Развитие дуальный чисел, векторов и кватернионов, а также гомогенных векторов и матриц

basic-geometry/basic-geometry.cbp

@@ -64,6 +64,22 @@
 			<Option compilerVar="CC" />
 		</Unit>
 		<Unit filename="cotes-number.h" />
+		<Unit filename="dual-number.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="dual-number.h" />
+		<Unit filename="dual-quaternion.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="dual-quaternion.h" />
+		<Unit filename="dual-vector3.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="dual-vector3.h" />
+		<Unit filename="hg-matrix3x3.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="hg-matrix3x3.h" />
 		<Unit filename="hg-vector3.c">
 			<Option compilerVar="CC" />
 		</Unit>

basic-geometry/cotes-number.h

@@ -250,36 +250,36 @@ inline void bgc_fp64_cotes_number_exclude(BGC_FP64_CotesNumber* difference, cons
 
 inline void bgc_fp32_cotes_number_get_rotation_matrix(BGC_FP32_Matrix2x2* matrix, const BGC_FP32_CotesNumber* number)
 {
-    matrix->row1_col1 = number->_cos;
-    matrix->row1_col2 = -number->_sin;
-    matrix->row2_col1 = number->_sin;
-    matrix->row2_col2 = number->_cos;
+    matrix->r1c1 = number->_cos;
+    matrix->r1c2 = -number->_sin;
+    matrix->r2c1 = number->_sin;
+    matrix->r2c2 = number->_cos;
 }
 
 inline void bgc_fp64_cotes_number_get_rotation_matrix(BGC_FP64_Matrix2x2* matrix, const BGC_FP64_CotesNumber* number)
 {
-    matrix->row1_col1 = number->_cos;
-    matrix->row1_col2 = -number->_sin;
-    matrix->row2_col1 = number->_sin;
-    matrix->row2_col2 = number->_cos;
+    matrix->r1c1 = number->_cos;
+    matrix->r1c2 = -number->_sin;
+    matrix->r2c1 = number->_sin;
+    matrix->r2c2 = number->_cos;
 }
 
 // ============== Reverse Matrix ================ //
 
 inline void bgc_fp32_cotes_number_get_reverse_matrix(BGC_FP32_Matrix2x2* matrix, const BGC_FP32_CotesNumber* number)
 {
-    matrix->row1_col1 = number->_cos;
-    matrix->row1_col2 = number->_sin;
-    matrix->row2_col1 = -number->_sin;
-    matrix->row2_col2 = number->_cos;
+    matrix->r1c1 = number->_cos;
+    matrix->r1c2 = number->_sin;
+    matrix->r2c1 = -number->_sin;
+    matrix->r2c2 = number->_cos;
 }
 
 inline void bgc_fp64_cotes_number_get_reverse_matrix(BGC_FP64_Matrix2x2* matrix, const BGC_FP64_CotesNumber* number)
 {
-    matrix->row1_col1 = number->_cos;
-    matrix->row1_col2 = number->_sin;
-    matrix->row2_col1 = -number->_sin;
-    matrix->row2_col2 = number->_cos;
+    matrix->r1c1 = number->_cos;
+    matrix->r1c2 = number->_sin;
+    matrix->r2c1 = -number->_sin;
+    matrix->r2c2 = number->_cos;
 }
 
 // ================ Turn Vector ================= //

basic-geometry/dual-number.c

@@ -11,3 +11,24 @@ inline void bgc_fp64_dual_number_copy(BGC_FP64_DualNumber* destination, const BG
 
 inline void bgc_fp32_dual_number_swap(BGC_FP32_DualNumber* first, BGC_FP32_DualNumber* second);
 inline void bgc_fp64_dual_number_swap(BGC_FP64_DualNumber* first, BGC_FP64_DualNumber* second);
+
+inline void bgc_fp32_dual_number_add(BGC_FP32_DualNumber* sum, const BGC_FP32_DualNumber* first, const BGC_FP32_DualNumber* second);
+inline void bgc_fp64_dual_number_add(BGC_FP64_DualNumber* sum, const BGC_FP64_DualNumber* first, const BGC_FP64_DualNumber* second);
+
+inline void bgc_fp32_dual_number_add_scaled(BGC_FP32_DualNumber* sum, const BGC_FP32_DualNumber* base_number, const BGC_FP32_DualNumber* scalable_number, const float scale);
+inline void bgc_fp64_dual_number_add_scaled(BGC_FP64_DualNumber* sum, const BGC_FP64_DualNumber* base_number, const BGC_FP64_DualNumber* scalable_number, const double scale);
+
+inline void bgc_fp32_dual_number_subtract(BGC_FP32_DualNumber* difference, const BGC_FP32_DualNumber* minuend, const BGC_FP32_DualNumber* subtrahend);
+inline void bgc_fp64_dual_number_subtract(BGC_FP64_DualNumber* difference, const BGC_FP64_DualNumber* minuend, const BGC_FP64_DualNumber* subtrahend);
+
+inline void bgc_fp32_dual_number_multiply(BGC_FP32_DualNumber* product, const BGC_FP32_DualNumber* multiplicand, const float multiplier);
+inline void bgc_fp64_dual_number_multiply(BGC_FP64_DualNumber* product, const BGC_FP64_DualNumber* multiplicand, const double multiplier);
+
+inline void bgc_fp32_dual_number_divide(BGC_FP32_DualNumber* quotient, const BGC_FP32_DualNumber* dividend, const float divisor);
+inline void bgc_fp64_dual_number_divide(BGC_FP64_DualNumber* quotient, const BGC_FP64_DualNumber* dividend, const double divisor);
+
+inline void bgc_fp32_dual_number_get_mean2(BGC_FP32_DualNumber* mean, const BGC_FP32_DualNumber* first, const BGC_FP32_DualNumber* second);
+inline void bgc_fp64_dual_number_get_mean2(BGC_FP64_DualNumber* mean, const BGC_FP64_DualNumber* first, const BGC_FP64_DualNumber* second);
+
+inline void bgc_fp32_dual_number_get_mean3(BGC_FP32_DualNumber* mean, const BGC_FP32_DualNumber* first, const BGC_FP32_DualNumber* second, const BGC_FP32_DualNumber* third);
+inline void bgc_fp64_dual_number_get_mean3(BGC_FP64_DualNumber* mean, const BGC_FP64_DualNumber* first, const BGC_FP64_DualNumber* second, const BGC_FP64_DualNumber* third);

basic-geometry/dual-number.h

@@ -1,6 +1,8 @@
 #ifndef _BGC_DUAL_NUMBER_H_
 #define _BGC_DUAL_NUMBER_H_
 
+#include "utilities.h"
+
 // =================== Types ==================== //
 
 typedef struct {
@@ -67,4 +69,100 @@ inline void bgc_fp64_dual_number_swap(BGC_FP64_DualNumber* first, BGC_FP64_DualN
     first->dual = second->dual;
 }
 
+// ==================== Add ===================== //
+
+inline void bgc_fp32_dual_number_add(BGC_FP32_DualNumber* sum, const BGC_FP32_DualNumber* first, const BGC_FP32_DualNumber* second)
+{
+    sum->real = first->real + second->real;
+    sum->dual = first->dual + second->dual;
+}
+
+inline void bgc_fp64_dual_number_add(BGC_FP64_DualNumber* sum, const BGC_FP64_DualNumber* first, const BGC_FP64_DualNumber* second)
+{
+    sum->real = first->real + second->real;
+    sum->dual = first->dual + second->dual;
+}
+
+// ================= Add Scaled ================= //
+
+inline void bgc_fp32_dual_number_add_scaled(BGC_FP32_DualNumber* sum, const BGC_FP32_DualNumber* base_number, const BGC_FP32_DualNumber* scalable_number, const float scale)
+{
+    sum->real = base_number->real + scalable_number->real * scale;
+    sum->dual = base_number->dual + scalable_number->dual * scale;
+}
+
+inline void bgc_fp64_dual_number_add_scaled(BGC_FP64_DualNumber* sum, const BGC_FP64_DualNumber* base_number, const BGC_FP64_DualNumber* scalable_number, const double scale)
+{
+    sum->real = base_number->real + scalable_number->real * scale;
+    sum->dual = base_number->dual + scalable_number->dual * scale;
+}
+
+// ================== Subtract ================== //
+
+inline void bgc_fp32_dual_number_subtract(BGC_FP32_DualNumber* difference, const BGC_FP32_DualNumber* minuend, const BGC_FP32_DualNumber* subtrahend)
+{
+    difference->real = minuend->real - subtrahend->real;
+    difference->dual = minuend->dual - subtrahend->dual;
+}
+
+inline void bgc_fp64_dual_number_subtract(BGC_FP64_DualNumber* difference, const BGC_FP64_DualNumber* minuend, const BGC_FP64_DualNumber* subtrahend)
+{
+    difference->real = minuend->real - subtrahend->real;
+    difference->dual = minuend->dual - subtrahend->dual;
+}
+
+// ================== Multiply ================== //
+
+inline void bgc_fp32_dual_number_multiply(BGC_FP32_DualNumber* product, const BGC_FP32_DualNumber* multiplicand, const float multiplier)
+{
+    product->real = multiplicand->real * multiplier;
+    product->dual = multiplicand->dual * multiplier;
+}
+
+inline void bgc_fp64_dual_number_multiply(BGC_FP64_DualNumber* product, const BGC_FP64_DualNumber* multiplicand, const double multiplier)
+{
+    product->real = multiplicand->real * multiplier;
+    product->dual = multiplicand->dual * multiplier;
+}
+
+// =================== Divide =================== //
+
+inline void bgc_fp32_dual_number_divide(BGC_FP32_DualNumber* quotient, const BGC_FP32_DualNumber* dividend, const float divisor)
+{
+    bgc_fp32_dual_number_multiply(quotient, dividend, 1.0f / divisor);
+}
+
+inline void bgc_fp64_dual_number_divide(BGC_FP64_DualNumber* quotient, const BGC_FP64_DualNumber* dividend, const double divisor)
+{
+    bgc_fp64_dual_number_multiply(quotient, dividend, 1.0 / divisor);
+}
+
+// ================ Mean of Two ================= //
+
+inline void bgc_fp32_dual_number_get_mean2(BGC_FP32_DualNumber* mean, const BGC_FP32_DualNumber* first, const BGC_FP32_DualNumber* second)
+{
+    mean->real = (first->real + second->real) * 0.5f;
+    mean->dual = (first->dual + second->dual) * 0.5f;
+}
+
+inline void bgc_fp64_dual_number_get_mean2(BGC_FP64_DualNumber* mean, const BGC_FP64_DualNumber* first, const BGC_FP64_DualNumber* second)
+{
+    mean->real = (first->real + second->real) * 0.5;
+    mean->dual = (first->dual + second->dual) * 0.5;
+}
+
+// =============== Mean of Three ================ //
+
+inline void bgc_fp32_dual_number_get_mean3(BGC_FP32_DualNumber* mean, const BGC_FP32_DualNumber* first, const BGC_FP32_DualNumber* second, const BGC_FP32_DualNumber* third)
+{
+    mean->real = (first->real + second->real + third->real) * BGC_FP32_ONE_THIRD;
+    mean->dual = (first->dual + second->dual + third->dual) * BGC_FP32_ONE_THIRD;
+}
+
+inline void bgc_fp64_dual_number_get_mean3(BGC_FP64_DualNumber* mean, const BGC_FP64_DualNumber* first, const BGC_FP64_DualNumber* second, const BGC_FP64_DualNumber* third)
+{
+    mean->real = (first->real + second->real + third->real) * BGC_FP64_ONE_THIRD;
+    mean->dual = (first->dual + second->dual + third->dual) * BGC_FP64_ONE_THIRD;
+}
+
 #endif

basic-geometry/dual-quaternion.c

@@ -0,0 +1,10 @@
+#include "dual-quaternion.h"
+
+extern inline void bgc_fp32_dual_quaternion_reset(BGC_FP32_DualQuaternion* quaternion);
+extern inline void bgc_fp64_dual_quaternion_reset(BGC_FP64_DualQuaternion* quaternion);
+
+extern inline void bgc_fp32_dual_quaternion_copy(BGC_FP32_DualQuaternion* destination, const BGC_FP32_DualQuaternion* source);
+extern inline void bgc_fp64_dual_quaternion_copy(BGC_FP64_DualQuaternion* destination, const BGC_FP64_DualQuaternion* source);
+
+extern inline void bgc_fp32_dual_quaternion_swap(BGC_FP32_DualQuaternion* first, BGC_FP32_DualQuaternion* second);
+extern inline void bgc_fp64_dual_quaternion_swap(BGC_FP64_DualQuaternion* first, BGC_FP64_DualQuaternion* second);

basic-geometry/dual-quaternion.h

@@ -0,0 +1,58 @@
+#ifndef _BGC_DUAL_QUATERNION_H_
+#define _BGC_DUAL_QUATERNION_H_
+
+#include "quaternion.h"
+
+// =================== Types ==================== //
+
+typedef struct {
+    BGC_FP32_Quaternion real, dual;
+} BGC_FP32_DualQuaternion;
+
+typedef struct {
+    BGC_FP64_Quaternion real, dual;
+} BGC_FP64_DualQuaternion;
+
+// =================== Reset ==================== //
+
+inline void bgc_fp32_dual_quaternion_reset(BGC_FP32_DualQuaternion* quaternion)
+{
+    bgc_fp32_quaternion_reset(&quaternion->real);
+    bgc_fp32_quaternion_reset(&quaternion->dual);
+}
+
+inline void bgc_fp64_dual_quaternion_reset(BGC_FP64_DualQuaternion* quaternion)
+{
+    bgc_fp64_quaternion_reset(&quaternion->real);
+    bgc_fp64_quaternion_reset(&quaternion->dual);
+}
+
+// ==================== Copy ==================== //
+
+inline void bgc_fp32_dual_quaternion_copy(BGC_FP32_DualQuaternion* destination, const BGC_FP32_DualQuaternion* source)
+{
+    bgc_fp32_quaternion_copy(&destination->real, &source->real);
+    bgc_fp32_quaternion_copy(&destination->dual, &source->dual);
+}
+
+inline void bgc_fp64_dual_quaternion_copy(BGC_FP64_DualQuaternion* destination, const BGC_FP64_DualQuaternion* source)
+{
+    bgc_fp64_quaternion_copy(&destination->real, &source->real);
+    bgc_fp64_quaternion_copy(&destination->dual, &source->dual);
+}
+
+// ==================== Swap ==================== //
+
+inline void bgc_fp32_dual_quaternion_swap(BGC_FP32_DualQuaternion* first, BGC_FP32_DualQuaternion* second)
+{
+    bgc_fp32_quaternion_swap(&first->real, &second->real);
+    bgc_fp32_quaternion_swap(&first->dual, &second->dual);
+}
+
+inline void bgc_fp64_dual_quaternion_swap(BGC_FP64_DualQuaternion* first, BGC_FP64_DualQuaternion* second)
+{
+    bgc_fp64_quaternion_swap(&first->real, &second->real);
+    bgc_fp64_quaternion_swap(&first->dual, &second->dual);
+}
+
+#endif

basic-geometry/dual-vector3.c

@@ -1,22 +1,34 @@
 #include "./dual-vector3.h"
 
-inline void bgc_fp32_dual_vector3_reset(BGC_FP32_DualVector3* vector);
-inline void bgc_fp64_dual_vector3_reset(BGC_FP64_DualVector3* vector);
+extern inline void bgc_fp32_dual_vector3_reset(BGC_FP32_DualVector3* vector);
+extern inline void bgc_fp64_dual_vector3_reset(BGC_FP64_DualVector3* vector);
 
-inline void bgc_fp32_dual_vector3_make(BGC_FP32_DualVector3* vector, const BGC_FP32_Vector3* real, const BGC_FP32_Vector3* dual);
-inline void bgc_fp64_dual_vector3_make(BGC_FP64_DualVector3* vector, const BGC_FP64_Vector3* real, const BGC_FP64_Vector3* dual);
+extern inline void bgc_fp32_dual_vector3_make(BGC_FP32_DualVector3* vector, const BGC_FP32_Vector3* real, const BGC_FP32_Vector3* dual);
+extern inline void bgc_fp64_dual_vector3_make(BGC_FP64_DualVector3* vector, const BGC_FP64_Vector3* real, const BGC_FP64_Vector3* dual);
 
-inline void bgc_fp32_dual_vector3_set_real_values(BGC_FP32_DualVector3* vector, const float x1, const float x2, const float x3);
-inline void bgc_fp64_dual_vector3_set_real_values(BGC_FP64_DualVector3* vector, const double x1, const double x2, const double x3);
+extern inline void bgc_fp32_dual_vector3_copy(BGC_FP32_DualVector3* destination, const BGC_FP32_DualVector3* source);
+extern inline void bgc_fp64_dual_vector3_copy(BGC_FP64_DualVector3* destination, const BGC_FP64_DualVector3* source);
 
-inline void bgc_fp32_dual_vector3_set_dual_values(BGC_FP32_DualVector3* vector, const float x1, const float x2, const float x3);
-inline void bgc_fp64_dual_vector3_set_dual_values(BGC_FP64_DualVector3* vector, const double x1, const double x2, const double x3);
+extern inline void bgc_fp32_dual_vector3_swap(BGC_FP32_DualVector3* first, BGC_FP32_DualVector3* second);
+extern inline void bgc_fp64_dual_vector3_swap(BGC_FP64_DualVector3* first, BGC_FP64_DualVector3* second);
 
-inline void bgc_fp32_dual_vector3_add(BGC_FP32_DualVector3* sum, const BGC_FP32_DualVector3* first, const BGC_FP32_DualVector3* second);
-inline void bgc_fp64_dual_vector3_add(BGC_FP64_DualVector3* sum, const BGC_FP64_DualVector3* first, const BGC_FP64_DualVector3* second);
+extern inline void bgc_fp32_dual_vector3_set_real_values(BGC_FP32_DualVector3* vector, const float x1, const float x2, const float x3);
+extern inline void bgc_fp64_dual_vector3_set_real_values(BGC_FP64_DualVector3* vector, const double x1, const double x2, const double x3);
 
-inline void bgc_fp32_dual_vector3_add_scaled(BGC_FP32_DualVector3* sum, const BGC_FP32_DualVector3* base_vector, const BGC_FP32_DualVector3* scalable_vector, const float scale);
-inline void bgc_fp64_dual_vector3_add_scaled(BGC_FP64_DualVector3* sum, const BGC_FP64_DualVector3* base_vector, const BGC_FP64_DualVector3* scalable_vector, const double scale);
+extern inline void bgc_fp32_dual_vector3_set_dual_values(BGC_FP32_DualVector3* vector, const float x1, const float x2, const float x3);
+extern inline void bgc_fp64_dual_vector3_set_dual_values(BGC_FP64_DualVector3* vector, const double x1, const double x2, const double x3);
 
-inline void bgc_fp32_dual_vector3_subtract(BGC_FP32_DualVector3* difference, const BGC_FP32_DualVector3* minuend, const BGC_FP32_DualVector3* subtrahend);
-inline void bgc_fp64_dual_vector3_subtract(BGC_FP64_DualVector3* difference, const BGC_FP64_DualVector3* minuend, const BGC_FP64_DualVector3* subtrahend);
+extern inline void bgc_fp32_dual_vector3_add(BGC_FP32_DualVector3* sum, const BGC_FP32_DualVector3* first, const BGC_FP32_DualVector3* second);
+extern inline void bgc_fp64_dual_vector3_add(BGC_FP64_DualVector3* sum, const BGC_FP64_DualVector3* first, const BGC_FP64_DualVector3* second);
+
+extern inline void bgc_fp32_dual_vector3_add_scaled(BGC_FP32_DualVector3* sum, const BGC_FP32_DualVector3* base_vector, const BGC_FP32_DualVector3* scalable_vector, const float scale);
+extern inline void bgc_fp64_dual_vector3_add_scaled(BGC_FP64_DualVector3* sum, const BGC_FP64_DualVector3* base_vector, const BGC_FP64_DualVector3* scalable_vector, const double scale);
+
+extern inline void bgc_fp32_dual_vector3_subtract(BGC_FP32_DualVector3* difference, const BGC_FP32_DualVector3* minuend, const BGC_FP32_DualVector3* subtrahend);
+extern inline void bgc_fp64_dual_vector3_subtract(BGC_FP64_DualVector3* difference, const BGC_FP64_DualVector3* minuend, const BGC_FP64_DualVector3* subtrahend);
+
+extern inline void bgc_fp32_dual_vector3_multiply(BGC_FP32_DualVector3* product, const BGC_FP32_DualVector3* multiplicand, const float multiplier);
+extern inline void bgc_fp64_dual_vector3_multiply(BGC_FP64_DualVector3* product, const BGC_FP64_DualVector3* multiplicand, const double multiplier);
+
+extern inline void bgc_fp32_dual_vector3_divide(BGC_FP32_DualVector3* quotient, const BGC_FP32_DualVector3* dividend, const float divisor);
+extern inline void bgc_fp64_dual_vector3_divide(BGC_FP64_DualVector3* quotient, const BGC_FP64_DualVector3* dividend, const double divisor);

basic-geometry/dual-vector3.h

@@ -41,6 +41,34 @@ inline void bgc_fp64_dual_vector3_make(BGC_FP64_DualVector3* vector, const BGC_F
     bgc_fp64_vector3_copy(&vector->dual, dual);
 }
 
+// ==================== Copy ==================== //
+
+inline void bgc_fp32_dual_vector3_copy(BGC_FP32_DualVector3* destination, const BGC_FP32_DualVector3* source)
+{
+    bgc_fp32_vector3_copy(&destination->real, &source->real);
+    bgc_fp32_vector3_copy(&destination->dual, &source->dual);
+}
+
+inline void bgc_fp64_dual_vector3_copy(BGC_FP64_DualVector3* destination, const BGC_FP64_DualVector3* source)
+{
+    bgc_fp64_vector3_copy(&destination->real, &source->real);
+    bgc_fp64_vector3_copy(&destination->dual, &source->dual);
+}
+
+// ==================== Swap ==================== //
+
+inline void bgc_fp32_dual_vector3_swap(BGC_FP32_DualVector3* first, BGC_FP32_DualVector3* second)
+{
+    bgc_fp32_vector3_swap(&first->real, &second->real);
+    bgc_fp32_vector3_swap(&first->dual, &second->dual);
+}
+
+inline void bgc_fp64_dual_vector3_swap(BGC_FP64_DualVector3* first, BGC_FP64_DualVector3* second)
+{
+    bgc_fp64_vector3_swap(&first->real, &second->real);
+    bgc_fp64_vector3_swap(&first->dual, &second->dual);
+}
+
 // ================== Set Real ================== //
 
 inline void bgc_fp32_dual_vector3_set_real_values(BGC_FP32_DualVector3* vector, const float x1, const float x2, const float x3)
@@ -115,6 +143,32 @@ inline void bgc_fp64_dual_vector3_subtract(BGC_FP64_DualVector3* difference, con
     bgc_fp64_vector3_subtract(&difference->dual, &minuend->dual, &subtrahend->dual);
 }
 
+// ================== Multiply ================== //
+
+inline void bgc_fp32_dual_vector3_multiply(BGC_FP32_DualVector3* product, const BGC_FP32_DualVector3* multiplicand, const float multiplier)
+{
+    bgc_fp32_vector3_multiply(&product->real, &multiplicand->real, multiplier);
+    bgc_fp32_vector3_multiply(&product->dual, &multiplicand->dual, multiplier);
+}
+
+inline void bgc_fp64_dual_vector3_multiply(BGC_FP64_DualVector3* product, const BGC_FP64_DualVector3* multiplicand, const double multiplier)
+{
+    bgc_fp64_vector3_multiply(&product->real, &multiplicand->real, multiplier);
+    bgc_fp64_vector3_multiply(&product->dual, &multiplicand->dual, multiplier);
+}
+
+// =================== Divide =================== //
+
+inline void bgc_fp32_dual_vector3_divide(BGC_FP32_DualVector3* quotient, const BGC_FP32_DualVector3* dividend, const float divisor)
+{
+    bgc_fp32_dual_vector3_multiply(quotient, dividend, 1.0f / divisor);
+}
+
+inline void bgc_fp64_dual_vector3_divide(BGC_FP64_DualVector3* quotient, const BGC_FP64_DualVector3* dividend, const double divisor)
+{
+    bgc_fp64_dual_vector3_multiply(quotient, dividend, 1.0 / divisor);
+}
+
 // ================== Average2 ================== //
 
 inline void bgc_fp32_dual_vector3_get_mean2(BGC_FP32_DualVector3* mean, const BGC_FP32_DualVector3* vector1, const BGC_FP32_DualVector3* vector2)
@@ -133,14 +187,14 @@ inline void bgc_fp64_dual_vector3_get_mean2(BGC_FP64_DualVector3* mean, const BG
 
 inline void bgc_fp32_dual_vector3_get_mean3(BGC_FP32_DualVector3* mean, const BGC_FP32_DualVector3* vector1, const BGC_FP32_DualVector3* vector2, const BGC_FP32_DualVector3* vector3)
 {
-    bgc_fp32_vector3_get_mean2(&mean->real, &vector1->real, &vector2->real, &vector3->real);
-    bgc_fp32_vector3_get_mean2(&mean->dual, &vector1->dual, &vector2->dual, &vector3->dual);
+    bgc_fp32_vector3_get_mean3(&mean->real, &vector1->real, &vector2->real, &vector3->real);
+    bgc_fp32_vector3_get_mean3(&mean->dual, &vector1->dual, &vector2->dual, &vector3->dual);
 }
 
 inline void bgc_fp64_dual_vector3_get_mean3(BGC_FP64_DualVector3* mean, const BGC_FP64_DualVector3* vector1, const BGC_FP64_DualVector3* vector2, const BGC_FP64_DualVector3* vector3)
 {
-    bgc_fp64_vector3_get_mean2(&mean->real, &vector1->real, &vector2->real, &vector3->real);
-    bgc_fp64_vector3_get_mean2(&mean->dual, &vector1->dual, &vector2->dual, &vector3->dual);
+    bgc_fp64_vector3_get_mean3(&mean->real, &vector1->real, &vector2->real, &vector3->real);
+    bgc_fp64_vector3_get_mean3(&mean->dual, &vector1->dual, &vector2->dual, &vector3->dual);
 }
 
 #endif

basic-geometry/dual-versor.c

@@ -1,10 +0,0 @@
-#include "dual-versor.h"
-
-extern inline void bgc_fp32_dual_versor_reset(BGC_FP32_DualVersor* number);
-extern inline void bgc_fp64_dual_versor_reset(BGC_FP64_DualVersor* number);
-
-extern inline void bgc_fp32_dual_versor_copy(BGC_FP32_DualVersor* destination, const BGC_FP32_DualVersor* source);
-extern inline void bgc_fp64_dual_versor_copy(BGC_FP64_DualVersor* destination, const BGC_FP64_DualVersor* source);
-
-extern inline void bgc_fp32_dual_versor_swap(BGC_FP32_DualVersor* first, BGC_FP32_DualVersor* second);
-extern inline void bgc_fp64_dual_versor_swap(BGC_FP64_DualVersor* first, BGC_FP64_DualVersor* second);

basic-geometry/dual-versor.h

@@ -1,147 +0,0 @@
-#ifndef _BGC_DUAL_VERSOR_H_
-#define _BGC_DUAL_VERSOR_H_
-
-// =================== Types ==================== //
-
-typedef struct {
-    struct {
-        float s0, x1, x2, x3;
-    } _real, _dual;
-} BGC_FP32_DualVersor;
-
-typedef struct {
-    struct {
-        double s0, x1, x2, x3;
-    } _real, _dual;
-} BGC_FP64_DualVersor;
-
-// =================== Reset ==================== //
-
-inline void bgc_fp32_dual_versor_reset(BGC_FP32_DualVersor* number)
-{
-    number->_real.s0 = 1.0f;
-    number->_real.x1 = 0.0f;
-    number->_real.x2 = 0.0f;
-    number->_real.x3 = 0.0f;
-
-    number->_dual.s0 = 0.0f;
-    number->_dual.x1 = 0.0f;
-    number->_dual.x2 = 0.0f;
-    number->_dual.x3 = 0.0f;
-}
-
-inline void bgc_fp64_dual_versor_reset(BGC_FP64_DualVersor* number)
-{
-    number->_real.s0 = 1.0f;
-    number->_real.x1 = 0.0f;
-    number->_real.x2 = 0.0f;
-    number->_real.x3 = 0.0f;
-
-    number->_dual.s0 = 0.0f;
-    number->_dual.x1 = 0.0f;
-    number->_dual.x2 = 0.0f;
-    number->_dual.x3 = 0.0f;
-}
-
-// ==================== Copy ==================== //
-
-inline void bgc_fp32_dual_versor_copy(BGC_FP32_DualVersor* destination, const BGC_FP32_DualVersor* source)
-{
-    destination->_real.s0 = source->_real.s0;
-    destination->_real.x1 = source->_real.x1;
-    destination->_real.x2 = source->_real.x2;
-    destination->_real.x3 = source->_real.x3;
-
-    destination->_dual.s0 = source->_dual.s0;
-    destination->_dual.x1 = source->_dual.x1;
-    destination->_dual.x2 = source->_dual.x2;
-    destination->_dual.x3 = source->_dual.x3;
-}
-
-inline void bgc_fp64_dual_versor_copy(BGC_FP64_DualVersor* destination, const BGC_FP64_DualVersor* source)
-{
-    destination->_real.s0 = source->_real.s0;
-    destination->_real.x1 = source->_real.x1;
-    destination->_real.x2 = source->_real.x2;
-    destination->_real.x3 = source->_real.x3;
-
-    destination->_dual.s0 = source->_dual.s0;
-    destination->_dual.x1 = source->_dual.x1;
-    destination->_dual.x2 = source->_dual.x2;
-    destination->_dual.x3 = source->_dual.x3;
-}
-
-// ==================== Swap ==================== //
-
-inline void bgc_fp32_dual_versor_swap(BGC_FP32_DualVersor* first, BGC_FP32_DualVersor* second)
-{
-    // Real
-    float s0 = second->_real.s0;
-    float x1 = second->_real.x1;
-    float x2 = second->_real.x2;
-    float x3 = second->_real.x3;
-
-    second->_real.s0 = first->_real.s0;
-    second->_real.x1 = first->_real.x1;
-    second->_real.x2 = first->_real.x2;
-    second->_real.x3 = first->_real.x3;
-
-    first->_real.s0 = s0;
-    first->_real.x1 = x1;
-    first->_real.x2 = x2;
-    first->_real.x3 = x3;
-
-    // Dual
-    s0 = second->_dual.s0;
-    x1 = second->_dual.x1;
-    x2 = second->_dual.x2;
-    x3 = second->_dual.x3;
-
-    second->_dual.s0 = first->_dual.s0;
-    second->_dual.x1 = first->_dual.x1;
-    second->_dual.x2 = first->_dual.x2;
-    second->_dual.x3 = first->_dual.x3;
-
-    first->_dual.s0 = s0;
-    first->_dual.x1 = x1;
-    first->_dual.x2 = x2;
-    first->_dual.x3 = x3;
-}
-
-inline void bgc_fp64_dual_versor_swap(BGC_FP64_DualVersor* first, BGC_FP64_DualVersor* second)
-{
-    // Real
-    double s0 = second->_real.s0;
-    double x1 = second->_real.x1;
-    double x2 = second->_real.x2;
-    double x3 = second->_real.x3;
-
-    second->_real.s0 = first->_real.s0;
-    second->_real.x1 = first->_real.x1;
-    second->_real.x2 = first->_real.x2;
-    second->_real.x3 = first->_real.x3;
-
-    first->_real.s0 = s0;
-    first->_real.x1 = x1;
-    first->_real.x2 = x2;
-    first->_real.x3 = x3;
-
-    // Dual
-    s0 = second->_dual.s0;
-    x1 = second->_dual.x1;
-    x2 = second->_dual.x2;
-    x3 = second->_dual.x3;
-
-    second->_dual.s0 = first->_dual.s0;
-    second->_dual.x1 = first->_dual.x1;
-    second->_dual.x2 = first->_dual.x2;
-    second->_dual.x3 = first->_dual.x3;
-
-    first->_dual.s0 = s0;
-    first->_dual.x1 = x1;
-    first->_dual.x2 = x2;
-    first->_dual.x3 = x3;
-}
-
-
-#endif

basic-geometry/hg-matrix3x3.c

@@ -0,0 +1,7 @@
+#include "hg-matrix3x3.h"
+
+inline void bgc_fp32_hg_matrix3x3_reset(BGC_FP32_HgMatrix3x3* homogeneous_matrix);
+inline void bgc_fp64_hg_matrix3x3_reset(BGC_FP64_HgMatrix3x3* homogeneous_matrix);
+
+inline void bgc_fp32_hg_matrix3x3_make(BGC_FP32_HgMatrix3x3* homogeneous_matrix, const BGC_FP32_Matrix3x3* linear_matrix, const BGC_FP32_Vector3* shift);
+inline void bgc_fp64_hg_matrix3x3_make(BGC_FP64_HgMatrix3x3* homogeneous_matrix, const BGC_FP64_Matrix3x3* linear_matrix, const BGC_FP64_Vector3* shift);

basic-geometry/hg-matrix3x3.h

@@ -0,0 +1,123 @@
+#ifndef _BGC_HG_MATRIX3X3_H_INCLUDED_
+#define _BGC_HG_MATRIX3X3_H_INCLUDED_
+
+#include "vector3.h"
+#include "matrices.h"
+
+#include "hg-vector3.h"
+
+// =================== Types ==================== //
+
+typedef struct
+{
+    float r1c1, r1c2, r1c3, r1d0;
+    float r2c1, r2c2, r2c3, r2d0;
+    float r3c1, r3c2, r3c3, r3d0;
+    float d0c1, d0c2, d0c3, d0d0;
+} BGC_FP32_HgMatrix3x3;
+
+typedef struct
+{
+    double r1c1, r1c2, r1c3, r1d0;
+    double r2c1, r2c2, r2c3, r2d0;
+    double r3c1, r3c2, r3c3, r3d0;
+    double d0c1, d0c2, d0c3, d0d0;
+} BGC_FP64_HgMatrix3x3;
+
+// =================== Reset ==================== //
+
+inline void bgc_fp32_hg_matrix3x3_reset(BGC_FP32_HgMatrix3x3* homogeneous_matrix)
+{
+    homogeneous_matrix->r1c1 = 1.0f;
+    homogeneous_matrix->r1c2 = 0.0f;
+    homogeneous_matrix->r1c2 = 0.0f;
+    homogeneous_matrix->r1d0 = 0.0f;
+
+    homogeneous_matrix->r2c1 = 0.0f;
+    homogeneous_matrix->r2c2 = 1.0f;
+    homogeneous_matrix->r2c2 = 0.0f;
+    homogeneous_matrix->r2d0 = 0.0f;
+
+    homogeneous_matrix->r3c1 = 0.0f;
+    homogeneous_matrix->r3c2 = 0.0f;
+    homogeneous_matrix->r3c2 = 1.0f;
+    homogeneous_matrix->r3d0 = 0.0f;
+
+    homogeneous_matrix->d0c1 = 0.0f;
+    homogeneous_matrix->d0c2 = 0.0f;
+    homogeneous_matrix->d0c2 = 0.0f;
+    homogeneous_matrix->d0d0 = 1.0f;
+}
+
+inline void bgc_fp64_hg_matrix3x3_reset(BGC_FP64_HgMatrix3x3* homogeneous_matrix)
+{
+    homogeneous_matrix->r1c1 = 1.0;
+    homogeneous_matrix->r1c2 = 0.0;
+    homogeneous_matrix->r1c2 = 0.0;
+    homogeneous_matrix->r1d0 = 0.0;
+
+    homogeneous_matrix->r2c1 = 0.0;
+    homogeneous_matrix->r2c2 = 1.0;
+    homogeneous_matrix->r2c2 = 0.0;
+    homogeneous_matrix->r2d0 = 0.0;
+
+    homogeneous_matrix->r3c1 = 0.0;
+    homogeneous_matrix->r3c2 = 0.0;
+    homogeneous_matrix->r3c2 = 1.0;
+    homogeneous_matrix->r3d0 = 0.0;
+
+    homogeneous_matrix->d0c1 = 0.0;
+    homogeneous_matrix->d0c2 = 0.0;
+    homogeneous_matrix->d0c2 = 0.0;
+    homogeneous_matrix->d0d0 = 1.0;
+}
+
+// ==================== Make ==================== //
+
+inline void bgc_fp32_hg_matrix3x3_make(BGC_FP32_HgMatrix3x3* homogeneous_matrix, const BGC_FP32_Matrix3x3* linear_matrix, const BGC_FP32_Vector3* shift)
+{
+    homogeneous_matrix->r1c1 = linear_matrix->r1c1;
+    homogeneous_matrix->r1c2 = linear_matrix->r1c2;
+    homogeneous_matrix->r1c2 = linear_matrix->r1c3;
+    homogeneous_matrix->r1d0 = shift->x1;
+
+    homogeneous_matrix->r2c1 = linear_matrix->r2c1;
+    homogeneous_matrix->r2c2 = linear_matrix->r2c2;
+    homogeneous_matrix->r2c2 = linear_matrix->r2c3;
+    homogeneous_matrix->r2d0 = shift->x2;
+
+    homogeneous_matrix->r3c1 = linear_matrix->r3c1;
+    homogeneous_matrix->r3c2 = linear_matrix->r3c2;
+    homogeneous_matrix->r3c2 = linear_matrix->r3c3;
+    homogeneous_matrix->r3d0 = shift->x3;
+
+    homogeneous_matrix->d0c1 = 0.0f;
+    homogeneous_matrix->d0c2 = 0.0f;
+    homogeneous_matrix->d0c2 = 0.0f;
+    homogeneous_matrix->d0d0 = 1.0f;
+}
+
+inline void bgc_fp64_hg_matrix3x3_make(BGC_FP64_HgMatrix3x3* homogeneous_matrix, const BGC_FP64_Matrix3x3* linear_matrix, const BGC_FP64_Vector3* shift)
+{
+    homogeneous_matrix->r1c1 = linear_matrix->r1c1;
+    homogeneous_matrix->r1c2 = linear_matrix->r1c2;
+    homogeneous_matrix->r1c2 = linear_matrix->r1c3;
+    homogeneous_matrix->r1d0 = shift->x1;
+
+    homogeneous_matrix->r2c1 = linear_matrix->r2c1;
+    homogeneous_matrix->r2c2 = linear_matrix->r2c2;
+    homogeneous_matrix->r2c2 = linear_matrix->r2c3;
+    homogeneous_matrix->r2d0 = shift->x2;
+
+    homogeneous_matrix->r3c1 = linear_matrix->r3c1;
+    homogeneous_matrix->r3c2 = linear_matrix->r3c2;
+    homogeneous_matrix->r3c2 = linear_matrix->r3c3;
+    homogeneous_matrix->r3d0 = shift->x3;
+
+    homogeneous_matrix->d0c1 = 0.0;
+    homogeneous_matrix->d0c2 = 0.0;
+    homogeneous_matrix->d0c2 = 0.0;
+    homogeneous_matrix->d0d0 = 1.0;
+}
+
+#endif

basic-geometry/hg-vector3.h

@@ -8,13 +8,13 @@
 // Homogeneous 3D Vector
 typedef struct
 {
-    float x1, x2, x3, ratio;
+    float x1, x2, x3, d0;
 } BGC_FP32_HgVector3;
 
 // Homogeneous 3D Vector
 typedef struct
 {
-    double x1, x2, x3, ratio;
+    double x1, x2, x3, d0;
 } BGC_FP64_HgVector3;
 
 // ================ Reset Point ================= //
@@ -24,7 +24,7 @@ inline void bgc_fp32_hg_vector3_reset_point(BGC_FP32_HgVector3* homogeneous_vect
     homogeneous_vector->x1 = 0.0f;
     homogeneous_vector->x2 = 0.0f;
     homogeneous_vector->x3 = 0.0f;
-    homogeneous_vector->ratio = 1.0f;
+    homogeneous_vector->d0 = 1.0f;
 }
 
 inline void bgc_fp64_hg_vector3_reset_point(BGC_FP64_HgVector3* homogeneous_vector)
@@ -32,7 +32,7 @@ inline void bgc_fp64_hg_vector3_reset_point(BGC_FP64_HgVector3* homogeneous_vect
     homogeneous_vector->x1 = 0.0;
     homogeneous_vector->x2 = 0.0;
     homogeneous_vector->x3 = 0.0;
-    homogeneous_vector->ratio = 1.0;
+    homogeneous_vector->d0 = 1.0;
 }
 
 // ================ Reset Point ================= //
@@ -42,7 +42,7 @@ inline void bgc_fp32_hg_vector3_reset_vector(BGC_FP32_HgVector3* homogeneous_vec
     homogeneous_vector->x1 = 0.0f;
     homogeneous_vector->x2 = 0.0f;
     homogeneous_vector->x3 = 0.0f;
-    homogeneous_vector->ratio = 0.0f;
+    homogeneous_vector->d0 = 0.0f;
 }
 
 inline void bgc_fp64_hg_vector3_reset_vector(BGC_FP64_HgVector3* homogeneous_vector)
@@ -50,25 +50,25 @@ inline void bgc_fp64_hg_vector3_reset_vector(BGC_FP64_HgVector3* homogeneous_vec
     homogeneous_vector->x1 = 0.0;
     homogeneous_vector->x2 = 0.0;
     homogeneous_vector->x3 = 0.0;
-    homogeneous_vector->ratio = 0.0;
+    homogeneous_vector->d0 = 0.0;
 }
 
 // ==================== Make ==================== //
 
-inline void bgc_fp32_hg_vector3_make(BGC_FP32_HgVector3* homogeneous_vector, const float x1, const float x2, const float x3, const float ratio)
+inline void bgc_fp32_hg_vector3_make(BGC_FP32_HgVector3* homogeneous_vector, const float x1, const float x2, const float x3, const float d0)
 {
     homogeneous_vector->x1 = x1;
     homogeneous_vector->x2 = x2;
     homogeneous_vector->x3 = x3;
-    homogeneous_vector->ratio = ratio;
+    homogeneous_vector->d0 = d0;
 }
 
-inline void bgc_fp64_hg_vector3_make(BGC_FP64_HgVector3* homogeneous_vector, const double x1, const double x2, const double x3, const double ratio)
+inline void bgc_fp64_hg_vector3_make(BGC_FP64_HgVector3* homogeneous_vector, const double x1, const double x2, const double x3, const double d0)
 {
     homogeneous_vector->x1 = x1;
     homogeneous_vector->x2 = x2;
     homogeneous_vector->x3 = x3;
-    homogeneous_vector->ratio = ratio;
+    homogeneous_vector->d0 = d0;
 }
 
 // ================= Make Point ================= //
@@ -78,7 +78,7 @@ inline void bgc_fp32_hg_vector3_make_point(BGC_FP32_HgVector3* homogeneous_vecto
     homogeneous_vector->x1 = regular_vector->x1;
     homogeneous_vector->x2 = regular_vector->x2;
     homogeneous_vector->x3 = regular_vector->x3;
-    homogeneous_vector->ratio = 1.0f;
+    homogeneous_vector->d0 = 1.0f;
 }
 
 inline void bgc_fp64_hg_vector3_make_point(BGC_FP64_HgVector3* homogeneous_vector, const BGC_FP64_Vector3* regular_vector)
@@ -86,7 +86,7 @@ inline void bgc_fp64_hg_vector3_make_point(BGC_FP64_HgVector3* homogeneous_vecto
     homogeneous_vector->x1 = regular_vector->x1;
     homogeneous_vector->x2 = regular_vector->x2;
     homogeneous_vector->x3 = regular_vector->x3;
-    homogeneous_vector->ratio = 1.0;
+    homogeneous_vector->d0 = 1.0;
 }
 
 // ================ Make Vector ================= //
@@ -96,7 +96,7 @@ inline void bgc_fp32_hg_vector3_make_vector(BGC_FP32_HgVector3* homogeneous_vect
     homogeneous_vector->x1 = regular_vector->x1;
     homogeneous_vector->x2 = regular_vector->x2;
     homogeneous_vector->x3 = regular_vector->x3;
-    homogeneous_vector->ratio = 0.0f;
+    homogeneous_vector->d0 = 0.0f;
 }
 
 inline void bgc_fp64_hg_vector3_make_vector(BGC_FP64_HgVector3* homogeneous_vector, const BGC_FP64_Vector3* regular_vector)
@@ -104,31 +104,31 @@ inline void bgc_fp64_hg_vector3_make_vector(BGC_FP64_HgVector3* homogeneous_vect
     homogeneous_vector->x1 = regular_vector->x1;
     homogeneous_vector->x2 = regular_vector->x2;
     homogeneous_vector->x3 = regular_vector->x3;
-    homogeneous_vector->ratio = 0.0;
+    homogeneous_vector->d0 = 0.0;
 }
 
 // ================== Is Point ================== //
 
 inline int bgc_fp32_hg_vector3_is_point(const BGC_FP32_HgVector3* homogeneous_vector)
 {
-    return !bgc_fp32_is_zero(homogeneous_vector->ratio);
+    return !bgc_fp32_is_zero(homogeneous_vector->d0);
 }
 
 inline int bgc_fp64_hg_vector3_is_point(const BGC_FP64_HgVector3* homogeneous_vector)
 {
-    return !bgc_fp64_is_zero(homogeneous_vector->ratio);
+    return !bgc_fp64_is_zero(homogeneous_vector->d0);
 }
 
 // ================= Is Vector ================== //
 
 inline int bgc_fp32_hg_vector3_is_vector(const BGC_FP32_HgVector3* homogeneous_vector)
 {
-    return bgc_fp32_is_zero(homogeneous_vector->ratio);
+    return bgc_fp32_is_zero(homogeneous_vector->d0);
 }
 
 inline int bgc_fp64_hg_vector3_is_vector(const BGC_FP64_HgVector3* homogeneous_vector)
 {
-    return bgc_fp64_is_zero(homogeneous_vector->ratio);
+    return bgc_fp64_is_zero(homogeneous_vector->d0);
 }
 
 // ==================== Copy ==================== //
@@ -138,7 +138,7 @@ inline void bgc_fp32_hg_vector3_copy(BGC_FP32_HgVector3* destination, const BGC_
     destination->x1 = source->x1;
     destination->x2 = source->x2;
     destination->x3 = source->x3;
-    destination->ratio = source->ratio;
+    destination->d0 = source->d0;
 }
 
 inline void bgc_fp64_hg_vector3_copy(BGC_FP64_HgVector3* destination, const BGC_FP64_HgVector3* source)
@@ -146,7 +146,7 @@ inline void bgc_fp64_hg_vector3_copy(BGC_FP64_HgVector3* destination, const BGC_
     destination->x1 = source->x1;
     destination->x2 = source->x2;
     destination->x3 = source->x3;
-    destination->ratio = source->ratio;
+    destination->d0 = source->d0;
 }
 
 // ==================== Swap ==================== //
@@ -156,17 +156,17 @@ inline void bgc_fp32_hg_vector3_swap(BGC_FP32_HgVector3* first, BGC_FP32_HgVecto
     const float x1 = first->x1;
     const float x2 = first->x2;
     const float x3 = first->x3;
-    const float ratio = first->ratio;
+    const float d0 = first->d0;
 
     first->x1 = second->x1;
     first->x2 = second->x2;
     first->x3 = second->x3;
-    first->ratio = second->ratio;
+    first->d0 = second->d0;
 
     second->x1 = x1;
     second->x2 = x2;
     second->x3 = x3;
-    second->ratio = ratio;
+    second->d0 = d0;
 }
 
 inline void bgc_fp64_hg_vector3_swap(BGC_FP64_HgVector3* first, BGC_FP64_HgVector3* second)
@@ -174,17 +174,51 @@ inline void bgc_fp64_hg_vector3_swap(BGC_FP64_HgVector3* first, BGC_FP64_HgVecto
     const double x1 = first->x1;
     const double x2 = first->x2;
     const double x3 = first->x3;
-    const double ratio = first->ratio;
+    const double d0 = first->d0;
 
     first->x1 = second->x1;
     first->x2 = second->x2;
     first->x3 = second->x3;
-    first->ratio = second->ratio;
+    first->d0 = second->d0;
 
     second->x1 = x1;
     second->x2 = x2;
     second->x3 = x3;
-    second->ratio = ratio;
+    second->d0 = d0;
+}
+
+// ================== Rescale =================== //
+
+inline int bgc_fp32_hg_vector3_rescale(BGC_FP32_HgVector3* homogeneous_vector, const float new_ratio)
+{
+    if (bgc_fp32_is_zero(homogeneous_vector->d0)) {
+        return 0;
+    }
+
+    const float multiplier = new_ratio / homogeneous_vector->d0;
+
+    homogeneous_vector->x1 *= multiplier;
+    homogeneous_vector->x2 *= multiplier;
+    homogeneous_vector->x3 *= multiplier;
+    homogeneous_vector->d0 = new_ratio;
+
+    return 1;
+}
+
+inline int bgc_fp64_hg_vector3_rescale(BGC_FP64_HgVector3* homogeneous_vector, const double new_ratio)
+{
+    if (bgc_fp64_is_zero(homogeneous_vector->d0)) {
+        return 0;
+    }
+
+    const double multiplier = new_ratio / homogeneous_vector->d0;
+
+    homogeneous_vector->x1 *= multiplier;
+    homogeneous_vector->x2 *= multiplier;
+    homogeneous_vector->x3 *= multiplier;
+    homogeneous_vector->d0 = new_ratio;
+
+    return 1;
 }
 
 #endif

basic-geometry/matrices.h

@@ -4,361 +4,361 @@
 // ================== Matrix2x2 ================= //
 
 typedef struct {
-    float row1_col1, row1_col2;
-    float row2_col1, row2_col2;
+    float r1c1, r1c2;
+    float r2c1, r2c2;
 } BGC_FP32_Matrix2x2;
 
 typedef struct {
-    double row1_col1, row1_col2;
-    double row2_col1, row2_col2;
+    double r1c1, r1c2;
+    double r2c1, r2c2;
 } BGC_FP64_Matrix2x2;
 
 // ================== Matrix2x3 ================= //
 
 typedef struct {
-    float row1_col1, row1_col2;
-    float row2_col1, row2_col2;
-    float row3_col1, row3_col2;
+    float r1c1, r1c2;
+    float r2c1, r2c2;
+    float r3c1, r3c2;
 } BGC_FP32_Matrix2x3;
 
 typedef struct {
-    double row1_col1, row1_col2;
-    double row2_col1, row2_col2;
-    double row3_col1, row3_col2;
+    double r1c1, r1c2;
+    double r2c1, r2c2;
+    double r3c1, r3c2;
 } BGC_FP64_Matrix2x3;
 
 // ================== Matrix3x2 ================= //
 
 typedef struct {
-    float row1_col1, row1_col2, row1_col3;
-    float row2_col1, row2_col2, row2_col3;
+    float r1c1, r1c2, r1c3;
+    float r2c1, r2c2, r2c3;
 } BGC_FP32_Matrix3x2;
 
 typedef struct {
-    double row1_col1, row1_col2, row1_col3;
-    double row2_col1, row2_col2, row2_col3;
+    double r1c1, r1c2, r1c3;
+    double r2c1, r2c2, r2c3;
 } BGC_FP64_Matrix3x2;
 
 // ================== Matrix3x3 ================= //
 
 typedef struct {
-    float row1_col1, row1_col2, row1_col3;
-    float row2_col1, row2_col2, row2_col3;
-    float row3_col1, row3_col2, row3_col3;
+    float r1c1, r1c2, r1c3;
+    float r2c1, r2c2, r2c3;
+    float r3c1, r3c2, r3c3;
 } BGC_FP32_Matrix3x3;
 
 typedef struct {
-    double row1_col1, row1_col2, row1_col3;
-    double row2_col1, row2_col2, row2_col3;
-    double row3_col1, row3_col2, row3_col3;
+    double r1c1, r1c2, r1c3;
+    double r2c1, r2c2, r2c3;
+    double r3c1, r3c2, r3c3;
 } BGC_FP64_Matrix3x3;
 
 // ========== Matrix Product 2x2 at 2x2 ========= //
 
 inline void bgc_fp32_multiply_matrix2x2_by_matrix2x2(BGC_FP32_Matrix2x2* product, const BGC_FP32_Matrix2x2* matrix1, const BGC_FP32_Matrix2x2* matrix2)
 {
-    const float row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1;
-    const float row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2;
+    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
+    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
 
-    const float row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1;
-    const float row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2;
+    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
+    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
 
-    product->row1_col1 = row1_col1;
-    product->row1_col2 = row1_col2;
+    product->r1c1 = r1c1;
+    product->r1c2 = r1c2;
 
-    product->row2_col1 = row2_col1;
-    product->row2_col2 = row2_col2;
+    product->r2c1 = r2c1;
+    product->r2c2 = r2c2;
 }
 
 inline void bgc_fp64_multiply_matrix2x2_by_matrix2x2(BGC_FP64_Matrix2x2* product, const BGC_FP64_Matrix2x2* matrix1, const BGC_FP64_Matrix2x2* matrix2)
 {
-    const double row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1;
-    const double row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2;
+    const double r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
+    const double r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
 
-    const double row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1;
-    const double row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2;
+    const double r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
+    const double r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
 
-    product->row1_col1 = row1_col1;
-    product->row1_col2 = row1_col2;
+    product->r1c1 = r1c1;
+    product->r1c2 = r1c2;
 
-    product->row2_col1 = row2_col1;
-    product->row2_col2 = row2_col2;
+    product->r2c1 = r2c1;
+    product->r2c2 = r2c2;
 }
 
 // ========== Matrix Product 2x2 at 3x2 ========= //
 
 inline void bgc_fp32_multiply_matrix2x2_by_matrix3x2(BGC_FP32_Matrix3x2* product, const BGC_FP32_Matrix2x2* matrix1, const BGC_FP32_Matrix3x2* matrix2)
 {
-    const float row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1;
-    const float row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2;
-    const float row1_col3 = matrix1->row1_col1 * matrix2->row1_col3 + matrix1->row1_col2 * matrix2->row2_col3;
+    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
+    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
+    const float r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3;
 
-    const float row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1;
-    const float row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2;
-    const float row2_col3 = matrix1->row2_col1 * matrix2->row1_col3 + matrix1->row2_col2 * matrix2->row2_col3;
+    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
+    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
+    const float r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3;
 
-    product->row1_col1 = row1_col1;
-    product->row1_col2 = row1_col2;
-    product->row1_col3 = row1_col3;
+    product->r1c1 = r1c1;
+    product->r1c2 = r1c2;
+    product->r1c3 = r1c3;
 
-    product->row2_col1 = row2_col1;
-    product->row2_col2 = row2_col2;
-    product->row2_col3 = row2_col3;
+    product->r2c1 = r2c1;
+    product->r2c2 = r2c2;
+    product->r2c3 = r2c3;
 }
 
 inline void bgc_fp64_multiply_matrix2x2_by_matrix3x2(BGC_FP64_Matrix3x2* product, const BGC_FP64_Matrix2x2* matrix1, const BGC_FP64_Matrix3x2* matrix2)
 {
-    const double row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1;
-    const double row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2;
-    const double row1_col3 = matrix1->row1_col1 * matrix2->row1_col3 + matrix1->row1_col2 * matrix2->row2_col3;
+    const double r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
+    const double r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
+    const double r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3;
 
-    const double row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1;
-    const double row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2;
-    const double row2_col3 = matrix1->row2_col1 * matrix2->row1_col3 + matrix1->row2_col2 * matrix2->row2_col3;
+    const double r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
+    const double r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
+    const double r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3;
 
-    product->row1_col1 = row1_col1;
-    product->row1_col2 = row1_col2;
-    product->row1_col3 = row1_col3;
+    product->r1c1 = r1c1;
+    product->r1c2 = r1c2;
+    product->r1c3 = r1c3;
 
-    product->row2_col1 = row2_col1;
-    product->row2_col2 = row2_col2;
-    product->row2_col3 = row2_col3;
+    product->r2c1 = r2c1;
+    product->r2c2 = r2c2;
+    product->r2c3 = r2c3;
 }
 
 // ========== Matrix Product 2x3 at 2x2 ========= //
 
 inline void bgc_fp32_multiply_matrix2x3_by_matrix2x2(BGC_FP32_Matrix2x3* product, const BGC_FP32_Matrix2x3* matrix1, const BGC_FP32_Matrix2x2* matrix2)
 {
-    const float row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1;
-    const float row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2;
+    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
+    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
 
-    const float row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1;
-    const float row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2;
+    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
+    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
 
-    const float row3_col1 = matrix1->row3_col1 * matrix2->row1_col1 + matrix1->row3_col2 * matrix2->row2_col1;
-    const float row3_col2 = matrix1->row3_col1 * matrix2->row1_col2 + matrix1->row3_col2 * matrix2->row2_col2;
+    const float r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1;
+    const float r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2;
 
-    product->row1_col1 = row1_col1;
-    product->row1_col2 = row1_col2;
+    product->r1c1 = r1c1;
+    product->r1c2 = r1c2;
 
-    product->row2_col1 = row2_col1;
-    product->row2_col2 = row2_col2;
+    product->r2c1 = r2c1;
+    product->r2c2 = r2c2;
 
-    product->row3_col1 = row3_col1;
-    product->row3_col2 = row3_col2;
+    product->r3c1 = r3c1;
+    product->r3c2 = r3c2;
 }
 
 inline void bgc_fp64_multiply_matrix2x3_by_matrix2x2(BGC_FP64_Matrix2x3* product, const BGC_FP64_Matrix2x3* matrix1, const BGC_FP64_Matrix2x2* matrix2)
 {
-    const double row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1;
-    const double row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2;
+    const double r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
+    const double r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
 
-    const double row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1;
-    const double row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2;
+    const double r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
+    const double r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
 
-    const double row3_col1 = matrix1->row3_col1 * matrix2->row1_col1 + matrix1->row3_col2 * matrix2->row2_col1;
-    const double row3_col2 = matrix1->row3_col1 * matrix2->row1_col2 + matrix1->row3_col2 * matrix2->row2_col2;
+    const double r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1;
+    const double r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2;
 
-    product->row1_col1 = row1_col1;
-    product->row1_col2 = row1_col2;
+    product->r1c1 = r1c1;
+    product->r1c2 = r1c2;
 
-    product->row2_col1 = row2_col1;
-    product->row2_col2 = row2_col2;
+    product->r2c1 = r2c1;
+    product->r2c2 = r2c2;
 
-    product->row3_col1 = row3_col1;
-    product->row3_col2 = row3_col2;
+    product->r3c1 = r3c1;
+    product->r3c2 = r3c2;
 }
 
 // ========== Matrix Product 2x3 at 3x2 ========= //
 
 inline void bgc_fp32_multiply_matrix2x3_by_matrix3x2(BGC_FP32_Matrix3x3* product, const BGC_FP32_Matrix2x3* matrix1, const BGC_FP32_Matrix3x2* matrix2)
 {
-    product->row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1;
-    product->row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2;
-    product->row1_col3 = matrix1->row1_col1 * matrix2->row1_col3 + matrix1->row1_col2 * matrix2->row2_col3;
+    product->r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
+    product->r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
+    product->r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3;
 
-    product->row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1;
-    product->row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2;
-    product->row2_col3 = matrix1->row2_col1 * matrix2->row1_col3 + matrix1->row2_col2 * matrix2->row2_col3;
+    product->r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
+    product->r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
+    product->r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3;
 
-    product->row3_col1 = matrix1->row3_col1 * matrix2->row1_col1 + matrix1->row3_col2 * matrix2->row2_col1;
-    product->row3_col2 = matrix1->row3_col1 * matrix2->row1_col2 + matrix1->row3_col2 * matrix2->row2_col2;
-    product->row3_col3 = matrix1->row3_col1 * matrix2->row1_col3 + matrix1->row3_col2 * matrix2->row2_col3;
+    product->r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1;
+    product->r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2;
+    product->r3c3 = matrix1->r3c1 * matrix2->r1c3 + matrix1->r3c2 * matrix2->r2c3;
 }
 
 inline void bgc_fp64_multiply_matrix2x3_by_matrix3x2(BGC_FP64_Matrix3x3* product, const BGC_FP64_Matrix2x3* matrix1, const BGC_FP64_Matrix3x2* matrix2)
 {
-    product->row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1;
-    product->row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2;
-    product->row1_col3 = matrix1->row1_col1 * matrix2->row1_col3 + matrix1->row1_col2 * matrix2->row2_col3;
+    product->r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
+    product->r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
+    product->r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3;
 
-    product->row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1;
-    product->row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2;
-    product->row2_col3 = matrix1->row2_col1 * matrix2->row1_col3 + matrix1->row2_col2 * matrix2->row2_col3;
+    product->r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
+    product->r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
+    product->r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3;
 
-    product->row3_col1 = matrix1->row3_col1 * matrix2->row1_col1 + matrix1->row3_col2 * matrix2->row2_col1;
-    product->row3_col2 = matrix1->row3_col1 * matrix2->row1_col2 + matrix1->row3_col2 * matrix2->row2_col2;
-    product->row3_col3 = matrix1->row3_col1 * matrix2->row1_col3 + matrix1->row3_col2 * matrix2->row2_col3;
+    product->r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1;
+    product->r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2;
+    product->r3c3 = matrix1->r3c1 * matrix2->r1c3 + matrix1->r3c2 * matrix2->r2c3;
 }
 
 // ========== Matrix Product 3x2 at 2x3 ========= //
 
 inline void bgc_fp32_multiply_matrix3x2_by_matrix2x3(BGC_FP32_Matrix2x2* product, const BGC_FP32_Matrix3x2* matrix1, const BGC_FP32_Matrix2x3* matrix2)
 {
-    product->row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1 + matrix1->row1_col3 * matrix2->row3_col1;
-    product->row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2 + matrix1->row1_col3 * matrix2->row3_col2;
+    product->r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
+    product->r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;
 
-    product->row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1 + matrix1->row2_col3 * matrix2->row3_col1;
-    product->row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2 + matrix1->row2_col3 * matrix2->row3_col2;
+    product->r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
+    product->r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
 }
 
 inline void bgc_fp64_multiply_matrix3x2_by_matrix2x3(BGC_FP64_Matrix2x2* product, const BGC_FP64_Matrix3x2* matrix1, const BGC_FP64_Matrix2x3* matrix2)
 {
-    product->row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1 + matrix1->row1_col3 * matrix2->row3_col1;
-    product->row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2 + matrix1->row1_col3 * matrix2->row3_col2;
+    product->r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
+    product->r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;
 
-    product->row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1 + matrix1->row2_col3 * matrix2->row3_col1;
-    product->row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2 + matrix1->row2_col3 * matrix2->row3_col2;
+    product->r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
+    product->r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
 }
 
 // ========== Matrix Product 3x2 at 3x3 ========= //
 
 inline void bgc_fp32_multiply_matrix3x2_by_matrix3x3(BGC_FP32_Matrix3x2* product, const BGC_FP32_Matrix3x2* matrix1, const BGC_FP32_Matrix3x3* matrix2)
 {
-    const float row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1 + matrix1->row1_col3 * matrix2->row3_col1;
-    const float row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2 + matrix1->row1_col3 * matrix2->row3_col2;
-    const float row1_col3 = matrix1->row1_col1 * matrix2->row1_col3 + matrix1->row1_col2 * matrix2->row2_col3 + matrix1->row1_col3 * matrix2->row3_col3;
+    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
+    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;
+    const float r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3 + matrix1->r1c3 * matrix2->r3c3;
 
-    const float row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1 + matrix1->row2_col3 * matrix2->row3_col1;
-    const float row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2 + matrix1->row2_col3 * matrix2->row3_col2;
-    const float row2_col3 = matrix1->row2_col1 * matrix2->row1_col3 + matrix1->row2_col2 * matrix2->row2_col3 + matrix1->row2_col3 * matrix2->row3_col3;
+    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
+    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
+    const float r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3 + matrix1->r2c3 * matrix2->r3c3;
 
-    product->row1_col1 = row1_col1;
-    product->row1_col2 = row1_col2;
-    product->row1_col3 = row1_col3;
+    product->r1c1 = r1c1;
+    product->r1c2 = r1c2;
+    product->r1c3 = r1c3;
 
-    product->row2_col1 = row2_col1;
-    product->row2_col2 = row2_col2;
-    product->row2_col3 = row2_col3;
+    product->r2c1 = r2c1;
+    product->r2c2 = r2c2;
+    product->r2c3 = r2c3;
 }
 
 inline void bgc_fp64_multiply_matrix3x2_by_matrix3x3(BGC_FP64_Matrix3x2* product, const BGC_FP64_Matrix3x2* matrix1, const BGC_FP64_Matrix3x3* matrix2)
 {
-    const double row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1 + matrix1->row1_col3 * matrix2->row3_col1;
-    const double row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2 + matrix1->row1_col3 * matrix2->row3_col2;
-    const double row1_col3 = matrix1->row1_col1 * matrix2->row1_col3 + matrix1->row1_col2 * matrix2->row2_col3 + matrix1->row1_col3 * matrix2->row3_col3;
+    const double r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
+    const double r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;
+    const double r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3 + matrix1->r1c3 * matrix2->r3c3;
 
-    const double row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1 + matrix1->row2_col3 * matrix2->row3_col1;
-    const double row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2 + matrix1->row2_col3 * matrix2->row3_col2;
-    const double row2_col3 = matrix1->row2_col1 * matrix2->row1_col3 + matrix1->row2_col2 * matrix2->row2_col3 + matrix1->row2_col3 * matrix2->row3_col3;
+    const double r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
+    const double r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
+    const double r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3 + matrix1->r2c3 * matrix2->r3c3;
 
-    product->row1_col1 = row1_col1;
-    product->row1_col2 = row1_col2;
-    product->row1_col3 = row1_col3;
+    product->r1c1 = r1c1;
+    product->r1c2 = r1c2;
+    product->r1c3 = r1c3;
 
-    product->row2_col1 = row2_col1;
-    product->row2_col2 = row2_col2;
-    product->row2_col3 = row2_col3;
+    product->r2c1 = r2c1;
+    product->r2c2 = r2c2;
+    product->r2c3 = r2c3;
 }
 
 // ========== Matrix Product 3x3 at 2x3 ========= //
 
 inline void bgc_fp32_multiply_matrix3x3_by_matrix2x3(BGC_FP32_Matrix2x3* product, const BGC_FP32_Matrix3x3* matrix1, const BGC_FP32_Matrix2x3* matrix2)
 {
-    const float row1_col1 = matrix1->row1_col1 * matrix2->row1_col1 + matrix1->row1_col2 * matrix2->row2_col1 + matrix1->row1_col3 * matrix2->row3_col1;
-    const float row1_col2 = matrix1->row1_col1 * matrix2->row1_col2 + matrix1->row1_col2 * matrix2->row2_col2 + matrix1->row1_col3 * matrix2->row3_col2;
+    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
+    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;
 
-    const float row2_col1 = matrix1->row2_col1 * matrix2->row1_col1 + matrix1->row2_col2 * matrix2->row2_col1 + matrix1->row2_col3 * matrix2->row3_col1;
-    const float row2_col2 = matrix1->row2_col1 * matrix2->row1_col2 + matrix1->row2_col2 * matrix2->row2_col2 + matrix1->row2_col3 * matrix2->row3_col2;
+    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
+    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
 
-    const float row3_col1 = matrix1->row3_col1 * matrix2->row1_col1 + matrix1->row3_col2 * matrix2->row2_col1 + matrix1->row3_col3 * matrix2->row3_col1;
-    const float row3_col2 = matrix1->row3_col1 * matrix2->row1_col2 + matrix1->row3_col2 * matrix2->row2_col2 + matrix1->row3_col3 * matrix2->row3_col2;
+    const float r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1 + matrix1->r3c3 * matrix2->r3c1;
+    const float r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2 + matrix1->r3c3 * matrix2->r3c2;
 
-    product->row1_col1 = row1_col1;
-    product->row1_col2 = row1_col2;
+    product->r1c1 = r1c1;
+    product->r1c2 = r1c2;
 
-    product->row2_col1 = row2_col1;
-    product->row2_col2 = row2_col2;
+    product->r2c1 = r2c1;
+    product->r2c2 = r2c2;
 
-    product->row3_col1 = row3_col1;
-    product->row3_col2 = row3_col2;
+    product->r3c1 = r3c1;
+    product->r3c2 = r3c2;
 }
 
 inline void bgc_fp64_multiply_matrix3x3_by_matrix2x3(BGC_FP64_Matrix2x3* product, const BGC_FP64_Matrix3x3* matrix1, const BGC_FP64_Matrix2x3* matrix2)
 {