_swap_fp64(BgcMatrix2x3FP64* matrix1, BgcMatrix2x3FP64*
     matrix1->r3c2 = r3c2;
 }
 
-// ============= Copy to twin type ============== //
+// ================== Convert =================== //
 
 inline void bgc_matrix2x3_convert_fp64_to_fp32(const BgcMatrix2x3FP64* from, BgcMatrix2x3FP32* to)
 {
@@ -145,58 +145,6 @@ inline void bgc_matrix2x3_convert_fp32_to_fp64(const BgcMatrix2x3FP32* from, Bgc
     to->r3c2 = from->r3c2;
 }
 
-// =============== Set transposed =============== //
-
-inline void bgc_matrix2x3_set_transposed_fp32(const BgcMatrix3x2FP32* from, BgcMatrix2x3FP32* to)
-{
-    to->r1c1 = from->r1c1;
-    to->r1c2 = from->r2c1;
-
-    to->r2c1 = from->r1c2;
-    to->r2c2 = from->r2c2;
-
-    to->r3c1 = from->r1c3;
-    to->r3c2 = from->r2c3;
-}
-
-inline void bgc_matrix2x3_set_transposed_fp64(const BgcMatrix3x2FP64* from, BgcMatrix2x3FP64* to)
-{
-    to->r1c1 = from->r1c1;
-    to->r1c2 = from->r2c1;
-
-    to->r2c1 = from->r1c2;
-    to->r2c2 = from->r2c2;
-
-    to->r3c1 = from->r1c3;
-    to->r3c2 = from->r2c3;
-}
-
-// =============== Set transposed =============== //
-
-inline void bgc_matrix2x3_set_transposed_fp32_fp64(const BgcMatrix3x2FP64* from, BgcMatrix2x3FP32* to)
-{
-    to->r1c1 = (float) from->r1c1;
-    to->r1c2 = (float) from->r2c1;
-
-    to->r2c1 = (float) from->r1c2;
-    to->r2c2 = (float) from->r2c2;
-
-    to->r3c1 = (float) from->r1c3;
-    to->r3c2 = (float) from->r2c3;
-}
-
-inline void bgc_matrix2x3_set_transposed_fp64_fp32(const BgcMatrix3x2FP32* from, BgcMatrix2x3FP64* to)
-{
-    to->r1c1 = from->r1c1;
-    to->r1c2 = from->r2c1;
-
-    to->r2c1 = from->r1c2;
-    to->r2c2 = from->r2c2;
-
-    to->r3c1 = from->r1c3;
-    to->r3c2 = from->r2c3;
-}
-
 // ================= Set Row 1 ================== //
 
 inline void bgc_matrix2x3_set_row1_fp32(const float c1, const float c2, BgcMatrix2x3FP32* matrix)
@@ -271,7 +219,34 @@ inline void bgc_matrix2x3_set_column2_fp64(const double r1, const double r2, con
     matrix->r3c2 = r3;
 }
 
-// ================== Addition ================== //
+// ============== Make transposed =============== //
+
+inline void bgc_matrix2x3_make_transposed_fp32(const BgcMatrix3x2FP32* matrix, BgcMatrix2x3FP32* transposed)
+{
+    transposed->r1c1 = matrix->r1c1;
+    transposed->r1c2 = matrix->r2c1;
+
+    transposed->r2c1 = matrix->r1c2;
+    transposed->r2c2 = matrix->r2c2;
+
+    transposed->r3c1 = matrix->r1c3;
+    transposed->r3c2 = matrix->r2c3;
+}
+
+inline void bgc_matrix2x3_make_transposed_fp64(const BgcMatrix3x2FP64* matrix, BgcMatrix2x3FP64* transposed)
+{
+    transposed->r1c1 = matrix->r1c1;
+    transposed->r1c2 = matrix->r2c1;
+
+    transposed->r2c1 = matrix->r1c2;
+    transposed->r2c2 = matrix->r2c2;
+
+    transposed->r3c1 = matrix->r1c3;
+    transposed->r3c2 = matrix->r2c3;
+}
+
+
+// ==================== Add ===================== //
 
 inline void bgc_matrix2x3_add_fp32(const BgcMatrix2x3FP32* matrix1, const BgcMatrix2x3FP32* matrix2, BgcMatrix2x3FP32* sum)
 {
@@ -323,7 +298,7 @@ inline void bgc_matrix2x3_add_scaled_fp64(const BgcMatrix2x3FP64* basic_matrix,
     sum->r3c2 = basic_matrix->r3c2 + scalable_matrix->r3c2 * scale;
 }
 
-// ================ Subtraction ================= //
+// ================== Subtract ================== //
 
 inline void bgc_matrix2x3_subtract_fp32(const BgcMatrix2x3FP32* minuend, const BgcMatrix2x3FP32* subtrahend, BgcMatrix2x3FP32* difference)
 {
@@ -349,7 +324,33 @@ inline void bgc_matrix2x3_subtract_fp64(const BgcMatrix2x3FP64* minuend, const B
     difference->r3c2 = minuend->r3c2 - subtrahend->r3c2;
 }
 
-// =============== Multiplication =============== //
+// ============== Subtract scaled =============== //
+
+inline void bgc_matrix2x3_subtract_scaled_fp32(const BgcMatrix2x3FP32* basic_matrix, const BgcMatrix2x3FP32* scalable_matrix, const float scale, BgcMatrix2x3FP32* difference)
+{
+    difference->r1c1 = basic_matrix->r1c1 - scalable_matrix->r1c1 * scale;
+    difference->r1c2 = basic_matrix->r1c2 - scalable_matrix->r1c2 * scale;
+
+    difference->r2c1 = basic_matrix->r2c1 - scalable_matrix->r2c1 * scale;
+    difference->r2c2 = basic_matrix->r2c2 - scalable_matrix->r2c2 * scale;
+
+    difference->r3c1 = basic_matrix->r3c1 - scalable_matrix->r3c1 * scale;
+    difference->r3c2 = basic_matrix->r3c2 - scalable_matrix->r3c2 * scale;
+}
+
+inline void bgc_matrix2x3_subtract_scaled_fp64(const BgcMatrix2x3FP64* basic_matrix, const BgcMatrix2x3FP64* scalable_matrix, const double scale, BgcMatrix2x3FP64* difference)
+{
+    difference->r1c1 = basic_matrix->r1c1 - scalable_matrix->r1c1 * scale;
+    difference->r1c2 = basic_matrix->r1c2 - scalable_matrix->r1c2 * scale;
+
+    difference->r2c1 = basic_matrix->r2c1 - scalable_matrix->r2c1 * scale;
+    difference->r2c2 = basic_matrix->r2c2 - scalable_matrix->r2c2 * scale;
+
+    difference->r3c1 = basic_matrix->r3c1 - scalable_matrix->r3c1 * scale;
+    difference->r3c2 = basic_matrix->r3c2 - scalable_matrix->r3c2 * scale;
+}
+
+// ================== Multiply ================== //
 
 inline void bgc_matrix2x3_multiply_fp32(const BgcMatrix2x3FP32* multiplicand, const float multiplier, BgcMatrix2x3FP32* product)
 {
@@ -375,7 +376,7 @@ inline void bgc_matrix2x3_multiply_fp64(const BgcMatrix2x3FP64* multiplicand, co
     product->r3c2 = multiplicand->r3c2 * multiplier;
 }
 
-// ================== Division ================== //
+// =================== Divide =================== //
 
 inline void bgc_matrix2x3_divide_fp32(const BgcMatrix2x3FP32* dividend, const float divisor, BgcMatrix2x3FP32* quotient)
 {
diff --git a/basic-geometry/matrix3x2.c b/basic-geometry/matrix3x2.c
index af712e5..82c63e0 100644
--- a/basic-geometry/matrix3x2.c
+++ b/basic-geometry/matrix3x2.c
@@ -12,12 +12,6 @@ extern inline void bgc_matrix3x2_swap_fp64(BgcMatrix3x2FP64* matrix1, BgcMatrix3
 extern inline void bgc_matrix3x2_convert_fp64_to_fp32(const BgcMatrix3x2FP64* from, BgcMatrix3x2FP32* to);
 extern inline void bgc_matrix3x2_convert_fp32_to_fp64(const BgcMatrix3x2FP32* from, BgcMatrix3x2FP64* to);
 
-extern inline void bgc_matrix3x2_set_transposed_fp32(const BgcMatrix2x3FP32* from, BgcMatrix3x2FP32* to);
-extern inline void bgc_matrix3x2_set_transposed_fp64(const BgcMatrix2x3FP64* from, BgcMatrix3x2FP64* to);
-
-extern inline void bgc_matrix3x2_set_transposed_fp32_fp64(const BgcMatrix2x3FP64* from, BgcMatrix3x2FP32* to);
-extern inline void bgc_matrix3x2_set_transposed_fp64_fp32(const BgcMatrix2x3FP32* from, BgcMatrix3x2FP64* to);
-
 extern inline void bgc_matrix3x2_set_row1_fp32(const float c1, const float c2, const float c3, BgcMatrix3x2FP32* matrix);
 extern inline void bgc_matrix3x2_set_row1_fp64(const double c1, const double c2, const double c3, BgcMatrix3x2FP64* matrix);
 
@@ -33,6 +27,9 @@ extern inline void bgc_matrix3x2_set_column2_fp64(const double r1, const double
 extern inline void bgc_matrix3x2_set_column3_fp32(const float r1, const float r2, BgcMatrix3x2FP32* matrix);
 extern inline void bgc_matrix3x2_set_column3_fp64(const double r1, const double r2, BgcMatrix3x2FP64* matrix);
 
+extern inline void bgc_matrix3x2_make_transposed_fp32(const BgcMatrix2x3FP32* from, BgcMatrix3x2FP32* to);
+extern inline void bgc_matrix3x2_make_transposed_fp64(const BgcMatrix2x3FP64* from, BgcMatrix3x2FP64* to);
+
 extern inline void bgc_matrix3x2_add_fp32(const BgcMatrix3x2FP32* matrix1, const BgcMatrix3x2FP32* matrix2, BgcMatrix3x2FP32* sum);
 extern inline void bgc_matrix3x2_add_fp64(const BgcMatrix3x2FP64* matrix1, const BgcMatrix3x2FP64* matrix2, BgcMatrix3x2FP64* sum);
 
@@ -42,6 +39,9 @@ extern inline void bgc_matrix3x2_add_scaled_fp64(const BgcMatrix3x2FP64* basic_m
 extern inline void bgc_matrix3x2_subtract_fp32(const BgcMatrix3x2FP32* minuend, const BgcMatrix3x2FP32* subtrahend, BgcMatrix3x2FP32* difference);
 extern inline void bgc_matrix3x2_subtract_fp64(const BgcMatrix3x2FP64* minuend, const BgcMatrix3x2FP64* subtrahend, BgcMatrix3x2FP64* difference);
 
+extern inline void bgc_matrix3x2_subtract_scaled_fp32(const BgcMatrix3x2FP32* basic_matrix, const BgcMatrix3x2FP32* scalable_matrix, const float scale, BgcMatrix3x2FP32* difference);
+extern inline void bgc_matrix3x2_subtract_scaled_fp64(const BgcMatrix3x2FP64* basic_matrix, const BgcMatrix3x2FP64* scalable_matrix, const double scale, BgcMatrix3x2FP64* difference);
+
 extern inline void bgc_matrix3x2_multiply_fp32(const BgcMatrix3x2FP32* multiplicand, const float multiplier, BgcMatrix3x2FP32* product);
 extern inline void bgc_matrix3x2_multiply_fp64(const BgcMatrix3x2FP64* multiplicand, const double multiplier, BgcMatrix3x2FP64* product);
 
diff --git a/basic-geometry/matrix3x2.h b/basic-geometry/matrix3x2.h
index 83b4a2e..f49f6ec 100644
--- a/basic-geometry/matrix3x2.h
+++ b/basic-geometry/matrix3x2.h
@@ -109,7 +109,7 @@ inline void bgc_matrix3x2_swap_fp64(BgcMatrix3x2FP64* matrix1, BgcMatrix3x2FP64*
     matrix1->r2c3 = r2c3;
 }
 
-// ============= Set from twin type ============= //
+// ================== Convert =================== //
 
 inline void bgc_matrix3x2_convert_fp64_to_fp32(const BgcMatrix3x2FP64* from, BgcMatrix3x2FP32* to)
 {
@@ -133,54 +133,6 @@ inline void bgc_matrix3x2_convert_fp32_to_fp64(const BgcMatrix3x2FP32* from, Bgc
     to->r2c3 = from->r2c3;
 }
 
-// =============== Set transposed =============== //
-
-inline void bgc_matrix3x2_set_transposed_fp32(const BgcMatrix2x3FP32* from, BgcMatrix3x2FP32* to)
-{
-    to->r1c1 = from->r1c1;
-    to->r1c2 = from->r2c1;
-    to->r1c3 = from->r3c1;
-
-    to->r2c1 = from->r1c2;
-    to->r2c2 = from->r2c2;
-    to->r2c3 = from->r3c2;
-}
-
-inline void bgc_matrix3x2_set_transposed_fp64(const BgcMatrix2x3FP64* from, BgcMatrix3x2FP64* to)
-{
-    to->r1c1 = from->r1c1;
-    to->r1c2 = from->r2c1;
-    to->r1c3 = from->r3c1;
-
-    to->r2c1 = from->r1c2;
-    to->r2c2 = from->r2c2;
-    to->r2c3 = from->r3c2;
-}
-
-// =============== Set transposed =============== //
-
-inline void bgc_matrix3x2_set_transposed_fp32_fp64(const BgcMatrix2x3FP64* from, BgcMatrix3x2FP32* to)
-{
-    to->r1c1 = (float) from->r1c1;
-    to->r1c2 = (float) from->r2c1;
-    to->r1c3 = (float) from->r3c1;
-
-    to->r2c1 = (float) from->r1c2;
-    to->r2c2 = (float) from->r2c2;
-    to->r2c3 = (float) from->r3c2;
-}
-
-inline void bgc_matrix3x2_set_transposed_fp64_fp32(const BgcMatrix2x3FP32* from, BgcMatrix3x2FP64* to)
-{
-    to->r1c1 = from->r1c1;
-    to->r1c2 = from->r2c1;
-    to->r1c3 = from->r3c1;
-
-    to->r2c1 = from->r1c2;
-    to->r2c2 = from->r2c2;
-    to->r2c3 = from->r3c2;
-}
-
 // ================= Set Row 1 ================== //
 
 inline void bgc_matrix3x2_set_row1_fp32(const float c1, const float c2, const float c3, BgcMatrix3x2FP32* matrix)
@@ -255,7 +207,31 @@ inline void bgc_matrix3x2_set_column3_fp64(const double r1, const double r2, Bgc
     matrix->r2c3 = r2;
 }
 
-// ================== Addition ================== //
+// ============== Make transposed =============== //
+
+inline void bgc_matrix3x2_make_transposed_fp32(const BgcMatrix2x3FP32* from, BgcMatrix3x2FP32* to)
+{
+    to->r1c1 = from->r1c1;
+    to->r1c2 = from->r2c1;
+    to->r1c3 = from->r3c1;
+
+    to->r2c1 = from->r1c2;
+    to->r2c2 = from->r2c2;
+    to->r2c3 = from->r3c2;
+}
+
+inline void bgc_matrix3x2_make_transposed_fp64(const BgcMatrix2x3FP64* from, BgcMatrix3x2FP64* to)
+{
+    to->r1c1 = from->r1c1;
+    to->r1c2 = from->r2c1;
+    to->r1c3 = from->r3c1;
+
+    to->r2c1 = from->r1c2;
+    to->r2c2 = from->r2c2;
+    to->r2c3 = from->r3c2;
+}
+
+// ==================== Add ===================== //
 
 inline void bgc_matrix3x2_add_fp32(const BgcMatrix3x2FP32* matrix1, const BgcMatrix3x2FP32* matrix2, BgcMatrix3x2FP32* sum)
 {
@@ -303,7 +279,7 @@ inline void bgc_matrix3x2_add_scaled_fp64(const BgcMatrix3x2FP64* basic_matrix,
     sum->r2c3 = basic_matrix->r2c3 + scalable_matrix->r2c3 * scale;
 }
 
-// ================ Subtraction ================= //
+// ================== Subtract ================== //
 
 inline void bgc_matrix3x2_subtract_fp32(const BgcMatrix3x2FP32* minuend, const BgcMatrix3x2FP32* subtrahend, BgcMatrix3x2FP32* difference)
 {
@@ -327,7 +303,31 @@ inline void bgc_matrix3x2_subtract_fp64(const BgcMatrix3x2FP64* minuend, const B
     difference->r2c3 = minuend->r2c3 - subtrahend->r2c3;
 }
 
-// =============== Multiplication =============== //
+// ============== Subtract scaled =============== //
+
+inline void bgc_matrix3x2_subtract_scaled_fp32(const BgcMatrix3x2FP32* basic_matrix, const BgcMatrix3x2FP32* scalable_matrix, const float scale, BgcMatrix3x2FP32* difference)
+{
+    difference->r1c1 = basic_matrix->r1c1 - scalable_matrix->r1c1 * scale;
+    difference->r1c2 = basic_matrix->r1c2 - scalable_matrix->r1c2 * scale;
+    difference->r1c3 = basic_matrix->r1c3 - scalable_matrix->r1c3 * scale;
+
+    difference->r2c1 = basic_matrix->r2c1 - scalable_matrix->r2c1 * scale;
+    difference->r2c2 = basic_matrix->r2c2 - scalable_matrix->r2c2 * scale;
+    difference->r2c3 = basic_matrix->r2c3 - scalable_matrix->r2c3 * scale;
+}
+
+inline void bgc_matrix3x2_subtract_scaled_fp64(const BgcMatrix3x2FP64* basic_matrix, const BgcMatrix3x2FP64* scalable_matrix, const double scale, BgcMatrix3x2FP64* difference)
+{
+    difference->r1c1 = basic_matrix->r1c1 - scalable_matrix->r1c1 * scale;
+    difference->r1c2 = basic_matrix->r1c2 - scalable_matrix->r1c2 * scale;
+    difference->r1c3 = basic_matrix->r1c3 - scalable_matrix->r1c3 * scale;
+
+    difference->r2c1 = basic_matrix->r2c1 - scalable_matrix->r2c1 * scale;
+    difference->r2c2 = basic_matrix->r2c2 - scalable_matrix->r2c2 * scale;
+    difference->r2c3 = basic_matrix->r2c3 - scalable_matrix->r2c3 * scale;
+}
+
+// ================== Multiply ================== //
 
 inline void bgc_matrix3x2_multiply_fp32(const BgcMatrix3x2FP32* multiplicand, const float multiplier, BgcMatrix3x2FP32* product)
 {
@@ -351,7 +351,7 @@ inline void bgc_matrix3x2_multiply_fp64(const BgcMatrix3x2FP64* multiplicand, co
     product->r2c3 = multiplicand->r2c3 * multiplier;
 }
 
-// ================== Division ================== //
+// =================== Divide =================== //
 
 inline void bgc_matrix3x2_divide_fp32(const BgcMatrix3x2FP32* dividend, const float divisor, BgcMatrix3x2FP32* quotient)
 {
diff --git a/basic-geometry/matrix3x3.c b/basic-geometry/matrix3x3.c
index 3dc5189..d34959d 100644
--- a/basic-geometry/matrix3x3.c
+++ b/basic-geometry/matrix3x3.c
@@ -27,9 +27,6 @@ extern inline int bgc_matrix3x3_is_singular_fp64(const BgcMatrix3x3FP64* matrix)
 extern inline void bgc_matrix3x3_transpose_fp32(BgcMatrix3x3FP32* matrix);
 extern inline void bgc_matrix3x3_transpose_fp64(BgcMatrix3x3FP64* matrix);
 
-extern inline void bgc_matrix3x3_set_transposed_fp32(const BgcMatrix3x3FP32* matrix, BgcMatrix3x3FP32* result);
-extern inline void bgc_matrix3x3_set_transposed_fp64(const BgcMatrix3x3FP64* matrix, BgcMatrix3x3FP64* result);
-
 extern inline void bgc_matrix3x3_set_row1_fp32(const float c1, const float c2, const float c3, BgcMatrix3x3FP32* matrix);
 extern inline void bgc_matrix3x3_set_row1_fp64(const double c1, const double c2, const double c3, BgcMatrix3x3FP64* matrix);
 
@@ -48,6 +45,9 @@ extern inline void bgc_matrix3x3_set_column2_fp64(const double r1, const double
 extern inline void bgc_matrix3x3_set_column3_fp32(const float r1, const float r2, const float r3, BgcMatrix3x3FP32* matrix);
 extern inline void bgc_matrix3x3_set_column3_fp64(const double r1, const double r2, const double r3, BgcMatrix3x3FP64* matrix);
 
+extern inline void bgc_matrix3x3_make_transposed_fp32(const BgcMatrix3x3FP32* matrix, BgcMatrix3x3FP32* result);
+extern inline void bgc_matrix3x3_make_transposed_fp64(const BgcMatrix3x3FP64* matrix, BgcMatrix3x3FP64* result);
+
 extern inline void bgc_matrix3x3_add_fp32(const BgcMatrix3x3FP32* matrix1, const BgcMatrix3x3FP32* matrix2, BgcMatrix3x3FP32* sum);
 extern inline void bgc_matrix3x3_add_fp64(const BgcMatrix3x3FP64* matrix1, const BgcMatrix3x3FP64* matrix2, BgcMatrix3x3FP64* sum);
 
@@ -57,6 +57,9 @@ extern inline void bgc_matrix3x3_add_scaled_fp64(const BgcMatrix3x3FP64* basic_m
 extern inline void bgc_matrix3x3_subtract_fp32(const BgcMatrix3x3FP32* minuend, const BgcMatrix3x3FP32* subtrahend, BgcMatrix3x3FP32* difference);
 extern inline void bgc_matrix3x3_subtract_fp64(const BgcMatrix3x3FP64* minuend, const BgcMatrix3x3FP64* subtrahend, BgcMatrix3x3FP64* difference);
 
+extern inline void bgc_matrix3x3_subtract_scaled_fp32(const BgcMatrix3x3FP32* basic_matrix, const BgcMatrix3x3FP32* scalable_matrix, const float scale, BgcMatrix3x3FP32* difference);
+extern inline void bgc_matrix3x3_subtract_scaled_fp64(const BgcMatrix3x3FP64* basic_matrix, const BgcMatrix3x3FP64* scalable_matrix, const double scale, BgcMatrix3x3FP64* difference);
+
 extern inline void bgc_matrix3x3_multiply_fp32(const BgcMatrix3x3FP32* multiplicand, const float multiplier, BgcMatrix3x3FP32* product);
 extern inline void bgc_matrix3x3_multiply_fp64(const BgcMatrix3x3FP64* multiplicand, const double multiplier, BgcMatrix3x3FP64* product);
 
@@ -69,7 +72,7 @@ extern inline void bgc_matrix3x3_left_product_fp64(const BgcVector3FP64* vector,
 extern inline void bgc_matrix3x3_right_product_fp32(const BgcMatrix3x3FP32* matrix, const BgcVector3FP32* vector, BgcVector3FP32* result);
 extern inline void bgc_matrix3x3_right_product_fp64(const BgcMatrix3x3FP64* matrix, const BgcVector3FP64* vector, BgcVector3FP64* result);
 
-// ================= Inversion ================== //
+// =================== Invert =================== //
 
 int bgc_matrix3x3_invert_fp32(BgcMatrix3x3FP32* matrix)
 {
@@ -147,7 +150,7 @@ int bgc_matrix3x3_invert_fp64(BgcMatrix3x3FP64* matrix)
 
 // ================ Make Inverted =============== //
 
-int bgc_matrix3x3_set_inverted_fp32(const BgcMatrix3x3FP32* matrix, BgcMatrix3x3FP32* result)
+int bgc_matrix3x3_make_inverted_fp32(const BgcMatrix3x3FP32* matrix, BgcMatrix3x3FP32* result)
 {
     const float determinant = bgc_matrix3x3_get_determinant_fp32(matrix);
 
@@ -184,7 +187,7 @@ int bgc_matrix3x3_set_inverted_fp32(const BgcMatrix3x3FP32* matrix, BgcMatrix3x3
     return 1;
 }
 
-int bgc_matrix3x3_set_inverted_fp64(const BgcMatrix3x3FP64* matrix, BgcMatrix3x3FP64* result)
+int bgc_matrix3x3_make_inverted_fp64(const BgcMatrix3x3FP64* matrix, BgcMatrix3x3FP64* result)
 {
     const double determinant = bgc_matrix3x3_get_determinant_fp64(matrix);
 
diff --git a/basic-geometry/matrix3x3.h b/basic-geometry/matrix3x3.h
index 3454b04..8e1d9ca 100644
--- a/basic-geometry/matrix3x3.h
+++ b/basic-geometry/matrix3x3.h
@@ -212,7 +212,7 @@ inline void bgc_matrix3x3_swap_fp64(BgcMatrix3x3FP64* matrix1, BgcMatrix3x3FP64*
     matrix1->r3c3 = r3c3;
 }
 
-// ============= Set from twin type ============= //
+// ================== Convert =================== //
 
 inline void bgc_matrix3x3_convert_fp64_to_fp32(const BgcMatrix3x3FP64* from, BgcMatrix3x3FP32* to)
 {
@@ -272,13 +272,13 @@ inline int bgc_matrix3x3_is_singular_fp64(const BgcMatrix3x3FP64* matrix)
     return bgc_is_zero_fp64(bgc_matrix3x3_get_determinant_fp64(matrix));
 }
 
-// ================= Inversion ================== //
+// =================== Invert =================== //
 
 int bgc_matrix3x3_invert_fp32(BgcMatrix3x3FP32* matrix);
 
 int bgc_matrix3x3_invert_fp64(BgcMatrix3x3FP64* matrix);
 
-// =============== Transposition ================ //
+// ================= Transpose ================== //
 
 inline void bgc_matrix3x3_transpose_fp32(BgcMatrix3x3FP32* matrix)
 {
@@ -310,54 +310,6 @@ inline void bgc_matrix3x3_transpose_fp64(BgcMatrix3x3FP64* matrix)
     matrix->r3c2 = tmp;
 }
 
-// ================ Make Inverted =============== //
-
-int bgc_matrix3x3_set_inverted_fp32(const BgcMatrix3x3FP32* matrix, BgcMatrix3x3FP32* result);
-
-int bgc_matrix3x3_set_inverted_fp64(const BgcMatrix3x3FP64* matrix, BgcMatrix3x3FP64* result);
-
-// =============== Make Transposed ============== //
-
-inline void bgc_matrix3x3_set_transposed_fp32(const BgcMatrix3x3FP32* matrix, BgcMatrix3x3FP32* result)
-{
-    if (matrix == result) {
-        bgc_matrix3x3_transpose_fp32(result);
-        return;
-    }
-
-    result->r1c1 = matrix->r1c1;
-    result->r1c2 = matrix->r2c1;
-    result->r1c3 = matrix->r3c1;
-
-    result->r2c1 = matrix->r1c2;
-    result->r2c2 = matrix->r2c2;
-    result->r2c3 = matrix->r3c2;
-
-    result->r3c1 = matrix->r1c3;
-    result->r3c2 = matrix->r2c3;
-    result->r3c3 = matrix->r3c3;
-}
-
-inline void bgc_matrix3x3_set_transposed_fp64(const BgcMatrix3x3FP64* matrix, BgcMatrix3x3FP64* result)
-{
-    if (matrix == result) {
-        bgc_matrix3x3_transpose_fp64(result);
-        return;
-    }
-
-    result->r1c1 = matrix->r1c1;
-    result->r1c2 = matrix->r2c1;
-    result->r1c3 = matrix->r3c1;
-
-    result->r2c1 = matrix->r1c2;
-    result->r2c2 = matrix->r2c2;
-    result->r2c3 = matrix->r3c2;
-
-    result->r3c1 = matrix->r1c3;
-    result->r3c2 = matrix->r2c3;
-    result->r3c3 = matrix->r3c3;
-}
-
 // ================= Set Row 1 ================== //
 
 inline void bgc_matrix3x3_set_row1_fp32(const float c1, const float c2, const float c3, BgcMatrix3x3FP32* matrix)
@@ -454,7 +406,55 @@ inline void bgc_matrix3x3_set_column3_fp64(const double r1, const double r2, con
     matrix->r3c3 = r3;
 }
 
-// ================== Addition ================== //
+// ================ Make Inverted =============== //
+
+int bgc_matrix3x3_make_inverted_fp32(const BgcMatrix3x3FP32* matrix, BgcMatrix3x3FP32* result);
+
+int bgc_matrix3x3_make_inverted_fp64(const BgcMatrix3x3FP64* matrix, BgcMatrix3x3FP64* result);
+
+// =============== Make Transposed ============== //
+
+inline void bgc_matrix3x3_make_transposed_fp32(const BgcMatrix3x3FP32* matrix, BgcMatrix3x3FP32* result)
+{
+    if (matrix == result) {
+        bgc_matrix3x3_transpose_fp32(result);
+        return;
+    }
+
+    result->r1c1 = matrix->r1c1;
+    result->r1c2 = matrix->r2c1;
+    result->r1c3 = matrix->r3c1;
+
+    result->r2c1 = matrix->r1c2;
+    result->r2c2 = matrix->r2c2;
+    result->r2c3 = matrix->r3c2;
+
+    result->r3c1 = matrix->r1c3;
+    result->r3c2 = matrix->r2c3;
+    result->r3c3 = matrix->r3c3;
+}
+
+inline void bgc_matrix3x3_make_transposed_fp64(const BgcMatrix3x3FP64* matrix, BgcMatrix3x3FP64* result)
+{
+    if (matrix == result) {
+        bgc_matrix3x3_transpose_fp64(result);
+        return;
+    }
+
+    result->r1c1 = matrix->r1c1;
+    result->r1c2 = matrix->r2c1;
+    result->r1c3 = matrix->r3c1;
+
+    result->r2c1 = matrix->r1c2;
+    result->r2c2 = matrix->r2c2;
+    result->r2c3 = matrix->r3c2;
+
+    result->r3c1 = matrix->r1c3;
+    result->r3c2 = matrix->r2c3;
+    result->r3c3 = matrix->r3c3;
+}
+
+// ==================== Add ===================== //
 
 inline void bgc_matrix3x3_add_fp32(const BgcMatrix3x3FP32* matrix1, const BgcMatrix3x3FP32* matrix2, BgcMatrix3x3FP32* sum)
 {
@@ -518,7 +518,7 @@ inline void bgc_matrix3x3_add_scaled_fp64(const BgcMatrix3x3FP64* basic_matrix,
     sum->r3c3 = basic_matrix->r3c3 + scalable_matrix->r3c3 * scale;
 }
 
-// ================ Subtraction ================= //
+// ================== Subtract ================== //
 
 inline void bgc_matrix3x3_subtract_fp32(const BgcMatrix3x3FP32* minuend, const BgcMatrix3x3FP32* subtrahend, BgcMatrix3x3FP32* difference)
 {
@@ -550,7 +550,39 @@ inline void bgc_matrix3x3_subtract_fp64(const BgcMatrix3x3FP64* minuend, const B
     difference->r3c3 = minuend->r3c3 - subtrahend->r3c3;
 }
 
-// =============== Multiplication =============== //
+// ================= Add scaled ================= //
+
+inline void bgc_matrix3x3_subtract_scaled_fp32(const BgcMatrix3x3FP32* basic_matrix, const BgcMatrix3x3FP32* scalable_matrix, const float scale, BgcMatrix3x3FP32* difference)
+{
+    difference->r1c1 = basic_matrix->r1c1 - scalable_matrix->r1c1 * scale;
+    difference->r1c2 = basic_matrix->r1c2 - scalable_matrix->r1c2 * scale;
+    difference->r1c3 = basic_matrix->r1c3 - scalable_matrix->r1c3 * scale;
+
+    difference->r2c1 = basic_matrix->r2c1 - scalable_matrix->r2c1 * scale;
+    difference->r2c2 = basic_matrix->r2c2 - scalable_matrix->r2c2 * scale;
+    difference->r2c3 = basic_matrix->r2c3 - scalable_matrix->r2c3 * scale;
+
+    difference->r3c1 = basic_matrix->r3c1 - scalable_matrix->r3c1 * scale;
+    difference->r3c2 = basic_matrix->r3c2 - scalable_matrix->r3c2 * scale;
+    difference->r3c3 = basic_matrix->r3c3 - scalable_matrix->r3c3 * scale;
+}
+
+inline void bgc_matrix3x3_subtract_scaled_fp64(const BgcMatrix3x3FP64* basic_matrix, const BgcMatrix3x3FP64* scalable_matrix, const double scale, BgcMatrix3x3FP64* difference)
+{
+    difference->r1c1 = basic_matrix->r1c1 - scalable_matrix->r1c1 * scale;
+    difference->r1c2 = basic_matrix->r1c2 - scalable_matrix->r1c2 * scale;
+    difference->r1c3 = basic_matrix->r1c3 - scalable_matrix->r1c3 * scale;
+
+    difference->r2c1 = basic_matrix->r2c1 - scalable_matrix->r2c1 * scale;
+    difference->r2c2 = basic_matrix->r2c2 - scalable_matrix->r2c2 * scale;
+    difference->r2c3 = basic_matrix->r2c3 - scalable_matrix->r2c3 * scale;
+
+    difference->r3c1 = basic_matrix->r3c1 - scalable_matrix->r3c1 * scale;
+    difference->r3c2 = basic_matrix->r3c2 - scalable_matrix->r3c2 * scale;
+    difference->r3c3 = basic_matrix->r3c3 - scalable_matrix->r3c3 * scale;
+}
+
+// ================== Multiply ================== //
 
 inline void bgc_matrix3x3_multiply_fp32(const BgcMatrix3x3FP32* multiplicand, const float multiplier, BgcMatrix3x3FP32* product)
 {
@@ -582,7 +614,7 @@ inline void bgc_matrix3x3_multiply_fp64(const BgcMatrix3x3FP64* multiplicand, co
     product->r3c3 = multiplicand->r3c3 * multiplier;
 }
 
-// ================== Division ================== //
+// =================== Divide =================== //
 
 inline void bgc_matrix3x3_divide_fp32(const BgcMatrix3x3FP32* dividend, const float divisor, BgcMatrix3x3FP32* quotient)
 {
diff --git a/basic-geometry/quaternion.c b/basic-geometry/quaternion.c
index 847b789..7d9755c 100644
--- a/basic-geometry/quaternion.c
+++ b/basic-geometry/quaternion.c
@@ -9,24 +9,6 @@ extern inline void bgc_quaternion_set_to_identity_fp64(BgcQuaternionFP64* quater
 extern inline void bgc_quaternion_set_values_fp32(const float s0, const float x1, const float x2, const float x3, BgcQuaternionFP32* quaternion);
 extern inline void bgc_quaternion_set_values_fp64(const double s0, const double x1, const double x2, const double x3, BgcQuaternionFP64* quaternion);
 
-extern inline void bgc_quaternion_copy_fp32(const BgcQuaternionFP32* from, BgcQuaternionFP32* to);
-extern inline void bgc_quaternion_copy_fp64(const BgcQuaternionFP64* from, BgcQuaternionFP64* to);
-
-extern inline void bgc_quaternion_swap_fp32(BgcQuaternionFP32* quarternion1, BgcQuaternionFP32* quarternion2);
-extern inline void bgc_quaternion_swap_fp64(BgcQuaternionFP64* quarternion1, BgcQuaternionFP64* quarternion2);
-
-extern inline void bgc_quaternion_convert_fp64_to_fp32(const BgcQuaternionFP64* quaternion, BgcQuaternionFP32* result);
-extern inline void bgc_quaternion_convert_fp32_to_fp64(const BgcQuaternionFP32* quaternion, BgcQuaternionFP64* result);
-
-extern inline void bgc_quaternion_conjugate_fp32(BgcQuaternionFP32* quaternion);
-extern inline void bgc_quaternion_conjugate_fp64(BgcQuaternionFP64* quaternion);
-
-extern inline void bgc_quaternion_set_conjugate_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* result);
-extern inline void bgc_quaternion_set_conjugate_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* result);
-
-extern inline void bgc_quaternion_set_conjugate_fp64_to_fp32(const BgcQuaternionFP64* quaternion, BgcQuaternionFP32* result);
-extern inline void bgc_quaternion_set_conjugate_fp32_to_fp64(const BgcQuaternionFP32* quaternion, BgcQuaternionFP64* result);
-
 extern inline float bgc_quaternion_get_square_modulus_fp32(const BgcQuaternionFP32* quaternion);
 extern inline double bgc_quaternion_get_square_modulus_fp64(const BgcQuaternionFP64* quaternion);
 
@@ -39,14 +21,35 @@ extern inline int bgc_quaternion_is_zero_fp64(const BgcQuaternionFP64* quaternio
 extern inline int bgc_quaternion_is_unit_fp32(const BgcQuaternionFP32* quaternion);
 extern inline int bgc_quaternion_is_unit_fp64(const BgcQuaternionFP64* quaternion);
 
+extern inline void bgc_quaternion_copy_fp32(const BgcQuaternionFP32* from, BgcQuaternionFP32* to);
+extern inline void bgc_quaternion_copy_fp64(const BgcQuaternionFP64* from, BgcQuaternionFP64* to);
+
+extern inline void bgc_quaternion_swap_fp32(BgcQuaternionFP32* quarternion1, BgcQuaternionFP32* quarternion2);
+extern inline void bgc_quaternion_swap_fp64(BgcQuaternionFP64* quarternion1, BgcQuaternionFP64* quarternion2);
+
+extern inline void bgc_quaternion_convert_fp64_to_fp32(const BgcQuaternionFP64* quaternion, BgcQuaternionFP32* result);
+extern inline void bgc_quaternion_convert_fp32_to_fp64(const BgcQuaternionFP32* quaternion, BgcQuaternionFP64* result);
+
+extern inline void bgc_quaternion_conjugate_fp32(BgcQuaternionFP32* quaternion);
+extern inline void bgc_quaternion_conjugate_fp64(BgcQuaternionFP64* quaternion);
+
 extern inline int bgc_quaternion_normalize_fp32(BgcQuaternionFP32* quaternion);
 extern inline int bgc_quaternion_normalize_fp64(BgcQuaternionFP64* quaternion);
 
-extern inline void bgc_quaternion_get_rotation_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* matrix);
-extern inline void bgc_quaternion_get_rotation_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* matrix);
+extern inline void bgc_quaternion_make_conjugate_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* conjugate);
+extern inline void bgc_quaternion_make_conjugate_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* conjugate);
 
-extern inline void bgc_quaternion_get_reverse_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* matrix);
-extern inline void bgc_quaternion_get_reverse_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* matrix);
+extern inline int bgc_quaternion_make_normalized_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* normalized);
+extern inline int bgc_quaternion_make_normalized_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* normalized);
+
+extern inline void bgc_quaternion_make_product_fp32(const BgcQuaternionFP32* left, const BgcQuaternionFP32* right, BgcQuaternionFP32* product);
+extern inline void bgc_quaternion_make_product_fp64(const BgcQuaternionFP64* left, const BgcQuaternionFP64* right, BgcQuaternionFP64* product);
+
+extern inline void bgc_quaternion_make_rotation_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* rotation);
+extern inline void bgc_quaternion_make_rotation_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* rotation);
+
+extern inline void bgc_quaternion_make_reverse_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* reverse);
+extern inline void bgc_quaternion_make_reverse_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* reverse);
 
 extern inline void bgc_quaternion_add_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2, BgcQuaternionFP32* sum);
 extern inline void bgc_quaternion_add_fp64(const BgcQuaternionFP64* quaternion1, const BgcQuaternionFP64* quaternion2, BgcQuaternionFP64* sum);
@@ -57,14 +60,14 @@ extern inline void bgc_quaternion_add_scaled_fp64(const BgcQuaternionFP64* basic
 extern inline void bgc_quaternion_subtract_fp32(const BgcQuaternionFP32* minuend, const BgcQuaternionFP32* subtrahend, BgcQuaternionFP32* difference);
 extern inline void bgc_quaternion_subtract_fp64(const BgcQuaternionFP64* minuend, const BgcQuaternionFP64* subtrahend, BgcQuaternionFP64* difference);
 
+extern inline void bgc_quaternion_subtract_scaled_fp32(const BgcQuaternionFP32* basic_quaternion, const BgcQuaternionFP32* scalable_quaternion, const float scale, BgcQuaternionFP32* difference);
+extern inline void bgc_quaternion_subtract_scaled_fp64(const BgcQuaternionFP64* basic_quaternion, const BgcQuaternionFP64* scalable_quaternion, const double scale, BgcQuaternionFP64* difference);
+
 extern inline void bgc_quaternion_multiply_fp32(const BgcQuaternionFP32* multiplicand, const float multipier, BgcQuaternionFP32* product);
 extern inline void bgc_quaternion_multiply_fp64(const BgcQuaternionFP64* multiplicand, const double multipier, BgcQuaternionFP64* product);
 
 extern inline void bgc_quaternion_divide_fp32(const BgcQuaternionFP32* dividend, const float divisor, BgcQuaternionFP32* quotient);
 extern inline void bgc_quaternion_divide_fp64(const BgcQuaternionFP64* dividend, const double divisor, BgcQuaternionFP64* quotient);
 
-extern inline void bgc_quaternion_get_product_fp32(const BgcQuaternionFP32* left, const BgcQuaternionFP32* right, BgcQuaternionFP32* product);
-extern inline void bgc_quaternion_get_product_fp64(const BgcQuaternionFP64* left, const BgcQuaternionFP64* right, BgcQuaternionFP64* product);
-
 extern inline int bgc_quaternion_are_close_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2);
 extern inline int bgc_quaternion_are_close_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2);
diff --git a/basic-geometry/quaternion.h b/basic-geometry/quaternion.h
index ae774bf..6f9eaac 100644
--- a/basic-geometry/quaternion.h
+++ b/basic-geometry/quaternion.h
@@ -69,6 +69,54 @@ inline void bgc_quaternion_set_values_fp64(const double s0, const double x1, con
     quaternion->x3 = x3;
 }
 
+// ============= Get Square Modulus ============= //
+
+inline float bgc_quaternion_get_square_modulus_fp32(const BgcQuaternionFP32* quaternion)
+{
+    return (quaternion->s0 * quaternion->s0 + quaternion->x1 * quaternion->x1) + (quaternion->x2 * quaternion->x2 + quaternion->x3 * quaternion->x3);
+}
+
+inline double bgc_quaternion_get_square_modulus_fp64(const BgcQuaternionFP64* quaternion)
+{
+    return (quaternion->s0 * quaternion->s0 + quaternion->x1 * quaternion->x1) + (quaternion->x2 * quaternion->x2 + quaternion->x3 * quaternion->x3);
+}
+
+// ================ Get Modulus ================= //
+
+inline float bgc_quaternion_get_modulus_fp32(const BgcQuaternionFP32* quaternion)
+{
+    return sqrtf(bgc_quaternion_get_square_modulus_fp32(quaternion));
+}
+
+inline double bgc_quaternion_get_modulus_fp64(const BgcQuaternionFP64* quaternion)
+{
+    return sqrt(bgc_quaternion_get_square_modulus_fp64(quaternion));
+}
+
+// ================== Is Zero =================== //
+
+inline int bgc_quaternion_is_zero_fp32(const BgcQuaternionFP32* quaternion)
+{
+    return bgc_quaternion_get_square_modulus_fp32(quaternion) <= BGC_SQUARE_EPSYLON_FP32;
+}
+
+inline int bgc_quaternion_is_zero_fp64(const BgcQuaternionFP64* quaternion)
+{
+    return bgc_quaternion_get_square_modulus_fp64(quaternion) <= BGC_SQUARE_EPSYLON_FP64;
+}
+
+// ================== Is Unit =================== //
+
+inline int bgc_quaternion_is_unit_fp32(const BgcQuaternionFP32* quaternion)
+{
+    return bgc_is_sqare_unit_fp32(bgc_quaternion_get_square_modulus_fp32(quaternion));
+}
+
+inline int bgc_quaternion_is_unit_fp64(const BgcQuaternionFP64* quaternion)
+{
+    return bgc_is_sqare_unit_fp64(bgc_quaternion_get_square_modulus_fp64(quaternion));
+}
+
 // ==================== Copy ==================== //
 
 inline void bgc_quaternion_copy_fp32(const BgcQuaternionFP32* from, BgcQuaternionFP32* to)
@@ -125,7 +173,7 @@ inline void bgc_quaternion_swap_fp64(BgcQuaternionFP64* quarternion1, BgcQuatern
     quarternion1->x3 = x3;
 }
 
-// ============= Copy to twin type ============== //
+// ================== Convert =================== //
 
 inline void bgc_quaternion_convert_fp64_to_fp32(const BgcQuaternionFP64* quaternion, BgcQuaternionFP32* result)
 {
@@ -143,7 +191,7 @@ inline void bgc_quaternion_convert_fp32_to_fp64(const BgcQuaternionFP32* quatern
     result->x3 = quaternion->x3;
 }
 
-// ================= Inversion ================== //
+// ================= Conjugate ================== //
 
 inline void bgc_quaternion_conjugate_fp32(BgcQuaternionFP32* quaternion)
 {
@@ -159,101 +207,17 @@ inline void bgc_quaternion_conjugate_fp64(BgcQuaternionFP64* quaternion)
     quaternion->x3 = -quaternion->x3;
 }
 
-// ================ Set Conjugate =============== //
-
-inline void bgc_quaternion_set_conjugate_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* result)
-{
-    result->s0 = quaternion->s0;
-    result->x1 = -quaternion->x1;
-    result->x2 = -quaternion->x2;
-    result->x3 = -quaternion->x3;
-}
-
-inline void bgc_quaternion_set_conjugate_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* result)
-{
-    result->s0 = quaternion->s0;
-    result->x1 = -quaternion->x1;
-    result->x2 = -quaternion->x2;
-    result->x3 = -quaternion->x3;
-}
-
-// ================ Set Conjugate =============== //
-
-inline void bgc_quaternion_set_conjugate_fp64_to_fp32(const BgcQuaternionFP64* quaternion, BgcQuaternionFP32* result)
-{
-    result->s0 = (float) quaternion->s0;
-    result->x1 = (float) -quaternion->x1;
-    result->x2 = (float) -quaternion->x2;
-    result->x3 = (float) -quaternion->x3;
-}
-
-inline void bgc_quaternion_set_conjugate_fp32_to_fp64(const BgcQuaternionFP32* quaternion, BgcQuaternionFP64* result)
-{
-    result->s0 = quaternion->s0;
-    result->x1 = -quaternion->x1;
-    result->x2 = -quaternion->x2;
-    result->x3 = -quaternion->x3;
-}
-
-// ============= Get Square Modulus ============= //
-
-inline float bgc_quaternion_get_square_modulus_fp32(const BgcQuaternionFP32* quaternion)
-{
-    return (quaternion->s0 * quaternion->s0 + quaternion->x1 * quaternion->x1) + (quaternion->x2 * quaternion->x2 + quaternion->x3 * quaternion->x3);
-}
-
-inline double bgc_quaternion_get_square_modulus_fp64(const BgcQuaternionFP64* quaternion)
-{
-    return (quaternion->s0 * quaternion->s0 + quaternion->x1 * quaternion->x1) + (quaternion->x2 * quaternion->x2 + quaternion->x3 * quaternion->x3);
-}
-
-// ================ Get Modulus ================= //
-
-inline float bgc_quaternion_get_modulus_fp32(const BgcQuaternionFP32* quaternion)
-{
-    return sqrtf(bgc_quaternion_get_square_modulus_fp32(quaternion));
-}
-
-inline double bgc_quaternion_get_modulus_fp64(const BgcQuaternionFP64* quaternion)
-{
-    return sqrt(bgc_quaternion_get_square_modulus_fp64(quaternion));
-}
-
-// ================== Is Zero =================== //
-
-inline int bgc_quaternion_is_zero_fp32(const BgcQuaternionFP32* quaternion)
-{
-    return bgc_quaternion_get_square_modulus_fp32(quaternion) <= BGC_SQUARE_EPSYLON_FP32;
-}
-
-inline int bgc_quaternion_is_zero_fp64(const BgcQuaternionFP64* quaternion)
-{
-    return bgc_quaternion_get_square_modulus_fp64(quaternion) <= BGC_SQUARE_EPSYLON_FP64;
-}
-
-// ================== Is Unit =================== //
-
-inline int bgc_quaternion_is_unit_fp32(const BgcQuaternionFP32* quaternion)
-{
-    return bgc_is_sqare_value_unit_fp32(bgc_quaternion_get_square_modulus_fp32(quaternion));
-}
-
-inline int bgc_quaternion_is_unit_fp64(const BgcQuaternionFP64* quaternion)
-{
-    return bgc_is_sqare_value_unit_fp64(bgc_quaternion_get_square_modulus_fp64(quaternion));
-}
-
-// =============== Normalization ================ //
+// ================= Normalize ================== //
 
 inline int bgc_quaternion_normalize_fp32(BgcQuaternionFP32* quaternion)
 {
     const float square_modulus = bgc_quaternion_get_square_modulus_fp32(quaternion);
 
-    if (bgc_is_sqare_value_unit_fp32(square_modulus)) {
+    if (bgc_is_sqare_unit_fp32(square_modulus)) {
         return 1;
     }
 
-    if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
+    if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
         bgc_quaternion_reset_fp32(quaternion);
         return 0;
     }
@@ -272,11 +236,11 @@ inline int bgc_quaternion_normalize_fp64(BgcQuaternionFP64* quaternion)
 {
     const double square_modulus = bgc_quaternion_get_square_modulus_fp64(quaternion);
 
-    if (bgc_is_sqare_value_unit_fp64(square_modulus)) {
+    if (bgc_is_sqare_unit_fp64(square_modulus)) {
         return 1;
     }
 
-    if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
+    if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
         bgc_quaternion_reset_fp64(quaternion);
         return 0;
     }
@@ -291,9 +255,69 @@ inline int bgc_quaternion_normalize_fp64(BgcQuaternionFP64* quaternion)
     return 1;
 }
 
+// =============== Make Conjugate =============== //
+
+inline void bgc_quaternion_make_conjugate_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* conjugate)
+{
+    conjugate->s0 = quaternion->s0;
+    conjugate->x1 = -quaternion->x1;
+    conjugate->x2 = -quaternion->x2;
+    conjugate->x3 = -quaternion->x3;
+}
+
+inline void bgc_quaternion_make_conjugate_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* conjugate)
+{
+    conjugate->s0 = quaternion->s0;
+    conjugate->x1 = -quaternion->x1;
+    conjugate->x2 = -quaternion->x2;
+    conjugate->x3 = -quaternion->x3;
+}
+
+// ============== Make Normalized =============== //
+
+inline int bgc_quaternion_make_normalized_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* normalized)
+{
+    bgc_quaternion_copy_fp32(quaternion, normalized);
+    return bgc_quaternion_normalize_fp32(normalized);
+}
+
+inline int bgc_quaternion_make_normalized_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* normalized)
+{
+    bgc_quaternion_copy_fp64(quaternion, normalized);
+    return bgc_quaternion_normalize_fp64(normalized);
+}
+
+// ================== Product =================== //
+
+inline void bgc_quaternion_make_product_fp32(const BgcQuaternionFP32* left, const BgcQuaternionFP32* right, BgcQuaternionFP32* product)
+{
+    const float s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
+    const float x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
+    const float x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
+    const float x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
+
+    product->s0 = s0;
+    product->x1 = x1;
+    product->x2 = x2;
+    product->x3 = x3;
+}
+
+inline void bgc_quaternion_make_product_fp64(const BgcQuaternionFP64* left, const BgcQuaternionFP64* right, BgcQuaternionFP64* product)
+{
+    const double s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
+    const double x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
+    const double x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
+    const double x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
+
+    product->s0 = s0;
+    product->x1 = x1;
+    product->x2 = x2;
+    product->x3 = x3;
+}
+
 // ============ Make Rotation Matrix ============ //
 
-inline void bgc_quaternion_get_rotation_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* matrix)
+inline void bgc_quaternion_make_rotation_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* rotation)
 {
     const float s0s0 = quaternion->s0 * quaternion->s0;
     const float x1x1 = quaternion->x1 * quaternion->x1;
@@ -302,14 +326,13 @@ inline void bgc_quaternion_get_rotation_matrix_fp32(const BgcQuaternionFP32* qua
 
     const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
 
-    if (bgc_is_zero_fp32(square_modulus))
+    if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus)
     {
-        bgc_matrix3x3_set_to_identity_fp32(matrix);
+        bgc_matrix3x3_set_to_identity_fp32(rotation);
         return;
     }
 
     const float corrector1 = 1.0f / square_modulus;
-    const float corrector2 = 2.0f * corrector1;
 
     const float s0x1 = quaternion->s0 * quaternion->x1;
     const float s0x2 = quaternion->s0 * quaternion->x2;
@@ -318,20 +341,22 @@ inline void bgc_quaternion_get_rotation_matrix_fp32(const BgcQuaternionFP32* qua
     const float x1x3 = quaternion->x1 * quaternion->x3;
     const float x2x3 = quaternion->x2 * quaternion->x3;
 
-    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
-    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
-    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
+    const float corrector2 = 2.0f * corrector1;
 
-    matrix->r1c2 = corrector2 * (x1x2 - s0x3);
-    matrix->r2c3 = corrector2 * (x2x3 - s0x1);
-    matrix->r3c1 = corrector2 * (x1x3 - s0x2);
+    rotation->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
+    rotation->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
+    rotation->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
 
-    matrix->r2c1 = corrector2 * (x1x2 + s0x3);
-    matrix->r3c2 = corrector2 * (x2x3 + s0x1);
-    matrix->r1c3 = corrector2 * (x1x3 + s0x2);
+    rotation->r1c2 = corrector2 * (x1x2 - s0x3);
+    rotation->r2c3 = corrector2 * (x2x3 - s0x1);
+    rotation->r3c1 = corrector2 * (x1x3 - s0x2);
+
+    rotation->r2c1 = corrector2 * (x1x2 + s0x3);
+    rotation->r3c2 = corrector2 * (x2x3 + s0x1);
+    rotation->r1c3 = corrector2 * (x1x3 + s0x2);
 }
 
-inline void bgc_quaternion_get_rotation_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* matrix)
+inline void bgc_quaternion_make_rotation_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* rotation)
 {
     const double s0s0 = quaternion->s0 * quaternion->s0;
     const double x1x1 = quaternion->x1 * quaternion->x1;
@@ -340,14 +365,13 @@ inline void bgc_quaternion_get_rotation_matrix_fp64(const BgcQuaternionFP64* qua
 
     const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
 
-    if (bgc_is_zero_fp64(square_modulus))
+    if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus)
     {
-        bgc_matrix3x3_set_to_identity_fp64(matrix);
+        bgc_matrix3x3_set_to_identity_fp64(rotation);
         return;
     }
 
     const double corrector1 = 1.0f / square_modulus;
-    const double corrector2 = 2.0f * corrector1;
 
     const double s0x1 = quaternion->s0 * quaternion->x1;
     const double s0x2 = quaternion->s0 * quaternion->x2;
@@ -356,22 +380,24 @@ inline void bgc_quaternion_get_rotation_matrix_fp64(const BgcQuaternionFP64* qua
     const double x1x3 = quaternion->x1 * quaternion->x3;
     const double x2x3 = quaternion->x2 * quaternion->x3;
 
-    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
-    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
-    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
+    const double corrector2 = 2.0f * corrector1;
 
-    matrix->r1c2 = corrector2 * (x1x2 - s0x3);
-    matrix->r2c3 = corrector2 * (x2x3 - s0x1);
-    matrix->r3c1 = corrector2 * (x1x3 - s0x2);
+    rotation->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
+    rotation->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
+    rotation->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
 
-    matrix->r2c1 = corrector2 * (x1x2 + s0x3);
-    matrix->r3c2 = corrector2 * (x2x3 + s0x1);
-    matrix->r1c3 = corrector2 * (x1x3 + s0x2);
+    rotation->r1c2 = corrector2 * (x1x2 - s0x3);
+    rotation->r2c3 = corrector2 * (x2x3 - s0x1);
+    rotation->r3c1 = corrector2 * (x1x3 - s0x2);
+
+    rotation->r2c1 = corrector2 * (x1x2 + s0x3);
+    rotation->r3c2 = corrector2 * (x2x3 + s0x1);
+    rotation->r1c3 = corrector2 * (x1x3 + s0x2);
 }
 
 // ============ Make Reverse Matrix ============= //
 
-inline void bgc_quaternion_get_reverse_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* matrix)
+inline void bgc_quaternion_make_reverse_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* reverse)
 {
     const float s0s0 = quaternion->s0 * quaternion->s0;
     const float x1x1 = quaternion->x1 * quaternion->x1;
@@ -380,14 +406,13 @@ inline void bgc_quaternion_get_reverse_matrix_fp32(const BgcQuaternionFP32* quat
 
     const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
 
-    if (-BGC_EPSYLON_FP32 <= square_modulus && square_modulus <= BGC_EPSYLON_FP32)
+    if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus)
     {
-        bgc_matrix3x3_set_to_identity_fp32(matrix);
+        bgc_matrix3x3_set_to_identity_fp32(reverse);
         return;
     }
 
     const float corrector1 = 1.0f / square_modulus;
-    const float corrector2 = 2.0f * corrector1;
 
     const float s0x1 = quaternion->s0 * quaternion->x1;
     const float s0x2 = quaternion->s0 * quaternion->x2;
@@ -396,20 +421,22 @@ inline void bgc_quaternion_get_reverse_matrix_fp32(const BgcQuaternionFP32* quat
     const float x1x3 = quaternion->x1 * quaternion->x3;
     const float x2x3 = quaternion->x2 * quaternion->x3;
 
-    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
-    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
-    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
+    const float corrector2 = 2.0f * corrector1;
 
-    matrix->r1c2 = corrector2 * (x1x2 + s0x3);
-    matrix->r2c3 = corrector2 * (x2x3 + s0x1);
-    matrix->r3c1 = corrector2 * (x1x3 + s0x2);
+    reverse->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
+    reverse->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
+    reverse->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
 
-    matrix->r2c1 = corrector2 * (x1x2 - s0x3);
-    matrix->r3c2 = corrector2 * (x2x3 - s0x1);
-    matrix->r1c3 = corrector2 * (x1x3 - s0x2);
+    reverse->r1c2 = corrector2 * (x1x2 + s0x3);
+    reverse->r2c3 = corrector2 * (x2x3 + s0x1);
+    reverse->r3c1 = corrector2 * (x1x3 + s0x2);
+
+    reverse->r2c1 = corrector2 * (x1x2 - s0x3);
+    reverse->r3c2 = corrector2 * (x2x3 - s0x1);
+    reverse->r1c3 = corrector2 * (x1x3 - s0x2);
 }
 
-inline void bgc_quaternion_get_reverse_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* matrix)
+inline void bgc_quaternion_make_reverse_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* reverse)
 {
     const double s0s0 = quaternion->s0 * quaternion->s0;
     const double x1x1 = quaternion->x1 * quaternion->x1;
@@ -418,14 +445,13 @@ inline void bgc_quaternion_get_reverse_matrix_fp64(const BgcQuaternionFP64* quat
 
     const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
 
-    if (-BGC_EPSYLON_FP64 <= square_modulus && square_modulus <= BGC_EPSYLON_FP64)
+    if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus)
     {
-        bgc_matrix3x3_set_to_identity_fp64(matrix);
+        bgc_matrix3x3_set_to_identity_fp64(reverse);
         return;
     }
 
     const double corrector1 = 1.0f / square_modulus;
-    const double corrector2 = 2.0f * corrector1;
 
     const double s0x1 = quaternion->s0 * quaternion->x1;
     const double s0x2 = quaternion->s0 * quaternion->x2;
@@ -434,17 +460,19 @@ inline void bgc_quaternion_get_reverse_matrix_fp64(const BgcQuaternionFP64* quat
     const double x1x3 = quaternion->x1 * quaternion->x3;
     const double x2x3 = quaternion->x2 * quaternion->x3;
 
-    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
-    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
-    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
+    const double corrector2 = 2.0f * corrector1;
 
-    matrix->r1c2 = corrector2 * (x1x2 + s0x3);
-    matrix->r2c3 = corrector2 * (x2x3 + s0x1);
-    matrix->r3c1 = corrector2 * (x1x3 + s0x2);
+    reverse->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
+    reverse->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
+    reverse->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
 
-    matrix->r2c1 = corrector2 * (x1x2 - s0x3);
-    matrix->r3c2 = corrector2 * (x2x3 - s0x1);
-    matrix->r1c3 = corrector2 * (x1x3 - s0x2);
+    reverse->r1c2 = corrector2 * (x1x2 + s0x3);
+    reverse->r2c3 = corrector2 * (x2x3 + s0x1);
+    reverse->r3c1 = corrector2 * (x1x3 + s0x2);
+
+    reverse->r2c1 = corrector2 * (x1x2 - s0x3);
+    reverse->r3c2 = corrector2 * (x2x3 - s0x1);
+    reverse->r1c3 = corrector2 * (x1x3 - s0x2);
 }
 
 // ==================== Add ===================== //
@@ -501,7 +529,25 @@ inline void bgc_quaternion_subtract_fp64(const BgcQuaternionFP64 * minuend, cons
     difference->x3 = minuend->x3 - subtrahend->x3;
 }
 
-// =============== Multiplication =============== //
+// ============== Subtract scaled =============== //
+
+inline void bgc_quaternion_subtract_scaled_fp32(const BgcQuaternionFP32 * basic_quaternion, const BgcQuaternionFP32 * scalable_quaternion, const float scale, BgcQuaternionFP32 * difference)
+{
+    difference->s0 = basic_quaternion->s0 - scalable_quaternion->s0 * scale;
+    difference->x1 = basic_quaternion->x1 - scalable_quaternion->x1 * scale;
+    difference->x2 = basic_quaternion->x2 - scalable_quaternion->x2 * scale;
+    difference->x3 = basic_quaternion->x3 - scalable_quaternion->x3 * scale;
+}
+
+inline void bgc_quaternion_subtract_scaled_fp64(const BgcQuaternionFP64 * basic_quaternion, const BgcQuaternionFP64 * scalable_quaternion, const double scale, BgcQuaternionFP64 * difference)
+{
+    difference->s0 = basic_quaternion->s0 - scalable_quaternion->s0 * scale;
+    difference->x1 = basic_quaternion->x1 - scalable_quaternion->x1 * scale;
+    difference->x2 = basic_quaternion->x2 - scalable_quaternion->x2 * scale;
+    difference->x3 = basic_quaternion->x3 - scalable_quaternion->x3 * scale;
+}
+
+// ================== Multiply ================== //
 
 inline void bgc_quaternion_multiply_fp32(const BgcQuaternionFP32* multiplicand, const float multipier, BgcQuaternionFP32* product)
 {
@@ -519,7 +565,7 @@ inline void bgc_quaternion_multiply_fp64(const BgcQuaternionFP64* multiplicand,
     product->x3 = multiplicand->x3 * multipier;
 }
 
-// ================== Division ================== //
+// =================== Divide =================== //
 
 inline void bgc_quaternion_divide_fp32(const BgcQuaternionFP32* dividend, const float divisor, BgcQuaternionFP32* quotient)
 {
@@ -531,34 +577,6 @@ inline void bgc_quaternion_divide_fp64(const BgcQuaternionFP64* dividend, const
     bgc_quaternion_multiply_fp64(dividend, 1.0 / divisor, quotient);
 }
 
-// ================== Product =================== //
-
-inline void bgc_quaternion_get_product_fp32(const BgcQuaternionFP32* left, const BgcQuaternionFP32* right, BgcQuaternionFP32* product)
-{
-    const float s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
-    const float x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
-    const float x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
-    const float x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
-
-    product->s0 = s0;
-    product->x1 = x1;
-    product->x2 = x2;
-    product->x3 = x3;
-}
-
-inline void bgc_quaternion_get_product_fp64(const BgcQuaternionFP64* left, const BgcQuaternionFP64* right, BgcQuaternionFP64* product)
-{
-    const double s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
-    const double x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
-    const double x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
-    const double x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
-
-    product->s0 = s0;
-    product->x1 = x1;
-    product->x2 = x2;
-    product->x3 = x3;
-}
-
 // ================== Are Close ================= //
 
 inline int bgc_quaternion_are_close_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2)
diff --git a/basic-geometry/tangent-pair.c b/basic-geometry/tangent-pair.c
index e0bce76..e622d15 100644
--- a/basic-geometry/tangent-pair.c
+++ b/basic-geometry/tangent-pair.c
@@ -10,23 +10,29 @@ extern inline void bgc_tangent_pair_reset_fp64(BgcTangentPairFP64* tangent);
 extern inline void bgc_tangent_pair_set_values_fp32(const float x1, const float x2, BgcTangentPairFP32* tangent);
 extern inline void bgc_tangent_pair_set_values_fp64(const double x1, const double x2, BgcTangentPairFP64* tangent);
 
+extern inline void bgc_tangent_pair_set_turn_fp32(const float angle, const BgcAngleUnitEnum unit, BgcTangentPairFP32* tangent);
+extern inline void bgc_tangent_pair_set_turn_fp64(const double angle, const BgcAngleUnitEnum unit, BgcTangentPairFP64* tangent);
+
+extern inline float bgc_tangent_pair_get_angle_fp32(const BgcTangentPairFP32* tangent, const BgcAngleUnitEnum unit);
+extern inline double bgc_tangent_pair_get_angle_fp64(const BgcTangentPairFP64* tangent, const BgcAngleUnitEnum unit);
+
 extern inline void bgc_tangent_pair_copy_fp32(const BgcTangentPairFP32* from, BgcTangentPairFP32* to);
 extern inline void bgc_tangent_pair_copy_fp64(const BgcTangentPairFP64* from, BgcTangentPairFP64* to);
 
 extern inline void bgc_tangent_pair_swap_fp32(BgcTangentPairFP32* tangent1, BgcTangentPairFP32* tangent2);
 extern inline void bgc_tangent_pair_swap_fp64(BgcTangentPairFP64* tangent1, BgcTangentPairFP64* tangent2);
 
-extern inline void bgc_tangent_pair_set_turn_fp32(const float angle, const BgcAngleUnitEnum unit, BgcTangentPairFP32* tangent);
-extern inline void bgc_tangent_pair_set_turn_fp64(const double angle, const BgcAngleUnitEnum unit, BgcTangentPairFP64* tangent);
-
 extern inline void bgc_tangent_pair_convert_fp64_to_fp32(const BgcTangentPairFP64* from, BgcTangentPairFP32* to);
 extern inline void bgc_tangent_pair_convert_fp32_to_fp64(const BgcTangentPairFP32* from, BgcTangentPairFP64* to);
 
 extern inline void bgc_tangent_pair_invert_fp32(BgcTangentPairFP32* tangent);
 extern inline void bgc_tangent_pair_invert_fp64(BgcTangentPairFP64* tangent);
 
-extern inline void bgc_tangent_pair_set_inverted_fp32(const BgcTangentPairFP32* tangent, BgcTangentPairFP32* result);
-extern inline void bgc_tangent_pair_set_inverted_fp64(const BgcTangentPairFP64* tangent, BgcTangentPairFP64* result);
+extern inline void bgc_tangent_pair_combine_fp32(const BgcTangentPairFP32* tangent1, const BgcTangentPairFP32* tangent2, BgcTangentPairFP32* result);
+extern inline void bgc_tangent_pair_combine_fp64(const BgcTangentPairFP64* tangent1, const BgcTangentPairFP64* tangent2, BgcTangentPairFP64* result);
+
+extern inline void bgc_tangent_pair_make_inverted_fp32(const BgcTangentPairFP32* tangent, BgcTangentPairFP32* result);
+extern inline void bgc_tangent_pair_make_inverted_fp64(const BgcTangentPairFP64* tangent, BgcTangentPairFP64* result);
 
 extern inline void bgc_tangent_pair_make_rotation_matrix_fp32(const BgcTangentPairFP32* tangent, BgcMatrix2x2FP32* matrix);
 extern inline void bgc_tangent_pair_make_rotation_matrix_fp64(const BgcTangentPairFP64* tangent, BgcMatrix2x2FP64* matrix);
@@ -34,12 +40,6 @@ extern inline void bgc_tangent_pair_make_rotation_matrix_fp64(const BgcTangentPa
 extern inline void bgc_tangent_pair_make_reverse_matrix_fp32(const BgcTangentPairFP32* tangent, BgcMatrix2x2FP32* matrix);
 extern inline void bgc_tangent_pair_make_reverse_matrix_fp64(const BgcTangentPairFP64* tangent, BgcMatrix2x2FP64* matrix);
 
-extern inline float bgc_tangent_pair_get_angle_fp32(const BgcTangentPairFP32* tangent, const BgcAngleUnitEnum unit);
-extern inline double bgc_tangent_pair_get_angle_fp64(const BgcTangentPairFP64* tangent, const BgcAngleUnitEnum unit);
-
-extern inline void bgc_tangent_pair_combine_fp32(const BgcTangentPairFP32* tangent1, const BgcTangentPairFP32* tangent2, BgcTangentPairFP32* result);
-extern inline void bgc_tangent_pair_combine_fp64(const BgcTangentPairFP64* tangent1, const BgcTangentPairFP64* tangent2, BgcTangentPairFP64* result);
-
 extern inline void bgc_tangent_pair_turn_vector_fp32(const BgcTangentPairFP32* tangent, const BgcVector2FP32* vector, BgcVector2FP32* result);
 extern inline void bgc_tangent_pair_turn_vector_fp64(const BgcTangentPairFP64* tangent, const BgcVector2FP64* vector, BgcVector2FP64* result);
 
diff --git a/basic-geometry/tangent-pair.h b/basic-geometry/tangent-pair.h
index e2fd296..ff4e59b 100644
--- a/basic-geometry/tangent-pair.h
+++ b/basic-geometry/tangent-pair.h
@@ -68,7 +68,7 @@ inline void bgc_tangent_pair_set_values_fp32(const float x1, const float x2, Bgc
     twin->cos = x1;
     twin->sin = x2;
 
-    if (!bgc_is_sqare_value_unit_fp32(square_modulus)) {
+    if (!bgc_is_sqare_unit_fp32(square_modulus)) {
         _bgc_tangent_pair_normalize_fp32(square_modulus, twin);
     }
 }
@@ -82,11 +82,77 @@ inline void bgc_tangent_pair_set_values_fp64(const double x1, const double x2, B
     twin->cos = x1;
     twin->sin = x2;
 
-    if (!bgc_is_sqare_value_unit_fp64(square_modulus)) {
+    if (!bgc_is_sqare_unit_fp64(square_modulus)) {
         _bgc_tangent_pair_normalize_fp64(square_modulus, twin);
     }
 }
 
+// ================== Set Turn ================== //
+
+inline void bgc_tangent_pair_set_turn_fp32(const float angle, const BgcAngleUnitEnum unit, BgcTangentPairFP32* tangent)
+{
+    const float radians = bgc_angle_to_radians_fp32(angle, unit);
+
+    _BgcTwinTangentPairFP32* twin = (_BgcTwinTangentPairFP32*)tangent;
+
+    twin->cos = cosf(radians);
+    twin->sin = sinf(radians);
+}
+
+inline void bgc_tangent_pair_set_turn_fp64(const double angle, const BgcAngleUnitEnum unit, BgcTangentPairFP64* tangent)
+{
+    const double radians = bgc_angle_to_radians_fp64(angle, unit);
+
+    _BgcTwinTangentPairFP64* twin = (_BgcTwinTangentPairFP64*)tangent;
+
+    twin->cos = cos(radians);
+    twin->sin = sin(radians);
+}
+
+// =================== Angle =================== //
+
+inline float bgc_tangent_pair_get_angle_fp32(const BgcTangentPairFP32* tangent, const BgcAngleUnitEnum unit)
+{
+    if (tangent->cos >= 1.0f - BGC_EPSYLON_FP32) {
+        return 0.0f;
+    }
+
+    if (tangent->cos <= -1.0f + BGC_EPSYLON_FP32) {
+        return bgc_angle_get_half_circle_fp32(unit);
+    }
+
+    if (tangent->sin >= 1.0f - BGC_EPSYLON_FP32) {
+        return bgc_angle_get_quater_circle_fp32(unit);
+    }
+
+    if (tangent->sin <= -1.0f + BGC_EPSYLON_FP32) {
+        return 0.75f * bgc_angle_get_full_circle_fp32(unit);
+    }
+
+    return bgc_radians_to_units_fp32(atan2f(tangent->cos, tangent->sin), unit);
+}
+
+inline double bgc_tangent_pair_get_angle_fp64(const BgcTangentPairFP64* tangent, const BgcAngleUnitEnum unit)
+{
+    if (tangent->cos >= 1.0 - BGC_EPSYLON_FP64) {
+        return 0.0;
+    }
+
+    if (tangent->cos <= -1.0 + BGC_EPSYLON_FP64) {
+        return bgc_angle_get_half_circle_fp64(unit);
+    }
+
+    if (tangent->sin >= 1.0 - BGC_EPSYLON_FP64) {
+        return bgc_angle_get_quater_circle_fp64(unit);
+    }
+
+    if (tangent->sin <= -1.0 + BGC_EPSYLON_FP64) {
+        return 0.75 * bgc_angle_get_full_circle_fp64(unit);
+    }
+
+    return bgc_radians_to_units_fp64(atan2(tangent->cos, tangent->sin), unit);
+}
+
 // ==================== Copy ==================== //
 
 inline void bgc_tangent_pair_copy_fp32(const BgcTangentPairFP32* from, BgcTangentPairFP32* to)
@@ -139,29 +205,7 @@ inline void bgc_tangent_pair_swap_fp64(BgcTangentPairFP64* tangent1, BgcTangentP
     twin2->sin = sin;
 }
 
-// ================== Set Turn ================== //
-
-inline void bgc_tangent_pair_set_turn_fp32(const float angle, const BgcAngleUnitEnum unit, BgcTangentPairFP32* tangent)
-{
-    const float radians = bgc_angle_to_radians_fp32(angle, unit);
-
-    _BgcTwinTangentPairFP32* twin = (_BgcTwinTangentPairFP32*)tangent;
-
-    twin->cos = cosf(radians);
-    twin->sin = sinf(radians);
-}
-
-inline void bgc_tangent_pair_set_turn_fp64(const double angle, const BgcAngleUnitEnum unit, BgcTangentPairFP64* tangent)
-{
-    const double radians = bgc_angle_to_radians_fp64(angle, unit);
-
-    _BgcTwinTangentPairFP64* twin = (_BgcTwinTangentPairFP64*)tangent;
-
-    twin->cos = cos(radians);
-    twin->sin = sin(radians);
-}
-
-// ============= Copy to twin type ============== //
+// ================== Convert =================== //
 
 inline void bgc_tangent_pair_convert_fp64_to_fp32(const BgcTangentPairFP64* from, BgcTangentPairFP32* to)
 {
@@ -173,7 +217,7 @@ inline void bgc_tangent_pair_convert_fp32_to_fp64(const BgcTangentPairFP32* from
     bgc_tangent_pair_set_values_fp64((double)from->cos, (double)from->sin, to);
 }
 
-// ================= Inversion ================== //
+// =================== Invert =================== //
 
 inline void bgc_tangent_pair_invert_fp32(BgcTangentPairFP32* tangent)
 {
@@ -185,9 +229,29 @@ inline void bgc_tangent_pair_invert_fp64(BgcTangentPairFP64* tangent)
     ((_BgcTwinTangentPairFP64*)tangent)->sin = -tangent->sin;
 }
 
+// ================ Combination ================= //
+
+inline void bgc_tangent_pair_combine_fp32(const BgcTangentPairFP32* tangent1, const BgcTangentPairFP32* tangent2, BgcTangentPairFP32* result)
+{
+    bgc_tangent_pair_set_values_fp32(
+        tangent1->cos * tangent2->cos - tangent1->sin * tangent2->sin,
+        tangent1->cos * tangent2->sin + tangent1->sin * tangent2->cos,
+        result
+    );
+}
+
+inline void bgc_tangent_pair_combine_fp64(const BgcTangentPairFP64* tangent1, const BgcTangentPairFP64* tangent2, BgcTangentPairFP64* result)
+{
+    bgc_tangent_pair_set_values_fp64(
+        tangent1->cos * tangent2->cos - tangent1->sin * tangent2->sin,
+        tangent1->cos * tangent2->sin + tangent1->sin * tangent2->cos,
+        result
+    );
+}
+
 // ================ Set Inverted ================ //
 
-inline void bgc_tangent_pair_set_inverted_fp32(const BgcTangentPairFP32* tangent, BgcTangentPairFP32* result)
+inline void bgc_tangent_pair_make_inverted_fp32(const BgcTangentPairFP32* tangent, BgcTangentPairFP32* result)
 {
     _BgcTwinTangentPairFP32* twin = (_BgcTwinTangentPairFP32*)result;
 
@@ -195,7 +259,7 @@ inline void bgc_tangent_pair_set_inverted_fp32(const BgcTangentPairFP32* tangent
     twin->sin = -tangent->sin;
 }
 
-inline void bgc_tangent_pair_set_inverted_fp64(const BgcTangentPairFP64* tangent, BgcTangentPairFP64* result)
+inline void bgc_tangent_pair_make_inverted_fp64(const BgcTangentPairFP64* tangent, BgcTangentPairFP64* result)
 {
     _BgcTwinTangentPairFP64* twin = (_BgcTwinTangentPairFP64*)result;
 
@@ -239,70 +303,6 @@ inline void bgc_tangent_pair_make_reverse_matrix_fp64(const BgcTangentPairFP64*
     matrix->r2c2 = tangent->cos;
 }
 
-// =================== Angle =================== //
-
-inline float bgc_tangent_pair_get_angle_fp32(const BgcTangentPairFP32* tangent, const BgcAngleUnitEnum unit)
-{
-    if (tangent->cos >= 1.0f - BGC_EPSYLON_FP32) {
-        return 0.0f;
-    }
-
-    if (tangent->cos <= -1.0f + BGC_EPSYLON_FP32) {
-        return bgc_angle_get_half_circle_fp32(unit);
-    }
-
-    if (tangent->sin >= 1.0f - BGC_EPSYLON_FP32) {
-        return bgc_angle_get_quater_circle_fp32(unit);
-    }
-
-    if (tangent->sin <= -1.0f + BGC_EPSYLON_FP32) {
-        return 0.75f * bgc_angle_get_full_circle_fp32(unit);
-    }
-
-    return bgc_radians_to_units_fp32(atan2f(tangent->cos, tangent->sin), unit);
-}
-
-inline double bgc_tangent_pair_get_angle_fp64(const BgcTangentPairFP64* tangent, const BgcAngleUnitEnum unit)
-{
-    if (tangent->cos >= 1.0 - BGC_EPSYLON_FP64) {
-        return 0.0;
-    }
-
-    if (tangent->cos <= -1.0 + BGC_EPSYLON_FP64) {
-        return bgc_angle_get_half_circle_fp64(unit);
-    }
-
-    if (tangent->sin >= 1.0 - BGC_EPSYLON_FP64) {
-        return bgc_angle_get_quater_circle_fp64(unit);
-    }
-
-    if (tangent->sin <= -1.0 + BGC_EPSYLON_FP64) {
-        return 0.75 * bgc_angle_get_full_circle_fp64(unit);
-    }
-
-    return bgc_radians_to_units_fp64(atan2(tangent->cos, tangent->sin), unit);
-}
-
-// ================ Combination ================= //
-
-inline void bgc_tangent_pair_combine_fp32(const BgcTangentPairFP32* tangent1, const BgcTangentPairFP32* tangent2, BgcTangentPairFP32* result)
-{
-    bgc_tangent_pair_set_values_fp32(
-        tangent1->cos * tangent2->cos - tangent1->sin * tangent2->sin,
-        tangent1->cos * tangent2->sin + tangent1->sin * tangent2->cos,
-        result
-    );
-}
-
-inline void bgc_tangent_pair_combine_fp64(const BgcTangentPairFP64* tangent1, const BgcTangentPairFP64* tangent2, BgcTangentPairFP64* result)
-{
-    bgc_tangent_pair_set_values_fp64(
-        tangent1->cos * tangent2->cos - tangent1->sin * tangent2->sin,
-        tangent1->cos * tangent2->sin + tangent1->sin * tangent2->cos,
-        result
-    );
-}
-
 // ================ Turn Vector ================= //
 
 inline void bgc_tangent_pair_turn_vector_fp32(const BgcTangentPairFP32* tangent, const BgcVector2FP32* vector, BgcVector2FP32* result)
diff --git a/basic-geometry/utilities.c b/basic-geometry/utilities.c
index cdd8ff8..e863c4b 100644
--- a/basic-geometry/utilities.c
+++ b/basic-geometry/utilities.c
@@ -7,8 +7,8 @@ extern inline int bgc_is_zero_fp64(const double square_value);
 extern inline int bgc_is_unit_fp32(const float square_value);
 extern inline int bgc_is_unit_fp64(const double square_value);
 
-extern inline int bgc_is_sqare_value_unit_fp32(const float square_value);
-extern inline int bgc_is_sqare_value_unit_fp64(const double square_value);
+extern inline int bgc_is_sqare_unit_fp32(const float square_value);
+extern inline int bgc_is_sqare_unit_fp64(const double square_value);
 
 extern inline int bgc_are_close_fp32(const float value1, const float value2);
 extern inline int bgc_are_close_fp64(const double value1, const double value2);
diff --git a/basic-geometry/utilities.h b/basic-geometry/utilities.h
index db868e2..4b2887d 100644
--- a/basic-geometry/utilities.h
+++ b/basic-geometry/utilities.h
@@ -47,12 +47,12 @@ inline int bgc_is_unit_fp64(const double square_value)
 }
 
 
-inline int bgc_is_sqare_value_unit_fp32(const float square_value)
+inline int bgc_is_sqare_unit_fp32(const float square_value)
 {
     return (1.0f - 2.0f * BGC_EPSYLON_FP32 <= square_value) && (square_value <= 1.0f + 2.0f * BGC_EPSYLON_FP32);
 }
 
-inline int bgc_is_sqare_value_unit_fp64(const double square_value)
+inline int bgc_is_sqare_unit_fp64(const double square_value)
 {
     return (1.0 - 2.0 * BGC_EPSYLON_FP64 <= square_value) && (square_value <= 1.0 + 2.0 * BGC_EPSYLON_FP64);
 }
diff --git a/basic-geometry/vector2.c b/basic-geometry/vector2.c
index dfb83af..348acf9 100644
--- a/basic-geometry/vector2.c
+++ b/basic-geometry/vector2.c
@@ -5,6 +5,18 @@ extern inline void bgc_vector2_reset_fp64(BgcVector2FP64* vector);
 
 extern inline void bgc_vector2_set_values_fp32(const float x1, const float x2, BgcVector2FP32* to);
 extern inline void bgc_vector2_set_values_fp64(const double x1, const double x2, BgcVector2FP64* to);
+
+extern inline float bgc_vector2_get_square_modulus_fp32(const BgcVector2FP32* vector);
+extern inline double bgc_vector2_get_square_modulus_fp64(const BgcVector2FP64* vector);
+
+extern inline float bgc_vector2_get_modulus_fp32(const BgcVector2FP32* vector);
+extern inline double bgc_vector2_get_modulus_fp64(const BgcVector2FP64* vector);
+
+extern inline int bgc_vector2_is_zero_fp32(const BgcVector2FP32* vector);
+extern inline int bgc_vector2_is_zero_fp64(const BgcVector2FP64* vector);
+
+extern inline int bgc_vector2_is_unit_fp32(const BgcVector2FP32* vector);
+extern inline int bgc_vector2_is_unit_fp64(const BgcVector2FP64* vector);
 
 extern inline void bgc_vector2_copy_fp32(const BgcVector2FP32* from, BgcVector2FP32* to);
 extern inline void bgc_vector2_copy_fp64(const BgcVector2FP64* from, BgcVector2FP64* to);
@@ -15,24 +27,18 @@ extern inline void bgc_vector2_swap_fp64(BgcVector2FP64* vector1, BgcVector2FP64
 extern inline void bgc_vector2_convert_fp64_to_fp32(const BgcVector2FP64* from, BgcVector2FP32* to);
 extern inline void bgc_vector2_convert_fp32_to_fp64(const BgcVector2FP32* from, BgcVector2FP64* to);
 
-extern inline void bgc_vector2_set_reverse_fp32(const BgcVector2FP32* from, BgcVector2FP32* to);
-extern inline void bgc_vector2_set_reverse_fp64(const BgcVector2FP64* from, BgcVector2FP64* to);
-
-extern inline void bgc_vector2_set_reverse_fp64_to_fp32(const BgcVector2FP64* from, BgcVector2FP32* to);
-extern inline void bgc_vector2_set_reverse_fp32_to_fp64(const BgcVector2FP32* from, BgcVector2FP64* to);
-
-extern inline float bgc_vector2_get_square_modulus_fp32(const BgcVector2FP32* vector);
-extern inline double bgc_vector2_get_square_modulus_fp64(const BgcVector2FP64* vector);
-
-extern inline float bgc_vector2_get_modulus_fp32(const BgcVector2FP32* vector);
-extern inline double bgc_vector2_get_modulus_fp64(const BgcVector2FP64* vector);
-
-extern inline int bgc_vector2_is_zero_fp32(const BgcVector2FP32* vector);
-extern inline int bgc_vector2_is_zero_fp64(const BgcVector2FP64* vector);
-
-extern inline int bgc_vector2_is_unit_fp32(const BgcVector2FP32* vector);
-extern inline int bgc_vector2_is_unit_fp64(const BgcVector2FP64* vector);
-
+extern inline void bgc_vector2_reverse_fp32(BgcVector2FP32* vector);
+extern inline void bgc_vector2_reverse_fp64(BgcVector2FP64* vector);
+
+extern inline int bgc_vector2_normalize_fp32(BgcVector2FP32* vector);
+extern inline int bgc_vector2_normalize_fp64(BgcVector2FP64* vector);
+
+extern inline void bgc_vector2_make_reverse_fp32(const BgcVector2FP32* vector, BgcVector2FP32* reverse);
+extern inline void bgc_vector2_make_reverse_fp64(const BgcVector2FP64* vector, BgcVector2FP64* reverse);
+
+extern inline int bgc_vector2_make_normalized_fp32(const BgcVector2FP32* vector, BgcVector2FP32* result);
+extern inline int bgc_vector2_make_normalized_fp64(const BgcVector2FP64* vector, BgcVector2FP64* result);
+
 extern inline void bgc_vector2_add_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, BgcVector2FP32* sum);
 extern inline void bgc_vector2_add_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, BgcVector2FP64* sum);
 
@@ -42,17 +48,20 @@ extern inline void bgc_vector2_add_scaled_fp64(const BgcVector2FP64* basic_vecto
 extern inline void bgc_vector2_subtract_fp32(const BgcVector2FP32* minuend, const BgcVector2FP32* subtrahend, BgcVector2FP32* difference);
 extern inline void bgc_vector2_subtract_fp64(const BgcVector2FP64* minuend, const BgcVector2FP64* subtrahend, BgcVector2FP64* difference);
 
+extern inline void bgc_vector2_subtract_scaled_fp32(const BgcVector2FP32* basic_vector, const BgcVector2FP32* scalable_vector, const float scale, BgcVector2FP32* difference);
+extern inline void bgc_vector2_subtract_scaled_fp64(const BgcVector2FP64* basic_vector, const BgcVector2FP64* scalable_vector, const double scale, BgcVector2FP64* difference);
+
 extern inline void bgc_vector2_multiply_fp32(const BgcVector2FP32* multiplicand, const float multiplier, BgcVector2FP32* product);
 extern inline void bgc_vector2_multiply_fp64(const BgcVector2FP64* multiplicand, const double multiplier, BgcVector2FP64* product);
 
 extern inline void bgc_vector2_divide_fp32(const BgcVector2FP32* dividend, const float divisor, BgcVector2FP32* quotient);
 extern inline void bgc_vector2_divide_fp64(const BgcVector2FP64* dividend, const double divisor, BgcVector2FP64* quotient);
 
-extern inline void bgc_vector2_mean_of_two_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, BgcVector2FP32* result);
-extern inline void bgc_vector2_mean_of_two_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, BgcVector2FP64* result);
+extern inline void bgc_vector2_mean_of_two_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, BgcVector2FP32* mean);
+extern inline void bgc_vector2_mean_of_two_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, BgcVector2FP64* mean);
 
-extern inline void bgc_vector2_mean_of_three_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const BgcVector2FP32* vector3, BgcVector2FP32* result);
-extern inline void bgc_vector2_mean_of_three_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const BgcVector2FP64* vector3, BgcVector2FP64* result);
+extern inline void bgc_vector2_mean_of_three_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const BgcVector2FP32* vector3, BgcVector2FP32* mean);
+extern inline void bgc_vector2_mean_of_three_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const BgcVector2FP64* vector3, BgcVector2FP64* mean);
 
 extern inline float bgc_vector2_scalar_product_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2);
 extern inline double bgc_vector2_scalar_product_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2);
@@ -60,14 +69,8 @@ extern inline double bgc_vector2_scalar_product_fp64(const BgcVector2FP64* vecto
 extern inline float bgc_vector2_cross_product_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2);
 extern inline double bgc_vector2_cross_product_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2);
 
-extern inline void bgc_vector2_complex_product_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, BgcVector2FP32* result);
-extern inline void bgc_vector2_complex_product_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, BgcVector2FP64* result);
-
-extern inline int bgc_vector2_normalize_fp32(BgcVector2FP32* vector);
-extern inline int bgc_vector2_normalize_fp64(BgcVector2FP64* vector);
-
-extern inline int bgc_vector2_set_normalized_fp32(const BgcVector2FP32* vector, BgcVector2FP32* result);
-extern inline int bgc_vector2_set_normalized_fp64(const BgcVector2FP64* vector, BgcVector2FP64* result);
+extern inline void bgc_vector2_complex_product_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, BgcVector2FP32* product);
+extern inline void bgc_vector2_complex_product_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, BgcVector2FP64* product);
 
 extern inline float bgc_vector2_get_square_distance_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2);
 extern inline double bgc_vector2_get_square_distance_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2);
@@ -85,10 +88,6 @@ extern inline int bgc_vector2_are_close_fp64(const BgcVector2FP64* vector1, cons
 
 float bgc_vector2_get_angle_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const BgcAngleUnitEnum unit)
 {
-    if (vector1 == 0 || vector2 == 0) {
-        return 0.0f;
-    }
-
     const float square_modulus1 = bgc_vector2_get_square_modulus_fp32(vector1);
 
     if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP32) {
@@ -116,10 +115,6 @@ float bgc_vector2_get_angle_fp32(const BgcVector2FP32* vector1, const BgcVector2
 
 double bgc_vector2_get_angle_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const BgcAngleUnitEnum unit)
 {
-    if (vector1 == 0 || vector2 == 0) {
-        return 0.0;
-    }
-
     const double square_modulus1 = bgc_vector2_get_square_modulus_fp64(vector1);
 
     if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP64) {
diff --git a/basic-geometry/vector2.h b/basic-geometry/vector2.h
index c1d81d4..f603227 100644
--- a/basic-geometry/vector2.h
+++ b/basic-geometry/vector2.h
@@ -44,6 +44,50 @@ inline void bgc_vector2_set_values_fp64(const double x1, const double x2, BgcVec
     to->x2 = x2;
 }
 
+// ================== Modulus =================== //
+
+inline float bgc_vector2_get_square_modulus_fp32(const BgcVector2FP32* vector)
+{
+    return vector->x1 * vector->x1 + vector->x2 * vector->x2;
+}
+
+inline double bgc_vector2_get_square_modulus_fp64(const BgcVector2FP64* vector)
+{
+    return vector->x1 * vector->x1 + vector->x2 * vector->x2;
+}
+
+inline float bgc_vector2_get_modulus_fp32(const BgcVector2FP32* vector)
+{
+    return sqrtf(bgc_vector2_get_square_modulus_fp32(vector));
+}
+
+inline double bgc_vector2_get_modulus_fp64(const BgcVector2FP64* vector)
+{
+    return sqrt(bgc_vector2_get_square_modulus_fp64(vector));
+}
+
+// ================= Comparison ================= //
+
+inline int bgc_vector2_is_zero_fp32(const BgcVector2FP32* vector)
+{
+    return bgc_vector2_get_square_modulus_fp32(vector) <= BGC_SQUARE_EPSYLON_FP32;
+}
+
+inline int bgc_vector2_is_zero_fp64(const BgcVector2FP64* vector)
+{
+    return bgc_vector2_get_square_modulus_fp64(vector) <= BGC_SQUARE_EPSYLON_FP64;
+}
+
+inline int bgc_vector2_is_unit_fp32(const BgcVector2FP32* vector)
+{
+    return bgc_is_sqare_unit_fp32(bgc_vector2_get_square_modulus_fp32(vector));
+}
+
+inline int bgc_vector2_is_unit_fp64(const BgcVector2FP64* vector)
+{
+    return bgc_is_sqare_unit_fp64(bgc_vector2_get_square_modulus_fp64(vector));
+}
+
 // ==================== Copy ==================== //
 
 inline void bgc_vector2_copy_fp32(const BgcVector2FP32* from, BgcVector2FP32* to)
@@ -84,7 +128,7 @@ inline void bgc_vector2_swap_fp64(BgcVector2FP64* vector1, BgcVector2FP64* vecto
     vector1->x2 = x2;
 }
 
-// ============= Copy to twin type ============== //
+// ================== Convert =================== //
 
 inline void bgc_vector2_convert_fp64_to_fp32(const BgcVector2FP64* from, BgcVector2FP32* to)
 {
@@ -98,76 +142,118 @@ inline void bgc_vector2_convert_fp32_to_fp64(const BgcVector2FP32* from, BgcVect
     to->x2 = from->x2;
 }
 
-// =================== Reverse ================== //
+// ================== Reverse =================== //
 
-inline void bgc_vector2_set_reverse_fp32(const BgcVector2FP32* from, BgcVector2FP32* to)
+inline void bgc_vector2_reverse_fp32(BgcVector2FP32* vector)
 {
-    to->x1 = -from->x1;
-    to->x2 = -from->x2;
+    vector->x1 = -vector->x1;
+    vector->x2 = -vector->x2;
 }
 
-inline void bgc_vector2_set_reverse_fp64(const BgcVector2FP64* from, BgcVector2FP64* to)
+inline void bgc_vector2_reverse_fp64(BgcVector2FP64* vector)
 {
-    to->x1 = -from->x1;
-    to->x2 = -from->x2;
+    vector->x1 = -vector->x1;
+    vector->x2 = -vector->x2;
 }
 
-// ============= Reverse twin type ============== //
+// ================= Normalize ================== //
 
-inline void bgc_vector2_set_reverse_fp64_to_fp32(const BgcVector2FP64* from, BgcVector2FP32* to)
+inline int bgc_vector2_normalize_fp32(BgcVector2FP32* vector)
 {
-    to->x1 = (float) -from->x1;
-    to->x2 = (float) -from->x2;
+    const float square_modulus = bgc_vector2_get_square_modulus_fp32(vector);
+
+    if (bgc_is_sqare_unit_fp32(square_modulus)) {
+        return 1;
+    }
+
+    if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
+        vector->x1 = 0.0f;
+        vector->x2 = 0.0f;
+        return 0;
+    }
+
+    const float multiplicand = sqrtf(1.0f / square_modulus);
+
+    vector->x1 *= multiplicand;
+    vector->x2 *= multiplicand;
+
+    return 1;
 }
 
-inline void bgc_vector2_set_reverse_fp32_to_fp64(const BgcVector2FP32* from, BgcVector2FP64* to)
+inline int bgc_vector2_normalize_fp64(BgcVector2FP64* vector)
 {
-    to->x1 = -from->x1;
-    to->x2 = -from->x2;
+    const double square_modulus = bgc_vector2_get_square_modulus_fp64(vector);
+
+    if (bgc_is_sqare_unit_fp64(square_modulus)) {
+        return 1;
+    }
+
+    if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
+        vector->x1 = 0.0;
+        vector->x2 = 0.0;
+        return 0;
+    }
+
+    const double multiplicand = sqrt(1.0 / square_modulus);
+
+    vector->x1 *= multiplicand;
+    vector->x2 *= multiplicand;
+
+    return 1;
 }
 
-// =================== Module =================== //
+// ============= Complex Conjugate ============== //
 
-inline float bgc_vector2_get_square_modulus_fp32(const BgcVector2FP32* vector)
+inline void bgc_vector2_complex_conjugate_fp32(BgcVector2FP32* vector)
 {
-    return vector->x1 * vector->x1 + vector->x2 * vector->x2;
+    vector->x2 = -vector->x2;
 }
 
-inline double bgc_vector2_get_square_modulus_fp64(const BgcVector2FP64* vector)
+inline void bgc_vector2_complex_conjugate_fp64(BgcVector2FP64* vector)
 {
-    return vector->x1 * vector->x1 + vector->x2 * vector->x2;
+    vector->x2 = -vector->x2;
 }
 
-inline float bgc_vector2_get_modulus_fp32(const BgcVector2FP32* vector)
+// ================ Make Reverse ================ //
+
+inline void bgc_vector2_make_reverse_fp32(const BgcVector2FP32* vector, BgcVector2FP32* reverse)
 {
-    return sqrtf(bgc_vector2_get_square_modulus_fp32(vector));
+    reverse->x1 = -vector->x1;
+    reverse->x2 = -vector->x2;
 }
 
-inline double bgc_vector2_get_modulus_fp64(const BgcVector2FP64* vector)
+inline void bgc_vector2_make_reverse_fp64(const BgcVector2FP64* vector, BgcVector2FP64* reverse)
 {
-    return sqrt(bgc_vector2_get_square_modulus_fp64(vector));
+    reverse->x1 = -vector->x1;
+    reverse->x2 = -vector->x2;
 }
 
-// ================= Comparison ================= //
+// ============== Make Normalized =============== //
 
-inline int bgc_vector2_is_zero_fp32(const BgcVector2FP32* vector)
+inline int bgc_vector2_make_normalized_fp32(const BgcVector2FP32* vector, BgcVector2FP32* normalized)
 {
-    return bgc_vector2_get_square_modulus_fp32(vector) <= BGC_SQUARE_EPSYLON_FP32;
+    bgc_vector2_copy_fp32(vector, normalized);
+    return bgc_vector2_normalize_fp32(normalized);
 }
 
-inline int bgc_vector2_is_zero_fp64(const BgcVector2FP64* vector)
+inline int bgc_vector2_make_normalized_fp64(const BgcVector2FP64* vector, BgcVector2FP64* normalized)
 {
-    return bgc_vector2_get_square_modulus_fp64(vector) <= BGC_SQUARE_EPSYLON_FP64;
+    bgc_vector2_copy_fp64(vector, normalized);
+    return bgc_vector2_normalize_fp64(normalized);
 }
 
-inline int bgc_vector2_is_unit_fp32(const BgcVector2FP32* vector)
+// =========== Make Complex Conjugate =========== //
+
+inline void bgc_vector2_make_complex_conjugate_fp32(const BgcVector2FP32* vector, BgcVector2FP32* conjugate)
 {
-    return bgc_is_sqare_value_unit_fp32(bgc_vector2_get_square_modulus_fp32(vector));
+    conjugate->x1 = vector->x1;
+    conjugate->x2 = -vector->x2;
 }
 
-inline int bgc_vector2_is_unit_fp64(const BgcVector2FP64* vector)
+inline void bgc_vector2_make_complex_conjugate_fp64(const BgcVector2FP64* vector, BgcVector2FP64* conjugate)
 {
-    return bgc_is_sqare_value_unit_fp64(bgc_vector2_get_square_modulus_fp64(vector));
+    conjugate->x1 = vector->x1;
+    conjugate->x2 = -vector->x2;
 }
 
 // ==================== Add ===================== //
@@ -184,7 +270,7 @@ inline void bgc_vector2_add_fp64(const BgcVector2FP64* vector1, const BgcVector2
     sum->x2 = vector1->x2 + vector2->x2;
 }
 
-// ================ Append scaled =============== //
+// ================= Add scaled ================= //
 
 inline void bgc_vector2_add_scaled_fp32(const BgcVector2FP32* basic_vector, const BgcVector2FP32* scalable_vector, const float scale, BgcVector2FP32* sum)
 {
@@ -198,7 +284,7 @@ inline void bgc_vector2_add_scaled_fp64(const BgcVector2FP64* basic_vector, cons
     sum->x2 = basic_vector->x2 + scalable_vector->x2 * scale;
 }
 
-// ================ Subtraction ================= //
+// ================== Subtract ================== //
 
 inline void bgc_vector2_subtract_fp32(const BgcVector2FP32* minuend, const BgcVector2FP32* subtrahend, BgcVector2FP32* difference)
 {
@@ -212,7 +298,21 @@ inline void bgc_vector2_subtract_fp64(const BgcVector2FP64* minuend, const BgcVe
     difference->x2 = minuend->x2 - subtrahend->x2;
 }
 
-// =============== Multiplication =============== //
+// ============== Subtract scaled =============== //
+
+inline void bgc_vector2_subtract_scaled_fp32(const BgcVector2FP32* basic_vector, const BgcVector2FP32* scalable_vector, const float scale, BgcVector2FP32* difference)
+{
+    difference->x1 = basic_vector->x1 - scalable_vector->x1 * scale;
+    difference->x2 = basic_vector->x2 - scalable_vector->x2 * scale;
+}
+
+inline void bgc_vector2_subtract_scaled_fp64(const BgcVector2FP64* basic_vector, const BgcVector2FP64* scalable_vector, const double scale, BgcVector2FP64* difference)
+{
+    difference->x1 = basic_vector->x1 - scalable_vector->x1 * scale;
+    difference->x2 = basic_vector->x2 - scalable_vector->x2 * scale;
+}
+
+// ================== Multiply ================== //
 
 inline void bgc_vector2_multiply_fp32(const BgcVector2FP32* multiplicand, const float multiplier, BgcVector2FP32* product)
 {
@@ -226,7 +326,7 @@ inline void bgc_vector2_multiply_fp64(const BgcVector2FP64* multiplicand, const
     product->x2 = multiplicand->x2 * multiplier;
 }
 
-// ================== Division ================== //
+// =================== Divide =================== //
 
 inline void bgc_vector2_divide_fp32(const BgcVector2FP32* dividend, const float divisor, BgcVector2FP32* quotient)
 {
@@ -240,30 +340,30 @@ inline void bgc_vector2_divide_fp64(const BgcVector2FP64* dividend, const double
 
 // ================== Average2 ================== //
 
-inline void bgc_vector2_mean_of_two_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, BgcVector2FP32* result)
+inline void bgc_vector2_mean_of_two_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, BgcVector2FP32* mean)
 {
-    result->x1 = (vector1->x1 + vector2->x1) * 0.5f;
-    result->x2 = (vector1->x2 + vector2->x2) * 0.5f;
+    mean->x1 = (vector1->x1 + vector2->x1) * 0.5f;
+    mean->x2 = (vector1->x2 + vector2->x2) * 0.5f;
 }
 
-inline void bgc_vector2_mean_of_two_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, BgcVector2FP64* result)
+inline void bgc_vector2_mean_of_two_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, BgcVector2FP64* mean)
 {
-    result->x1 = (vector1->x1 + vector2->x1) * 0.5;
-    result->x2 = (vector1->x2 + vector2->x2) * 0.5;
+    mean->x1 = (vector1->x1 + vector2->x1) * 0.5;
+    mean->x2 = (vector1->x2 + vector2->x2) * 0.5;
 }
 
 // ================== Average3 ================== //
 
-inline void bgc_vector2_mean_of_three_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const BgcVector2FP32* vector3, BgcVector2FP32* result)
+inline void bgc_vector2_mean_of_three_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const BgcVector2FP32* vector3, BgcVector2FP32* mean)
 {
-    result->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * BGC_ONE_THIRD_FP32;
-    result->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * BGC_ONE_THIRD_FP32;
+    mean->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * BGC_ONE_THIRD_FP32;
+    mean->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * BGC_ONE_THIRD_FP32;
 }
 
-inline void bgc_vector2_mean_of_three_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const BgcVector2FP64* vector3, BgcVector2FP64* result)
+inline void bgc_vector2_mean_of_three_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const BgcVector2FP64* vector3, BgcVector2FP64* mean)
 {
-    result->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * BGC_ONE_THIRD_FP64;
-    result->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * BGC_ONE_THIRD_FP64;
+    mean->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * BGC_ONE_THIRD_FP64;
+    mean->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * BGC_ONE_THIRD_FP64;
 }
 
 // =============== Scalar Product =============== //
@@ -310,56 +410,6 @@ inline void bgc_vector2_complex_product_fp64(const BgcVector2FP64* vector1, cons
     result->x2 = x2;
 }
 
-// =============== Normalization ================ //
-
-inline int bgc_vector2_normalize_fp32(BgcVector2FP32* vector)
-{
-    const float square_modulus = bgc_vector2_get_square_modulus_fp32(vector);
-
-    if (bgc_is_sqare_value_unit_fp32(square_modulus)) {
-        return 1;
-    }
-
-    if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
-        bgc_vector2_reset_fp32(vector);
-        return 0;
-    }
-
-    bgc_vector2_multiply_fp32(vector, sqrtf(1.0f / square_modulus), vector);
-    return 1;
-}
-
-inline int bgc_vector2_normalize_fp64(BgcVector2FP64* vector)
-{
-    const double square_modulus = bgc_vector2_get_square_modulus_fp64(vector);
-
-    if (bgc_is_sqare_value_unit_fp64(square_modulus)) {
-        return 1;
-    }
-
-    if (square_modulus <= BGC_SQUARE_EPSYLON_FP64) {
-        bgc_vector2_reset_fp64(vector);
-        return 0;
-    }
-
-    bgc_vector2_multiply_fp64(vector, sqrt(1.0 / square_modulus), vector);
-    return 1;
-}
-
-// =============== Get Normalized =============== //
-
-inline int bgc_vector2_set_normalized_fp32(const BgcVector2FP32* vector, BgcVector2FP32* result)
-{
-    bgc_vector2_copy_fp32(vector, result);
-    return bgc_vector2_normalize_fp32(result);
-}
-
-inline int bgc_vector2_set_normalized_fp64(const BgcVector2FP64* vector, BgcVector2FP64* result)
-{
-    bgc_vector2_copy_fp64(vector, result);
-    return bgc_vector2_normalize_fp64(result);
-}
-
 // =================== Angle ==================== //
 
 float bgc_vector2_get_angle_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const BgcAngleUnitEnum unit);
diff --git a/basic-geometry/vector3.c b/basic-geometry/vector3.c
index 3abd179..ebcc698 100644
--- a/basic-geometry/vector3.c
+++ b/basic-geometry/vector3.c
@@ -5,6 +5,18 @@ extern inline void bgc_vector3_reset_fp64(BgcVector3FP64* vector);
 
 extern inline void bgc_vector3_set_values_fp32(const float x1, const float x2, const float x3, BgcVector3FP32* to);
 extern inline void bgc_vector3_set_values_fp64(const double x1, const double x2, const double x3, BgcVector3FP64* to);
+
+extern inline float bgc_vector3_get_square_modulus_fp32(const BgcVector3FP32* vector);
+extern inline double bgc_vector3_get_square_modulus_fp64(const BgcVector3FP64* vector);
+
+extern inline float bgc_vector3_get_modulus_fp32(const BgcVector3FP32* vector);
+extern inline double bgc_vector3_get_modulus_fp64(const BgcVector3FP64* vector);
+
+extern inline int bgc_vector3_is_zero_fp32(const BgcVector3FP32* vector);
+extern inline int bgc_vector3_is_zero_fp64(const BgcVector3FP64* vector);
+
+extern inline int bgc_vector3_is_unit_fp32(const BgcVector3FP32* vector);
+extern inline int bgc_vector3_is_unit_fp64(const BgcVector3FP64* vector);
 
 extern inline void bgc_vector3_copy_fp32(const BgcVector3FP32* from, BgcVector3FP32* to);
 extern inline void bgc_vector3_copy_fp64(const BgcVector3FP64* from, BgcVector3FP64* to);
@@ -15,36 +27,30 @@ extern inline void bgc_vector3_convert_fp32_to_fp64(const BgcVector3FP32* from,
 extern inline void bgc_vector3_swap_fp32(BgcVector3FP32* vector1, BgcVector3FP32* vector2);
 extern inline void bgc_vector3_swap_fp64(BgcVector3FP64* vector1, BgcVector3FP64* vector2);
 
-extern inline void bgc_vector3_invert_fp32(BgcVector3FP32* vector);
-extern inline void bgc_vector3_invert_fp64(BgcVector3FP64* vector);
-
-extern inline void bgc_vector3_set_inverted_fp32(const BgcVector3FP32* vector, BgcVector3FP32* result);
-extern inline void bgc_vector3_set_inverted_fp64(const BgcVector3FP64* vector, BgcVector3FP64* result);
-
-extern inline void bgc_vector3_set_inverted_fp32_to_fp64(const BgcVector3FP32* vector, BgcVector3FP64* result);
-extern inline void bgc_vector3_set_inverted_fp64_to_fp32(const BgcVector3FP64* vector, BgcVector3FP32* result);
-
-extern inline float bgc_vector3_get_square_modulus_fp32(const BgcVector3FP32* vector);
-extern inline double bgc_vector3_get_square_modulus_fp64(const BgcVector3FP64* vector);
-
-extern inline float bgc_vector3_get_modulus_fp32(const BgcVector3FP32* vector);
-extern inline double bgc_vector3_get_modulus_fp64(const BgcVector3FP64* vector);
-
-extern inline int bgc_vector3_is_zero_fp32(const BgcVector3FP32* vector);
-extern inline int bgc_vector3_is_zero_fp64(const BgcVector3FP64* vector);
-
-extern inline int bgc_vector3_is_unit_fp32(const BgcVector3FP32* vector);
-extern inline int bgc_vector3_is_unit_fp64(const BgcVector3FP64* vector);
-
+extern inline void bgc_vector3_reverse_fp32(BgcVector3FP32* vector);
+extern inline void bgc_vector3_reverse_fp64(BgcVector3FP64* vector);
+
+extern inline int bgc_vector3_normalize_fp32(BgcVector3FP32* vector);
+extern inline int bgc_vector3_normalize_fp64(BgcVector3FP64* vector);
+
+extern inline void bgc_vector3_make_reverse_fp32(const BgcVector3FP32* vector, BgcVector3FP32* reverse);
+extern inline void bgc_vector3_make_reverse_fp64(const BgcVector3FP64* vector, BgcVector3FP64* reverse);
+
+extern inline int bgc_vector3_make_normalized_fp32(const BgcVector3FP32* vector, BgcVector3FP32* normalized);
+extern inline int bgc_vector3_make_normalized_fp64(const BgcVector3FP64* vector, BgcVector3FP64* normalized);
+
 extern inline void bgc_vector3_add_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, BgcVector3FP32* sum);
 extern inline void bgc_vector3_add_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, BgcVector3FP64* sum);
 
-extern inline void bgc_vector3_add_scaled_fp32(const BgcVector3FP32* basic_vector, const BgcVector3FP32* scalable_vector, const float scale, BgcVector3FP32* result);
-extern inline void bgc_vector3_add_scaled_fp64(const BgcVector3FP64* basic_vector, const BgcVector3FP64* scalable_vector, const double scale, BgcVector3FP64* result);
+extern inline void bgc_vector3_add_scaled_fp32(const BgcVector3FP32* basic_vector, const BgcVector3FP32* scalable_vector, const float scale, BgcVector3FP32* sum);
+extern inline void bgc_vector3_add_scaled_fp64(const BgcVector3FP64* basic_vector, const BgcVector3FP64* scalable_vector, const double scale, BgcVector3FP64* sum);
 
 extern inline void bgc_vector3_subtract_fp32(const BgcVector3FP32* minuend, const BgcVector3FP32* subtrahend, BgcVector3FP32* difference);
 extern inline void bgc_vector3_subtract_fp64(const BgcVector3FP64* minuend, const BgcVector3FP64* subtrahend, BgcVector3FP64* difference);
 
+extern inline void bgc_vector3_subtract_scaled_fp32(const BgcVector3FP32* basic_vector, const BgcVector3FP32* scalable_vector, const float scale, BgcVector3FP32* difference);
+extern inline void bgc_vector3_subtract_scaled_fp64(const BgcVector3FP64* basic_vector, const BgcVector3FP64* scalable_vector, const double scale, BgcVector3FP64* difference);
+
 extern inline void bgc_vector3_multiply_fp32(const BgcVector3FP32* multiplicand, const float multiplier, BgcVector3FP32* product);
 extern inline void bgc_vector3_multiply_fp64(const BgcVector3FP64* multiplicand, const double multiplier, BgcVector3FP64* product);
 
@@ -69,12 +75,6 @@ extern inline void bgc_vector3_cross_product_fp64(const BgcVector3FP64* vector1,
 extern inline void bgc_vector3_double_cross_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcVector3FP32* vector3, BgcVector3FP32* result);
 extern inline void bgc_vector3_double_cross_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcVector3FP64* vector3, BgcVector3FP64* result);
 
-extern inline int bgc_vector3_normalize_fp32(BgcVector3FP32* vector);
-extern inline int bgc_vector3_normalize_fp64(BgcVector3FP64* vector);
-
-extern inline int bgc_vector3_set_normalized_fp32(const BgcVector3FP32* vector, BgcVector3FP32* result);
-extern inline int bgc_vector3_set_normalized_fp64(const BgcVector3FP64* vector, BgcVector3FP64* result);
-
 extern inline float bgc_vector3_get_square_distance_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2);
 extern inline double bgc_vector3_get_square_distance_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2);
 
@@ -91,10 +91,6 @@ extern inline int bgc_vector3_are_close_fp64(const BgcVector3FP64* vector1, cons
 
 float bgc_vector3_get_angle_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcAngleUnitEnum unit)
 {
-    if (vector1 == 0 || vector2 == 0) {
-        return 0.0f;
-    }
-
     const float square_modulus1 = bgc_vector3_get_square_modulus_fp32(vector1);
 
     if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP32) {
@@ -122,10 +118,6 @@ float bgc_vector3_get_angle_fp32(const BgcVector3FP32* vector1, const BgcVector3
 
 double bgc_vector3_get_angle_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcAngleUnitEnum unit)
 {
-    if (vector1 == 0 || vector2 == 0) {
-        return 0.0;
-    }
-
     const double square_modulus1 = bgc_vector3_get_square_modulus_fp64(vector1);
 
     if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP64) {
diff --git a/basic-geometry/vector3.h b/basic-geometry/vector3.h
index 1e1f8bc..8dfeda1 100644
--- a/basic-geometry/vector3.h
+++ b/basic-geometry/vector3.h
@@ -50,6 +50,50 @@ inline void bgc_vector3_set_values_fp64(const double x1, const double x2, const
     to->x3 = x3;
 }
 
+// ================== Modulus =================== //
+
+inline float bgc_vector3_get_square_modulus_fp32(const BgcVector3FP32* vector)
+{
+    return vector->x1 * vector->x1 + vector->x2 * vector->x2 + vector->x3 * vector->x3;
+}
+
+inline double bgc_vector3_get_square_modulus_fp64(const BgcVector3FP64* vector)
+{
+    return vector->x1 * vector->x1 + vector->x2 * vector->x2 + vector->x3 * vector->x3;
+}
+
+inline float bgc_vector3_get_modulus_fp32(const BgcVector3FP32* vector)
+{
+    return sqrtf(bgc_vector3_get_square_modulus_fp32(vector));
+}
+
+inline double bgc_vector3_get_modulus_fp64(const BgcVector3FP64* vector)
+{
+    return sqrt(bgc_vector3_get_square_modulus_fp64(vector));
+}
+
+// ================= Comparison ================= //
+
+inline int bgc_vector3_is_zero_fp32(const BgcVector3FP32* vector)
+{
+    return bgc_vector3_get_square_modulus_fp32(vector) <= BGC_SQUARE_EPSYLON_FP32;
+}
+
+inline int bgc_vector3_is_zero_fp64(const BgcVector3FP64* vector)
+{
+    return bgc_vector3_get_square_modulus_fp64(vector) <= BGC_SQUARE_EPSYLON_FP64;
+}
+
+inline int bgc_vector3_is_unit_fp32(const BgcVector3FP32* vector)
+{
+    return bgc_is_sqare_unit_fp32(bgc_vector3_get_square_modulus_fp32(vector));
+}
+
+inline int bgc_vector3_is_unit_fp64(const BgcVector3FP64* vector)
+{
+    return bgc_is_sqare_unit_fp64(bgc_vector3_get_square_modulus_fp64(vector));
+}
+
 // ==================== Copy ==================== //
 
 inline void bgc_vector3_copy_fp32(const BgcVector3FP32* from, BgcVector3FP32* to)
@@ -66,22 +110,6 @@ inline void bgc_vector3_copy_fp64(const BgcVector3FP64* from, BgcVector3FP64* to
     to->x3 = from->x3;
 }
 
-// ================== Convert =================== //
-
-inline void bgc_vector3_convert_fp64_to_fp32(const BgcVector3FP64* from, BgcVector3FP32* to)
-{
-    to->x1 = (float) from->x1;
-    to->x2 = (float) from->x2;
-    to->x3 = (float) from->x3;
-}
-
-inline void bgc_vector3_convert_fp32_to_fp64(const BgcVector3FP32* from, BgcVector3FP64* to)
-{
-    to->x1 = from->x1;
-    to->x2 = from->x2;
-    to->x3 = from->x3;
-}
-
 // ==================== Swap ==================== //
 
 inline void bgc_vector3_swap_fp32(BgcVector3FP32* vector1, BgcVector3FP32* vector2)
@@ -114,96 +142,116 @@ inline void bgc_vector3_swap_fp64(BgcVector3FP64* vector1, BgcVector3FP64* vecto
     vector1->x3 = x3;
 }
 
-// ==================== Invert ================== //
+// ================== Convert =================== //
 
-inline void bgc_vector3_invert_fp32(BgcVector3FP32* vector)
+inline void bgc_vector3_convert_fp64_to_fp32(const BgcVector3FP64* from, BgcVector3FP32* to)
+{
+    to->x1 = (float) from->x1;
+    to->x2 = (float) from->x2;
+    to->x3 = (float) from->x3;
+}
+
+inline void bgc_vector3_convert_fp32_to_fp64(const BgcVector3FP32* from, BgcVector3FP64* to)
+{
+    to->x1 = from->x1;
+    to->x2 = from->x2;
+    to->x3 = from->x3;
+}
+
+// ================== Reverse =================== //
+
+inline void bgc_vector3_reverse_fp32(BgcVector3FP32* vector)
 {
     vector->x1 = -vector->x1;
     vector->x2 = -vector->x2;
     vector->x3 = -vector->x3;
 }
 
-inline void bgc_vector3_invert_fp64(BgcVector3FP64* vector)
+inline void bgc_vector3_reverse_fp64(BgcVector3FP64* vector)
 {
     vector->x1 = -vector->x1;
     vector->x2 = -vector->x2;
     vector->x3 = -vector->x3;
 }
 
-// ================ Make Inverted =============== //
+// ================= Normalize ================== //
 
-inline void bgc_vector3_set_inverted_fp32(const BgcVector3FP32* vector, BgcVector3FP32* result)
+inline int bgc_vector3_normalize_fp32(BgcVector3FP32* vector)
 {
-    result->x1 = -vector->x1;
-    result->x2 = -vector->x2;
-    result->x3 = -vector->x3;
+    const float square_modulus = bgc_vector3_get_square_modulus_fp32(vector);
+
+    if (bgc_is_sqare_unit_fp32(square_modulus)) {
+        return 1;
+    }
+
+    if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
+        vector->x1 = 0.0f;
+        vector->x2 = 0.0f;
+        vector->x3 = 0.0f;
+        return 0;
+    }
+
+    const float multiplicand = sqrtf(1.0f / square_modulus);
+
+    vector->x1 *= multiplicand;
+    vector->x2 *= multiplicand;
+    vector->x3 *= multiplicand;
+
+    return 1;
 }
 
-inline void bgc_vector3_set_inverted_fp64(const BgcVector3FP64* vector, BgcVector3FP64* result)
+inline int bgc_vector3_normalize_fp64(BgcVector3FP64* vector)
 {
-    result->x1 = -vector->x1;
-    result->x2 = -vector->x2;
-    result->x3 = -vector->x3;
+    const double square_modulus = bgc_vector3_get_square_modulus_fp64(vector);
+
+    if (bgc_is_sqare_unit_fp64(square_modulus)) {
+        return 1;
+    }
+
+    if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
+        vector->x1 = 0.0;
+        vector->x2 = 0.0;
+        vector->x3 = 0.0;
+        return 0;
+    }
+
+    const double multiplicand = sqrt(1.0 / square_modulus);
+
+    vector->x1 *= multiplicand;
+    vector->x2 *= multiplicand;
+    vector->x3 *= multiplicand;
+
+    return 1;
 }
 
-// ============== Make Inverted Twin ============ //
+// ================ Make Reverse ================ //
 
-inline void bgc_vector3_set_inverted_fp32_to_fp64(const BgcVector3FP32* vector, BgcVector3FP64* result)
+inline void bgc_vector3_make_reverse_fp32(const BgcVector3FP32* vector, BgcVector3FP32* reverse)
 {
-    result->x1 = -vector->x1;
-    result->x2 = -vector->x2;
-    result->x3 = -vector->x3;
+    reverse->x1 = -vector->x1;
+    reverse->x2 = -vector->x2;
+    reverse->x3 = -vector->x3;
 }
 
-inline void bgc_vector3_set_inverted_fp64_to_fp32(const BgcVector3FP64* vector, BgcVector3FP32* result)
+inline void bgc_vector3_make_reverse_fp64(const BgcVector3FP64* vector, BgcVector3FP64* reverse)
 {
-    result->x1 = (float) -vector->x1;
-    result->x2 = (float) -vector->x2;
-    result->x3 = (float) -vector->x3;
+    reverse->x1 = -vector->x1;
+    reverse->x2 = -vector->x2;
+    reverse->x3 = -vector->x3;
 }
 
-// =================== Module =================== //
+// ============== Make Normalized =============== //
 
-inline float bgc_vector3_get_square_modulus_fp32(const BgcVector3FP32* vector)
+inline int bgc_vector3_make_normalized_fp32(const BgcVector3FP32* vector, BgcVector3FP32* normalized)
 {
-    return vector->x1 * vector->x1 + vector->x2 * vector->x2 + vector->x3 * vector->x3;
+    bgc_vector3_copy_fp32(vector, normalized);
+    return bgc_vector3_normalize_fp32(normalized);
 }
 
-inline double bgc_vector3_get_square_modulus_fp64(const BgcVector3FP64* vector)
+inline int bgc_vector3_make_normalized_fp64(const BgcVector3FP64* vector, BgcVector3FP64* normalized)
 {
-    return vector->x1 * vector->x1 + vector->x2 * vector->x2 + vector->x3 * vector->x3;
-}
-
-inline float bgc_vector3_get_modulus_fp32(const BgcVector3FP32* vector)
-{
-    return sqrtf(bgc_vector3_get_square_modulus_fp32(vector));
-}
-
-inline double bgc_vector3_get_modulus_fp64(const BgcVector3FP64* vector)
-{
-    return sqrt(bgc_vector3_get_square_modulus_fp64(vector));
-}
-
-// ================= Comparison ================= //
-
-inline int bgc_vector3_is_zero_fp32(const BgcVector3FP32* vector)
-{
-    return bgc_vector3_get_square_modulus_fp32(vector) <= BGC_SQUARE_EPSYLON_FP32;
-}
-
-inline int bgc_vector3_is_zero_fp64(const BgcVector3FP64* vector)
-{
-    return bgc_vector3_get_square_modulus_fp64(vector) <= BGC_SQUARE_EPSYLON_FP64;
-}
-
-inline int bgc_vector3_is_unit_fp32(const BgcVector3FP32* vector)
-{
-    return bgc_is_sqare_value_unit_fp32(bgc_vector3_get_square_modulus_fp32(vector));
-}
-
-inline int bgc_vector3_is_unit_fp64(const BgcVector3FP64* vector)
-{
-    return bgc_is_sqare_value_unit_fp64(bgc_vector3_get_square_modulus_fp64(vector));
+    bgc_vector3_copy_fp64(vector, normalized);
+    return bgc_vector3_normalize_fp64(normalized);
 }
 
 // ==================== Add ===================== //
@@ -238,7 +286,7 @@ inline void bgc_vector3_add_scaled_fp64(const BgcVector3FP64* basic_vector, cons
     result->x3 = basic_vector->x3 + scalable_vector->x3 * scale;
 }
 
-// ================ Subtraction ================= //
+// ================== Subtract ================== //
 
 inline void bgc_vector3_subtract_fp32(const BgcVector3FP32* minuend, const BgcVector3FP32* subtrahend, BgcVector3FP32* difference)
 {
@@ -254,7 +302,23 @@ inline void bgc_vector3_subtract_fp64(const BgcVector3FP64* minuend, const BgcVe
     difference->x3 = minuend->x3 - subtrahend->x3;
 }
 
-// =============== Multiplication =============== //
+// ============== Subtract scaled =============== //
+
+inline void bgc_vector3_subtract_scaled_fp32(const BgcVector3FP32* basic_vector, const BgcVector3FP32* scalable_vector, const float scale, BgcVector3FP32* result)
+{
+    result->x1 = basic_vector->x1 - scalable_vector->x1 * scale;
+    result->x2 = basic_vector->x2 - scalable_vector->x2 * scale;
+    result->x3 = basic_vector->x3 - scalable_vector->x3 * scale;
+}
+
+inline void bgc_vector3_subtract_scaled_fp64(const BgcVector3FP64* basic_vector, const BgcVector3FP64* scalable_vector, const double scale, BgcVector3FP64* result)
+{
+    result->x1 = basic_vector->x1 - scalable_vector->x1 * scale;
+    result->x2 = basic_vector->x2 - scalable_vector->x2 * scale;
+    result->x3 = basic_vector->x3 - scalable_vector->x3 * scale;
+}
+
+// ================== Multiply ================== //
 
 inline void bgc_vector3_multiply_fp32(const BgcVector3FP32* multiplicand, const float multiplier, BgcVector3FP32* product)
 {
@@ -270,7 +334,7 @@ inline void bgc_vector3_multiply_fp64(const BgcVector3FP64* multiplicand, const
     product->x3 = multiplicand->x3 * multiplier;
 }
 
-// ================== Division ================== //
+// =================== Divide =================== //
 
 inline void bgc_vector3_divide_fp32(const BgcVector3FP32* dividend, const float divisor, BgcVector3FP32* quotient)
 {
@@ -388,56 +452,6 @@ inline void bgc_vector3_double_cross_fp64(const BgcVector3FP64* vector1, const B
     result->x3 = vector2->x3 * ac - vector3->x3 * ab;
 }
 
-// =============== Normalization ================ //
-
-inline int bgc_vector3_normalize_fp32(BgcVector3FP32* vector)
-{
-    const float square_modulus = bgc_vector3_get_square_modulus_fp32(vector);
-
-    if (bgc_is_sqare_value_unit_fp32(square_modulus)) {
-        return 1;
-    }
-
-    if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
-        bgc_vector3_reset_fp32(vector);
-        return 0;
-    }
-
-    bgc_vector3_multiply_fp32(vector, sqrtf(1.0f / square_modulus), vector);
-    return 1;
-}
-
-inline int bgc_vector3_normalize_fp64(BgcVector3FP64* vector)
-{
-    const double square_modulus = bgc_vector3_get_square_modulus_fp64(vector);
-
-    if (bgc_is_sqare_value_unit_fp64(square_modulus)) {
-        return 1;
-    }
-
-    if (square_modulus <= BGC_SQUARE_EPSYLON_FP64) {
-        bgc_vector3_reset_fp64(vector);
-        return 0;
-    }
-
-    bgc_vector3_multiply_fp64(vector, sqrt(1.0 / square_modulus), vector);
-    return 1;
-}
-
-// =============== Set Normalized =============== //
-
-inline int bgc_vector3_set_normalized_fp32(const BgcVector3FP32* vector, BgcVector3FP32* result)
-{
-    bgc_vector3_copy_fp32(vector, result);
-    return bgc_vector3_normalize_fp32(result);
-}
-
-inline int bgc_vector3_set_normalized_fp64(const BgcVector3FP64* vector, BgcVector3FP64* result)
-{
-    bgc_vector3_copy_fp64(vector, result);
-    return bgc_vector3_normalize_fp64(result);
-}
-
 // =================== Angle ==================== //
 
 float bgc_vector3_get_angle_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcAngleUnitEnum unit);
diff --git a/basic-geometry/versor.c b/basic-geometry/versor.c
index 8be8990..578bcbc 100644
--- a/basic-geometry/versor.c
+++ b/basic-geometry/versor.c
@@ -13,18 +13,15 @@ extern inline void bgc_versor_reset_fp64(BgcVersorFP64* versor);
 extern inline void bgc_versor_set_values_fp32(const float s0, const float x1, const float x2, const float x3, BgcVersorFP32* versor);
 extern inline void bgc_versor_set_values_fp64(const double s0, const double x1, const double x2, const double x3, BgcVersorFP64* versor);
 
+extern inline void bgc_versor_set_rotation_fp32(const BgcRotation3FP32* rotation, BgcVersorFP32* result);
+extern inline void bgc_versor_set_rotation_fp64(const BgcRotation3FP64* rotation, BgcVersorFP64* result);
+
 extern inline void bgc_versor_copy_fp32(const BgcVersorFP32* from, BgcVersorFP32* to);
 extern inline void bgc_versor_copy_fp64(const BgcVersorFP64* from, BgcVersorFP64* to);
 
 extern inline void bgc_versor_swap_fp32(BgcVersorFP32* versor1, BgcVersorFP32* versor2);
 extern inline void bgc_versor_swap_fp64(BgcVersorFP64* versor1, BgcVersorFP64* versor2);
 
-extern inline void bgc_versor_set_turn_fp32(const BgcVector3FP32* axis, const float angle, const BgcAngleUnitEnum unit, BgcVersorFP32* result);
-extern inline void bgc_versor_set_turn_fp64(const BgcVector3FP32* axis, const double angle, const BgcAngleUnitEnum unit, BgcVersorFP64* result);
-
-extern inline void bgc_versor_set_rotation_fp32(const BgcRotation3FP32* rotation, BgcVersorFP32* result);
-extern inline void bgc_versor_set_rotation_fp64(const BgcRotation3FP64* rotation, BgcVersorFP64* result);
-
 extern inline int bgc_versor_is_identity_fp32(const BgcVersorFP32* versor);
 extern inline int bgc_versor_is_identity_fp64(const BgcVersorFP64* versor);
 
@@ -34,30 +31,30 @@ extern inline void bgc_versor_convert_fp32_to_fp64(const BgcVersorFP32* versor,
 extern inline void bgc_versor_shorten_fp32(BgcVersorFP32* versor);
 extern inline void bgc_versor_shorten_fp64(BgcVersorFP64* versor);
 
-extern inline void bgc_versor_set_shortened_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened);
-extern inline void bgc_versor_set_shortened_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened);
-
 extern inline void bgc_versor_invert_fp32(BgcVersorFP32* versor);
 extern inline void bgc_versor_invert_fp64(BgcVersorFP64* versor);
 
-extern inline void bgc_versor_set_inverted_fp32(const BgcVersorFP32* versor, BgcVersorFP32* to);
-extern inline void bgc_versor_set_inverted_fp64(const BgcVersorFP64* versor, BgcVersorFP64* to);
-
-extern inline void bgc_versor_set_inverted_fp64_to_fp32(const BgcVersorFP64* versor, BgcVersorFP32* to);
-extern inline void bgc_versor_set_inverted_fp32_to_fp64(const BgcVersorFP32* versor, BgcVersorFP64* to);
-
 extern inline void bgc_versor_combine_fp32(const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result);
 extern inline void bgc_versor_combine_fp64(const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result);
 
 extern inline void bgc_versor_combine3_fp32(const BgcVersorFP32* third, const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result);
 extern inline void bgc_versor_combine3_fp64(const BgcVersorFP64* third, const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result);
 
+extern inline void bgc_versor_make_shortened_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened);
+extern inline void bgc_versor_make_shortened_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened);
+
+extern inline void bgc_versor_make_inverted_fp32(const BgcVersorFP32* versor, BgcVersorFP32* to);
+extern inline void bgc_versor_make_inverted_fp64(const BgcVersorFP64* versor, BgcVersorFP64* to);
+
 extern inline void bgc_versor_make_rotation_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix);
 extern inline void bgc_versor_make_rotation_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix);
 
 extern inline void bgc_versor_make_reverse_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix);
 extern inline void bgc_versor_make_reverse_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix);
 
+extern inline void bgc_versor_make_both_matrixes_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse);
+extern inline void bgc_versor_make_both_matrixes_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse);
+
 extern inline void bgc_versor_turn_vector_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result);
 extern inline void bgc_versor_turn_vector_fp64(const BgcVersorFP64* versor, const BgcVector3FP64* vector, BgcVector3FP64* result);
 
@@ -67,7 +64,7 @@ extern inline void bgc_versor_turn_vector_back_fp64(const BgcVersorFP64* versor,
 extern inline int bgc_versor_are_close_fp32(const BgcVersorFP32* versor1, const BgcVersorFP32* versor2);
 extern inline int bgc_versor_are_close_fp64(const BgcVersorFP64* versor1, const BgcVersorFP64* versor2);
 
-// =============== Normalization ================ //
+// ================= Normalize ================== //
 
 void _bgc_versor_normalize_fp32(const float square_modulus, _BgcDarkTwinVersorFP32* twin)
 {
@@ -110,9 +107,9 @@ void _bgc_versor_normalize_fp64(const double square_modulus, _BgcDarkTwinVersorF
     twin->x3 *= multiplier;
 }
 
-// =============== Set Crude Turn =============== //
+// ================== Set Turn ================== //
 
-void bgc_versor_set_crude_turn_fp32(const float x1, const float x2, const float x3, const float angle, const BgcAngleUnitEnum unit, BgcVersorFP32* result)
+void bgc_versor_set_turn_fp32(const float x1, const float x2, const float x3, const float angle, const BgcAngleUnitEnum unit, BgcVersorFP32* result)
 {
     const float square_vector = x1 * x1 + x2 * x2 + x3 * x3;
 
@@ -135,7 +132,7 @@ void bgc_versor_set_crude_turn_fp32(const float x1, const float x2, const float
     bgc_versor_set_values_fp32(cosf(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier, result);
 }
 
-void bgc_versor_set_crude_turn_fp64(const double x1, const double x2, const double x3, const double angle, const BgcAngleUnitEnum unit, BgcVersorFP64* result)
+void bgc_versor_set_turn_fp64(const double x1, const double x2, const double x3, const double angle, const BgcAngleUnitEnum unit, BgcVersorFP64* result)
 {
     const double square_vector = x1 * x1 + x2 * x2 + x3 * x3;
 
@@ -158,22 +155,24 @@ void bgc_versor_set_crude_turn_fp64(const double x1, const double x2, const doub
     bgc_versor_set_values_fp64(cos(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier, result);
 }
 
-// ================= Rotation3 ================== //
+// =============== Make Rotation3 =============== //
 
-void bgc_versor_get_rotation_fp32(const BgcVersorFP32* versor, BgcRotation3FP32* result)
+void bgc_versor_make_rotation_fp32(const BgcVersorFP32* versor, BgcRotation3FP32* result)
 {
-    if (versor == 0 || result == 0) {
-        return;
-    }
-
     if (versor->s0 <= -(1.0f - BGC_EPSYLON_FP32) || 1.0f - BGC_EPSYLON_FP32 <= versor->s0) {
         bgc_rotation3_reset_fp32(result);
         return;
     }
 
-    const float square_vector = versor->x1 * versor->x1 + versor->x2 * versor->x2 + versor->x3 * versor->x3;
+    const float s0s0 = versor->s0 * versor->s0;
+    const float x1x1 = versor->x1 * versor->x1;
+    const float x2x2 = versor->x2 * versor->x2;
+    const float x3x3 = versor->x3 * versor->x3;
 
-    result->radians = 2.0f * acosf(versor->s0 / sqrtf(versor->s0 * versor->s0 + square_vector));
+    const float square_module = (s0s0 + x1x1) + (x2x2 + x3x3);
+    const float square_vector = x1x1 + (x2x2 + x3x3);
+
+    result->radians = 2.0f * acosf(versor->s0 / sqrtf(square_module));
 
     const float multiplier = sqrtf(1.0f / square_vector);
 
@@ -182,20 +181,22 @@ void bgc_versor_get_rotation_fp32(const BgcVersorFP32* versor, BgcRotation3FP32*
     result->axis.x3 = versor->x3 * multiplier;
 }
 
-void bgc_versor_get_rotation_fp64(const BgcVersorFP64* versor, BgcRotation3FP64* result)
+void bgc_versor_make_rotation_fp64(const BgcVersorFP64* versor, BgcRotation3FP64* result)
 {
-    if (versor == 0 || result == 0) {
-        return;
-    }
-
     if (versor->s0 <= -(1.0 - BGC_EPSYLON_FP64) || 1.0 - BGC_EPSYLON_FP64 <= versor->s0) {
         bgc_rotation3_reset_fp64(result);
         return;
     }
 
-    const double square_vector = versor->x1 * versor->x1 + versor->x2 * versor->x2 + versor->x3 * versor->x3;
+    const double s0s0 = versor->s0 * versor->s0;
+    const double x1x1 = versor->x1 * versor->x1;
+    const double x2x2 = versor->x2 * versor->x2;
+    const double x3x3 = versor->x3 * versor->x3;
 
-    result->radians = 2.0 * acos(versor->s0 / sqrt(versor->s0 * versor->s0 + square_vector));
+    const double square_module = (s0s0 + x1x1) + (x2x2 + x3x3);
+    const double square_vector = x1x1 + (x2x2 + x3x3);
+
+    result->radians = 2.0 * acos(versor->s0 / sqrt(square_module));
 
     const double multiplier = sqrt(1.0 / square_vector);
 
diff --git a/basic-geometry/versor.h b/basic-geometry/versor.h
index 747feb9..ac68f3c 100644
--- a/basic-geometry/versor.h
+++ b/basic-geometry/versor.h
@@ -73,7 +73,7 @@ inline void bgc_versor_set_values_fp32(const float s0, const float x1, const flo
 
     const float square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
 
-    if (!bgc_is_sqare_value_unit_fp32(square_modulus)) {
+    if (!bgc_is_sqare_unit_fp32(square_modulus)) {
         _bgc_versor_normalize_fp32(square_modulus, twin);
     }
 }
@@ -89,11 +89,29 @@ inline void bgc_versor_set_values_fp64(const double s0, const double x1, const d
 
     const double square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
 
-    if (!bgc_is_sqare_value_unit_fp64(square_modulus)) {
+    if (!bgc_is_sqare_unit_fp64(square_modulus)) {
         _bgc_versor_normalize_fp64(square_modulus, twin);
     }
 }
 
+// ================== Set Turn ================== //
+
+void bgc_versor_set_turn_fp32(const float x1, const float x2, const float x3, const float angle, const BgcAngleUnitEnum unit, BgcVersorFP32* result);
+
+void bgc_versor_set_turn_fp64(const double x1, const double x2, const double x3, const double angle, const BgcAngleUnitEnum unit, BgcVersorFP64* result);
+
+// ================ Set Rotation ================ //
+
+inline void bgc_versor_set_rotation_fp32(const BgcRotation3FP32* rotation, BgcVersorFP32* result)
+{
+    bgc_versor_set_turn_fp32(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS, result);
+}
+
+inline void bgc_versor_set_rotation_fp64(const BgcRotation3FP64* rotation, BgcVersorFP64* result)
+{
+    bgc_versor_set_turn_fp64(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS, result);
+}
+
 // ==================== Copy ==================== //
 
 inline void bgc_versor_copy_fp32(const BgcVersorFP32* from, BgcVersorFP32* to)
@@ -162,36 +180,6 @@ inline void bgc_versor_swap_fp64(BgcVersorFP64* versor1, BgcVersorFP64* versor2)
     twin2->x3 = x3;
 }
 
-// =============== Set Crude Turn =============== //
-
-void bgc_versor_set_crude_turn_fp32(const float x1, const float x2, const float x3, const float angle, const BgcAngleUnitEnum unit, BgcVersorFP32* result);
-
-void bgc_versor_set_crude_turn_fp64(const double x1, const double x2, const double x3, const double angle, const BgcAngleUnitEnum unit, BgcVersorFP64* result);
-
-// ================== Set Turn ================== //
-
-inline void bgc_versor_set_turn_fp32(const BgcVector3FP32* axis, const float angle, const BgcAngleUnitEnum unit, BgcVersorFP32* result)
-{
-    bgc_versor_set_crude_turn_fp32(axis->x1, axis->x2, axis->x3, angle, unit, result);
-}
-
-inline void bgc_versor_set_turn_fp64(const BgcVector3FP32* axis, const double angle, const BgcAngleUnitEnum unit, BgcVersorFP64* result)
-{
-    bgc_versor_set_crude_turn_fp64(axis->x1, axis->x2, axis->x3, angle, unit, result);
-}
-
-// ================ Set Rotation ================ //
-
-inline void bgc_versor_set_rotation_fp32(const BgcRotation3FP32* rotation, BgcVersorFP32* result)
-{
-    bgc_versor_set_crude_turn_fp32(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS, result);
-}
-
-inline void bgc_versor_set_rotation_fp64(const BgcRotation3FP64* rotation, BgcVersorFP64* result)
-{
-    bgc_versor_set_crude_turn_fp64(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS, result);
-}
-
 // ================= Comparison ================= //
 
 inline int bgc_versor_is_identity_fp32(const BgcVersorFP32* versor)
@@ -204,7 +192,7 @@ inline int bgc_versor_is_identity_fp64(const BgcVersorFP64* versor)
     return 1.0 - BGC_EPSYLON_FP64 <= versor->s0 || versor->s0 <= -(1.0 - BGC_EPSYLON_FP64);
 }
 
-// ============= Copy to twin type ============== //
+// ================== Convert =================== //
 
 inline void bgc_versor_convert_fp64_to_fp32(const BgcVersorFP64* versor, BgcVersorFP32* result)
 {
@@ -256,45 +244,7 @@ inline void bgc_versor_shorten_fp64(BgcVersorFP64* versor)
     twin->x3 = -versor->x3;
 }
 
-// ================== Shorten =================== //
-
-inline void bgc_versor_set_shortened_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened)
-{
-    _BgcDarkTwinVersorFP32* twin = (_BgcDarkTwinVersorFP32*)shortened;
-
-    if (versor->s0 >= 0.0f) {
-        twin->x1 = versor->s0;
-        twin->x1 = versor->x1;
-        twin->x2 = versor->x2;
-        twin->x3 = versor->x3;
-        return;
-    }
-
-    twin->x1 = -versor->s0;
-    twin->x1 = -versor->x1;
-    twin->x2 = -versor->x2;
-    twin->x3 = -versor->x3;
-}
-
-inline void bgc_versor_set_shortened_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened)
-{
-    _BgcDarkTwinVersorFP64* twin = (_BgcDarkTwinVersorFP64*)shortened;
-
-    if (versor->s0 >= 0.0) {
-        twin->x1 = versor->s0;
-        twin->x1 = versor->x1;
-        twin->x2 = versor->x2;
-        twin->x3 = versor->x3;
-        return;
-    }
-
-    twin->x1 = -versor->s0;
-    twin->x1 = -versor->x1;
-    twin->x2 = -versor->x2;
-    twin->x3 = -versor->x3;
-}
-
-// ================= Inversion ================== //
+// =================== Invert =================== //
 
 inline void bgc_versor_invert_fp32(BgcVersorFP32* versor)
 {
@@ -312,50 +262,6 @@ inline void bgc_versor_invert_fp64(BgcVersorFP64* versor)
     twin->x3 = -versor->x3;
 }
 
-// ================ Set Inverted ================ //
-
-inline void bgc_versor_set_inverted_fp32(const BgcVersorFP32* versor, BgcVersorFP32* to)
-{
-    _BgcDarkTwinVersorFP32* twin = (_BgcDarkTwinVersorFP32*)to;
-    twin->s0 = versor->s0;
-    twin->x1 = -versor->x1;
-    twin->x2 = -versor->x2;
-    twin->x3 = -versor->x3;
-}
-
-inline void bgc_versor_set_inverted_fp64(const BgcVersorFP64* versor, BgcVersorFP64* to)
-{
-    _BgcDarkTwinVersorFP64* twin = (_BgcDarkTwinVersorFP64*)to;
-    twin->s0 = versor->s0;
-    twin->x1 = -versor->x1;
-    twin->x2 = -versor->x2;
-    twin->x3 = -versor->x3;
-}
-
-// ================ Set Inverted ================ //
-
-inline void bgc_versor_set_inverted_fp64_to_fp32(const BgcVersorFP64* versor, BgcVersorFP32* to)
-{
-    bgc_versor_set_values_fp32(
-        (float) versor->s0,
-        (float) -versor->x1,
-        (float) -versor->x2,
-        (float) -versor->x3,
-        to
-    );
-}
-
-inline void bgc_versor_set_inverted_fp32_to_fp64(const BgcVersorFP32* versor, BgcVersorFP64* to)
-{
-    bgc_versor_set_values_fp64(
-        versor->s0,
-        -versor->x1,
-        -versor->x2,
-        -versor->x3,
-        to
-    );
-}
-
 // ================ Combination ================= //
 
 inline void bgc_versor_combine_fp32(const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result)
@@ -414,11 +320,69 @@ inline void bgc_versor_combine3_fp64(const BgcVersorFP64* third, const BgcVersor
     );
 }
 
-// ================= Rotation3 ================== //
+// =============== Make Rotation3 =============== //
 
-void bgc_versor_get_rotation_fp32(const BgcVersorFP32* versor, BgcRotation3FP32* result);
+void bgc_versor_make_rotation_fp32(const BgcVersorFP32* versor, BgcRotation3FP32* result);
 
-void bgc_versor_get_rotation_fp64(const BgcVersorFP64* versor, BgcRotation3FP64* result);
+void bgc_versor_make_rotation_fp64(const BgcVersorFP64* versor, BgcRotation3FP64* result);
+
+// =============== Make Shortened =============== //
+
+inline void bgc_versor_make_shortened_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened)
+{
+    _BgcDarkTwinVersorFP32* twin = (_BgcDarkTwinVersorFP32*)shortened;
+
+    if (versor->s0 >= 0.0f) {
+        twin->x1 = versor->s0;
+        twin->x1 = versor->x1;
+        twin->x2 = versor->x2;
+        twin->x3 = versor->x3;
+        return;
+    }
+
+    twin->x1 = -versor->s0;
+    twin->x1 = -versor->x1;
+    twin->x2 = -versor->x2;
+    twin->x3 = -versor->x3;
+}
+
+inline void bgc_versor_make_shortened_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened)
+{
+    _BgcDarkTwinVersorFP64* twin = (_BgcDarkTwinVersorFP64*)shortened;
+
+    if (versor->s0 >= 0.0) {
+        twin->x1 = versor->s0;
+        twin->x1 = versor->x1;
+        twin->x2 = versor->x2;
+        twin->x3 = versor->x3;
+        return;
+    }
+
+    twin->x1 = -versor->s0;
+    twin->x1 = -versor->x1;
+    twin->x2 = -versor->x2;
+    twin->x3 = -versor->x3;
+}
+
+// =============== Make Inverted ================ //
+
+inline void bgc_versor_make_inverted_fp32(const BgcVersorFP32* versor, BgcVersorFP32* to)
+{
+    _BgcDarkTwinVersorFP32* twin = (_BgcDarkTwinVersorFP32*)to;
+    twin->s0 = versor->s0;
+    twin->x1 = -versor->x1;
+    twin->x2 = -versor->x2;
+    twin->x3 = -versor->x3;
+}
+
+inline void bgc_versor_make_inverted_fp64(const BgcVersorFP64* versor, BgcVersorFP64* to)
+{
+    _BgcDarkTwinVersorFP64* twin = (_BgcDarkTwinVersorFP64*)to;
+    twin->s0 = versor->s0;
+    twin->x1 = -versor->x1;
+    twin->x2 = -versor->x2;
+    twin->x3 = -versor->x3;
+}
 
 // =========== Make Rotation Matrix3x3 ========== //
 
@@ -536,6 +500,20 @@ inline void bgc_versor_make_reverse_matrix_fp64(const BgcVersorFP64* versor, Bgc
     matrix->r1c3 = x1x3 - s0x2;
 }
 
+// ============= Make Both Matrixes ============= //
+
+inline void bgc_versor_make_both_matrixes_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse)
+{
+    bgc_versor_make_reverse_matrix_fp32(versor, reverse);
+    bgc_matrix3x3_make_transposed_fp32(reverse, rotation);
+}
+
+inline void bgc_versor_make_both_matrixes_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse)
+{
+    bgc_versor_make_reverse_matrix_fp64(versor, reverse);
+    bgc_matrix3x3_make_transposed_fp64(reverse, rotation);
+}
+
 // ================ Turn Vector ================= //
 
 inline void bgc_versor_turn_vector_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result)