Добавлеие позиционирования и аффинного преобразования для 2-мерного пространства, добавление функций для аффинных преобразований и позиционирования

basic-geometry-dev/basic-geometry-dev.cbp

@@ -42,6 +42,10 @@
 		<Compiler>
 			<Add option="-Wall" />
 		</Compiler>
+		<Unit filename="affine3.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="affine3.h" />
 		<Unit filename="main.c">
 			<Option compilerVar="CC" />
 		</Unit>

basic-geometry/affine2.c

@@ -0,0 +1,28 @@
+#include "affine2.h"
+
+extern inline void bgc_affine2_reset_fp32(BgcAffine2FP32 * affine);
+extern inline void bgc_affine2_reset_fp64(BgcAffine2FP64 * affine);
+
+extern inline void bgc_affine2_make_fp32(const BgcMatrix2x2FP32 * distortion, const BgcVector2FP32 * shift, BgcAffine2FP32 * affine);
+extern inline void bgc_affine2_make_fp64(const BgcMatrix2x2FP64 * distortion, const BgcVector2FP64 * shift, BgcAffine2FP64 * affine);
+
+extern inline void bgc_affine2_copy_fp32(const BgcAffine2FP32 * source, BgcAffine2FP32 * destination);
+extern inline void bgc_affine2_copy_fp64(const BgcAffine2FP64 * source, BgcAffine2FP64 * destination);
+
+extern inline void bgc_affine2_convert_fp64_to_fp32(const BgcAffine2FP64 * source, BgcAffine2FP32 * destination);
+extern inline void bgc_affine2_convert_fp32_to_fp64(const BgcAffine2FP32 * source, BgcAffine2FP64 * destination);
+
+extern inline int bgc_affine2_invert_fp32(BgcAffine2FP32 * affine);
+extern inline int bgc_affine2_invert_fp64(BgcAffine2FP64 * affine);
+
+extern inline int bgc_affine2_get_inverse_fp32(const BgcAffine2FP32 * source, BgcAffine2FP32 * destination);
+extern inline int bgc_affine2_get_inverse_fp64(const BgcAffine2FP64 * source, BgcAffine2FP64 * destination);
+
+extern inline void bgc_affine2_combine_fp32(const BgcAffine2FP32 * parent, const BgcAffine2FP32 * child, BgcAffine2FP32 * combination);
+extern inline void bgc_affine2_combine_fp64(const BgcAffine2FP64 * parent, const BgcAffine2FP64 * child, BgcAffine2FP64 * combination);
+
+extern inline void bgc_affine2_transform_point_fp32(const BgcAffine2FP32 * affine, const BgcVector2FP32 * initial_point, BgcVector2FP32 * transformed_point);
+extern inline void bgc_affine2_transform_point_fp64(const BgcAffine2FP64 * affine, const BgcVector2FP64 * initial_point, BgcVector2FP64 * transformed_point);
+
+extern inline void bgc_affine2_transform_vector_fp32(const BgcAffine2FP32 * affine, const BgcVector2FP32 * initial_vector, BgcVector2FP32 * transformed_vector);
+extern inline void bgc_affine2_transform_vector_fp64(const BgcAffine2FP64 * affine, const BgcVector2FP64 * initial_vector, BgcVector2FP64 * transformed_vector);

basic-geometry/affine2.h

@@ -0,0 +1,175 @@
+#ifndef _BGC_AFFINE2_H_INCLUDED_
+#define _BGC_AFFINE2_H_INCLUDED_
+
+#include "vector2.h"
+#include "matrixes.h"
+#include "matrix2x2.h"
+
+// ==================== Types ==================== //
+
+typedef struct {
+    BgcMatrix2x2FP32 distortion;
+    BgcVector2FP32 shift;
+} BgcAffine2FP32;
+
+typedef struct {
+    BgcMatrix2x2FP64 distortion;
+    BgcVector2FP64 shift;
+} BgcAffine2FP64;
+
+// ==================== Reset ==================== //
+
+inline void bgc_affine2_reset_fp32(BgcAffine2FP32 * affine)
+{
+    bgc_matrix2x2_set_to_identity_fp32(&affine->distortion);
+    bgc_vector2_reset_fp32(&affine->shift);
+}
+
+inline void bgc_affine2_reset_fp64(BgcAffine2FP64 * affine)
+{
+    bgc_matrix2x2_set_to_identity_fp64(&affine->distortion);
+    bgc_vector2_reset_fp64(&affine->shift);
+}
+
+// ==================== Make ===================== //
+
+inline void bgc_affine2_make_fp32(const BgcMatrix2x2FP32 * distortion, const BgcVector2FP32 * shift, BgcAffine2FP32 * affine)
+{
+    bgc_matrix2x2_copy_fp32(distortion, &affine->distortion);
+    bgc_vector2_copy_fp32(shift, &affine->shift);
+}
+
+inline void bgc_affine2_make_fp64(const BgcMatrix2x2FP64 * distortion, const BgcVector2FP64 * shift, BgcAffine2FP64 * affine)
+{
+    bgc_matrix2x2_copy_fp64(distortion, &affine->distortion);
+    bgc_vector2_copy_fp64(shift, &affine->shift);
+}
+
+
+// ==================== Copy ===================== //
+
+inline void bgc_affine2_copy_fp32(const BgcAffine2FP32 * source, BgcAffine2FP32 * destination)
+{
+    bgc_matrix2x2_copy_fp32(&source->distortion, &destination->distortion);
+    bgc_vector2_copy_fp32(&source->shift, &destination->shift);
+}
+
+inline void bgc_affine2_copy_fp64(const BgcAffine2FP64 * source, BgcAffine2FP64 * destination)
+{
+    bgc_matrix2x2_copy_fp64(&source->distortion, &destination->distortion);
+    bgc_vector2_copy_fp64(&source->shift, &destination->shift);
+}
+
+// =================== Convert =================== //
+
+inline void bgc_affine2_convert_fp64_to_fp32(const BgcAffine2FP64 * source, BgcAffine2FP32 * destination)
+{
+    bgc_matrix2x2_convert_fp64_to_fp32(&source->distortion, &destination->distortion);
+    bgc_vector2_convert_fp64_to_fp32(&source->shift, &destination->shift);
+}
+
+inline void bgc_affine2_convert_fp32_to_fp64(const BgcAffine2FP32 * source, BgcAffine2FP64 * destination)
+{
+    bgc_matrix2x2_convert_fp32_to_fp64(&source->distortion, &destination->distortion);
+    bgc_vector2_convert_fp32_to_fp64(&source->shift, &destination->shift);
+}
+
+// =================== Invert ==================== //
+
+inline int bgc_affine2_invert_fp32(BgcAffine2FP32 * affine)
+{
+    if (!bgc_matrix2x2_invert_fp32(&affine->distortion, &affine->distortion)) {
+        return 0;
+    }
+
+    bgc_matrix2x2_get_right_product_fp32(&affine->distortion, &affine->shift, &affine->shift);
+    bgc_vector2_make_opposite_fp32(&affine->shift);
+
+    return 1;
+}
+
+inline int bgc_affine2_invert_fp64(BgcAffine2FP64 * affine)
+{
+    if (!bgc_matrix2x2_invert_fp64(&affine->distortion, &affine->distortion)) {
+        return 0;
+    }
+
+    bgc_matrix2x2_get_right_product_fp64(&affine->distortion, &affine->shift, &affine->shift);
+    bgc_vector2_make_opposite_fp64(&affine->shift);
+
+    return 1;
+}
+
+// ================= Get Inverse ================= //
+
+inline int bgc_affine2_get_inverse_fp32(const BgcAffine2FP32 * source, BgcAffine2FP32 * destination)
+{
+    if (!bgc_matrix2x2_invert_fp32(&source->distortion, &destination->distortion)) {
+        return 0;
+    }
+
+    bgc_matrix2x2_get_right_product_fp32(&destination->distortion, &source->shift, &destination->shift);
+    bgc_vector2_make_opposite_fp32(&destination->shift);
+
+    return 1;
+}
+
+inline int bgc_affine2_get_inverse_fp64(const BgcAffine2FP64 * source, BgcAffine2FP64 * destination)
+{
+    if (!bgc_matrix2x2_invert_fp64(&source->distortion, &destination->distortion)) {
+        return 0;
+    }
+
+    bgc_matrix2x2_get_right_product_fp64(&destination->distortion, &source->shift, &destination->shift);
+    bgc_vector2_make_opposite_fp64(&destination->shift);
+
+    return 1;
+}
+
+// =================== Combine =================== //
+
+inline void bgc_affine2_combine_fp32(const BgcAffine2FP32 * parent, const BgcAffine2FP32 * child, BgcAffine2FP32 * combination)
+{
+    BgcVector2FP32 child_shift;
+    bgc_matrix2x2_get_right_product_fp32(&parent->distortion, &child->shift, &child_shift);
+    bgc_matrix_product_2x2_at_2x2_fp32(&parent->distortion, &child->distortion, &combination->distortion);
+    bgc_vector2_add_fp32(&parent->shift, &child_shift, &combination->shift);
+}
+
+inline void bgc_affine2_combine_fp64(const BgcAffine2FP64 * parent, const BgcAffine2FP64 * child, BgcAffine2FP64 * combination)
+{
+    BgcVector2FP64 child_shift;
+    bgc_matrix2x2_get_right_product_fp64(&parent->distortion, &child->shift, &child_shift);
+    bgc_matrix_product_2x2_at_2x2_fp64(&parent->distortion, &child->distortion, &combination->distortion);
+    bgc_vector2_add_fp64(&parent->shift, &child_shift, &combination->shift);
+}
+
+// =============== Transform Point =============== //
+
+inline void bgc_affine2_transform_point_fp32(const BgcAffine2FP32 * affine, const BgcVector2FP32 * initial_point, BgcVector2FP32 * transformed_point)
+{
+    BgcVector2FP32 distorted;
+    bgc_matrix2x2_get_right_product_fp32(&affine->distortion, initial_point, &distorted);
+    bgc_vector2_add_fp32(&affine->shift, &distorted, transformed_point);
+}
+
+inline void bgc_affine2_transform_point_fp64(const BgcAffine2FP64 * affine, const BgcVector2FP64 * initial_point, BgcVector2FP64 * transformed_point)
+{
+    BgcVector2FP64 distorted;
+    bgc_matrix2x2_get_right_product_fp64(&affine->distortion, initial_point, &distorted);
+    bgc_vector2_add_fp64(&affine->shift, &distorted, transformed_point);
+}
+
+// ============== Transform Vector =============== //
+
+inline void bgc_affine2_transform_vector_fp32(const BgcAffine2FP32 * affine, const BgcVector2FP32 * initial_vector, BgcVector2FP32 * transformed_vector)
+{
+    bgc_matrix2x2_get_right_product_fp32(&affine->distortion, initial_vector, transformed_vector);
+}
+
+inline void bgc_affine2_transform_vector_fp64(const BgcAffine2FP64 * affine, const BgcVector2FP64 * initial_vector, BgcVector2FP64 * transformed_vector)
+{
+    bgc_matrix2x2_get_right_product_fp64(&affine->distortion, initial_vector, transformed_vector);
+}
+
+#endif

basic-geometry/affine3.c

@@ -3,15 +3,21 @@
 extern inline void bgc_affine3_reset_fp32(BgcAffine3FP32 * affine);
 extern inline void bgc_affine3_reset_fp64(BgcAffine3FP64 * affine);
 
-extern inline void bgc_affine3_reset_distortion_fp32(BgcAffine3FP32 * affine);
-extern inline void bgc_affine3_reset_distortion_fp64(BgcAffine3FP64 * affine);
-
-extern inline void bgc_affine3_reset_shift_fp32(BgcAffine3FP32 * affine);
-extern inline void bgc_affine3_reset_shift_fp64(BgcAffine3FP64 * affine);
-
 extern inline void bgc_affine3_make_fp32(const BgcMatrix3x3FP32 * distortion, const BgcVector3FP32 * shift, BgcAffine3FP32 * affine);
 extern inline void bgc_affine3_make_fp64(const BgcMatrix3x3FP64 * distortion, const BgcVector3FP64 * shift, BgcAffine3FP64 * affine);
 
+extern inline void bgc_affine3_copy_fp32(const BgcAffine3FP32 * source, BgcAffine3FP32 * destination);
+extern inline void bgc_affine3_copy_fp64(const BgcAffine3FP64 * source, BgcAffine3FP64 * destination);
+
+extern inline void bgc_affine3_convert_fp64_to_fp32(const BgcAffine3FP64 * source, BgcAffine3FP32 * destination);
+extern inline void bgc_affine3_convert_fp32_to_fp64(const BgcAffine3FP32 * source, BgcAffine3FP64 * destination);
+
+extern inline int bgc_affine3_invert_fp32(BgcAffine3FP32 * affine);
+extern inline int bgc_affine3_invert_fp64(BgcAffine3FP64 * affine);
+
+extern inline int bgc_affine3_get_inverse_fp32(const BgcAffine3FP32 * source, BgcAffine3FP32 * destination);
+extern inline int bgc_affine3_get_inverse_fp64(const BgcAffine3FP64 * source, BgcAffine3FP64 * destination);
+
 extern inline void bgc_affine3_combine_fp32(const BgcAffine3FP32 * parent, const BgcAffine3FP32 * child, BgcAffine3FP32 * combination);
 extern inline void bgc_affine3_combine_fp64(const BgcAffine3FP64 * parent, const BgcAffine3FP64 * child, BgcAffine3FP64 * combination);
 

basic-geometry/affine3.h

@@ -1,7 +1,6 @@
 #ifndef _BGC_AFFINE3_H_INCLUDED_
 #define _BGC_AFFINE3_H_INCLUDED_
 
-#include "utilities.h"
 #include "vector3.h"
 #include "matrixes.h"
 #include "matrix3x3.h"
@@ -9,333 +8,167 @@
 // ==================== Types ==================== //
 
 typedef struct {
-#if BGC_AFFINE_USE_MATRIX
     BgcMatrix3x3FP32 distortion;
     BgcVector3FP32 shift;
-#else
-    float r1c1, r1c2, r1c3, shift1;
-    float r2c1, r2c2, r2c3, shift2;
-    float r3c1, r3c2, r3c3, shift3;
-#endif
 } BgcAffine3FP32;
 
 typedef struct {
-#if BGC_AFFINE_USE_MATRIX
     BgcMatrix3x3FP64 distortion;
     BgcVector3FP64 shift;
-#else
-    double r1c1, r1c2, r1c3, shift1;
-    double r2c1, r2c2, r2c3, shift2;
-    double r3c1, r3c2, r3c3, shift3;
-#endif
 } BgcAffine3FP64;
 
 // ==================== Reset ==================== //
 
 inline void bgc_affine3_reset_fp32(BgcAffine3FP32 * affine)
 {
-#if BGC_AFFINE_USE_MATRIX
     bgc_matrix3x3_set_to_identity_fp32(&affine->distortion);
     bgc_vector3_reset_fp32(&affine->shift);
-#else
-    affine->r1c1 = 1.0f;
-    affine->r1c2 = 0.0f;
-    affine->r1c3 = 0.0f;
-    affine->shift1 = 0.0f;
-
-    affine->r2c1 = 0.0f;
-    affine->r2c2 = 1.0f;
-    affine->r2c3 = 0.0f;
-    affine->shift2 = 0.0f;
-
-    affine->r3c1 = 0.0f;
-    affine->r3c2 = 0.0f;
-    affine->r3c3 = 1.0f;
-    affine->shift3 = 0.0f;
-#endif
 }
 
 inline void bgc_affine3_reset_fp64(BgcAffine3FP64 * affine)
 {
-#if BGC_AFFINE_USE_MATRIX
     bgc_matrix3x3_set_to_identity_fp64(&affine->distortion);
     bgc_vector3_reset_fp64(&affine->shift);
-#else
-    affine->r1c1 = 1.0;
-    affine->r1c2 = 0.0;
-    affine->r1c3 = 0.0;
-    affine->shift1 = 0.0;
-
-    affine->r2c1 = 0.0;
-    affine->r2c2 = 1.0;
-    affine->r2c3 = 0.0;
-    affine->shift2 = 0.0;
-
-    affine->r3c1 = 0.0;
-    affine->r3c2 = 0.0;
-    affine->r3c3 = 1.0;
-    affine->shift3 = 0.0;
-#endif
-}
-
-inline void bgc_affine3_reset_distortion_fp32(BgcAffine3FP32 * affine)
-{
-#if BGC_AFFINE_USE_MATRIX
-    bgc_matrix3x3_set_to_identity_fp32(&affine->distortion);
-#else
-    affine->r1c1 = 1.0f;
-    affine->r1c2 = 0.0f;
-    affine->r1c3 = 0.0f;
-
-    affine->r2c1 = 0.0f;
-    affine->r2c2 = 1.0f;
-    affine->r2c3 = 0.0f;
-
-    affine->r3c1 = 0.0f;
-    affine->r3c2 = 0.0f;
-    affine->r3c3 = 1.0f;
-#endif
-}
-
-inline void bgc_affine3_reset_distortion_fp64(BgcAffine3FP64 * affine)
-{
-#if BGC_AFFINE_USE_MATRIX
-    bgc_matrix3x3_set_to_identity_fp64(&affine->distortion);
-#else
-    affine->r1c1 = 1.0;
-    affine->r1c2 = 0.0;
-    affine->r1c3 = 0.0;
-
-    affine->r2c1 = 0.0;
-    affine->r2c2 = 1.0;
-    affine->r2c3 = 0.0;
-
-    affine->r3c1 = 0.0;
-    affine->r3c2 = 0.0;
-    affine->r3c3 = 1.0;
-#endif
-}
-
-inline void bgc_affine3_reset_shift_fp32(BgcAffine3FP32 * affine)
-{
-#if BGC_AFFINE_USE_MATRIX
-    bgc_vector3_reset_fp32(&affine->shift);
-#else
-    affine->shift1 = 0.0f;
-    affine->shift2 = 0.0f;
-    affine->shift3 = 0.0f;
-#endif
-}
-
-inline void bgc_affine3_reset_shift_fp64(BgcAffine3FP64 * affine)
-{
-#if BGC_AFFINE_USE_MATRIX
-    bgc_vector3_reset_fp64(&affine->shift);
-#else
-    affine->shift1 = 0.0;
-    affine->shift2 = 0.0;
-    affine->shift3 = 0.0;
-#endif
 }
 
 // ==================== Make ===================== //
 
 inline void bgc_affine3_make_fp32(const BgcMatrix3x3FP32 * distortion, const BgcVector3FP32 * shift, BgcAffine3FP32 * affine)
 {
-#if BGC_AFFINE_USE_MATRIX
     bgc_matrix3x3_copy_fp32(distortion, &affine->distortion);
     bgc_vector3_copy_fp32(shift, &affine->shift);
-#else
-    affine->r1c1 = distortion->r1c1;
-    affine->r1c2 = distortion->r1c2;
-    affine->r1c3 = distortion->r1c3;
-    affine->shift1 = shift->x1;
-
-    affine->r2c1 = distortion->r2c1;
-    affine->r2c2 = distortion->r2c2;
-    affine->r2c3 = distortion->r2c3;
-    affine->shift2 = shift->x2;
-
-    affine->r3c1 = distortion->r3c1;
-    affine->r3c2 = distortion->r3c2;
-    affine->r3c3 = distortion->r3c3;
-    affine->shift3 = shift->x3;
-#endif
 }
 
 inline void bgc_affine3_make_fp64(const BgcMatrix3x3FP64 * distortion, const BgcVector3FP64 * shift, BgcAffine3FP64 * affine)
 {
-#if BGC_AFFINE_USE_MATRIX
     bgc_matrix3x3_copy_fp64(distortion, &affine->distortion);
     bgc_vector3_copy_fp64(shift, &affine->shift);
-#else
+}
-    affine->r1c1 = distortion->r1c1;
-    affine->r1c2 = distortion->r1c2;
-    affine->r1c3 = distortion->r1c3;
-    affine->shift1 = shift->x1;
 
-    affine->r2c1 = distortion->r2c1;
+// ==================== Copy ===================== //
-    affine->r2c2 = distortion->r2c2;
-    affine->r2c3 = distortion->r2c3;
-    affine->shift2 = shift->x2;
 
-    affine->r3c1 = distortion->r3c1;
+inline void bgc_affine3_copy_fp32(const BgcAffine3FP32 * source, BgcAffine3FP32 * destination)
-    affine->r3c2 = distortion->r3c2;
+{
-    affine->r3c3 = distortion->r3c3;
+    bgc_matrix3x3_copy_fp32(&source->distortion, &destination->distortion);
-    affine->shift3 = shift->x3;
+    bgc_vector3_copy_fp32(&source->shift, &destination->shift);
-#endif
+}
+
+inline void bgc_affine3_copy_fp64(const BgcAffine3FP64 * source, BgcAffine3FP64 * destination)
+{
+    bgc_matrix3x3_copy_fp64(&source->distortion, &destination->distortion);
+    bgc_vector3_copy_fp64(&source->shift, &destination->shift);
+}
+
+// =================== Convert =================== //
+
+inline void bgc_affine3_convert_fp64_to_fp32(const BgcAffine3FP64 * source, BgcAffine3FP32 * destination)
+{
+    bgc_matrix3x3_convert_fp64_to_fp32(&source->distortion, &destination->distortion);
+    bgc_vector3_convert_fp64_to_fp32(&source->shift, &destination->shift);
+}
+
+inline void bgc_affine3_convert_fp32_to_fp64(const BgcAffine3FP32 * source, BgcAffine3FP64 * destination)
+{
+    bgc_matrix3x3_convert_fp32_to_fp64(&source->distortion, &destination->distortion);
+    bgc_vector3_convert_fp32_to_fp64(&source->shift, &destination->shift);
+}
+
+// =================== Invert ==================== //
+
+inline int bgc_affine3_invert_fp32(BgcAffine3FP32 * affine)
+{
+    if (!bgc_matrix3x3_invert_fp32(&affine->distortion, &affine->distortion)) {
+        return 0;
+    }
+
+    bgc_matrix3x3_get_right_product_fp32(&affine->distortion, &affine->shift, &affine->shift);
+    bgc_vector3_make_opposite_fp32(&affine->shift);
+
+    return 1;
+}
+
+inline int bgc_affine3_invert_fp64(BgcAffine3FP64 * affine)
+{
+    if (!bgc_matrix3x3_invert_fp64(&affine->distortion, &affine->distortion)) {
+        return 0;
+    }
+
+    bgc_matrix3x3_get_right_product_fp64(&affine->distortion, &affine->shift, &affine->shift);
+    bgc_vector3_make_opposite_fp64(&affine->shift);
+
+    return 1;
+}
+
+// ================= Get Inverse ================= //
+
+inline int bgc_affine3_get_inverse_fp32(const BgcAffine3FP32 * source, BgcAffine3FP32 * destination)
+{
+    if (!bgc_matrix3x3_invert_fp32(&source->distortion, &destination->distortion)) {
+        return 0;
+    }
+
+    bgc_matrix3x3_get_right_product_fp32(&destination->distortion, &source->shift, &destination->shift);
+    bgc_vector3_make_opposite_fp32(&destination->shift);
+
+    return 1;
+}
+
+inline int bgc_affine3_get_inverse_fp64(const BgcAffine3FP64 * source, BgcAffine3FP64 * destination)
+{
+    if (!bgc_matrix3x3_invert_fp64(&source->distortion, &destination->distortion)) {
+        return 0;
+    }
+
+    bgc_matrix3x3_get_right_product_fp64(&destination->distortion, &source->shift, &destination->shift);
+    bgc_vector3_make_opposite_fp64(&destination->shift);
+
+    return 1;
 }
 
 // =================== Combine =================== //
 
 inline void bgc_affine3_combine_fp32(const BgcAffine3FP32 * parent, const BgcAffine3FP32 * child, BgcAffine3FP32 * combination)
 {
-#if BGC_AFFINE_USE_MATRIX
     BgcVector3FP32 child_shift;
     bgc_matrix3x3_get_right_product_fp32(&parent->distortion, &child->shift, &child_shift);
     bgc_matrix_product_3x3_at_3x3_fp32(&parent->distortion, &child->distortion, &combination->distortion);
     bgc_vector3_add_fp32(&parent->shift, &child_shift, &combination->shift);
-#else
-    const float r1c1 = parent->r1c1 * child->r1c1 + parent->r1c2 * child->r2c1 + parent->r1c3 * child->r3c1;
-    const float r1c2 = parent->r1c1 * child->r1c2 + parent->r1c2 * child->r2c2 + parent->r1c3 * child->r3c2;
-    const float r1c3 = parent->r1c1 * child->r1c3 + parent->r1c2 * child->r2c3 + parent->r1c3 * child->r3c3;
-
-    const float r2c1 = parent->r2c1 * child->r1c1 + parent->r2c2 * child->r2c1 + parent->r2c3 * child->r3c1;
-    const float r2c2 = parent->r2c1 * child->r1c2 + parent->r2c2 * child->r2c2 + parent->r2c3 * child->r3c2;
-    const float r2c3 = parent->r2c1 * child->r1c3 + parent->r2c2 * child->r2c3 + parent->r2c3 * child->r3c3;
-
-    const float r3c1 = parent->r3c1 * child->r1c1 + parent->r3c2 * child->r2c1 + parent->r3c3 * child->r3c1;
-    const float r3c2 = parent->r3c1 * child->r1c2 + parent->r3c2 * child->r2c2 + parent->r3c3 * child->r3c2;
-    const float r3c3 = parent->r3c1 * child->r1c3 + parent->r3c2 * child->r2c3 + parent->r3c3 * child->r3c3;
-
-    const float shift1 = parent->r1c1 * child->shift1 + parent->r1c2 * child->shift2 + parent->r1c3 * child->shift3;
-    const float shift2 = parent->r2c1 * child->shift1 + parent->r2c2 * child->shift2 + parent->r2c3 * child->shift3;
-    const float shift3 = parent->r3c1 * child->shift1 + parent->r3c2 * child->shift2 + parent->r3c3 * child->shift3;
-
-    combination->r1c1 = r1c1;
-    combination->r1c2 = r1c2;
-    combination->r1c3 = r1c3;
-    combination->shift1 = shift1;
-
-    combination->r2c1 = r2c1;
-    combination->r2c2 = r2c2;
-    combination->r2c3 = r2c3;
-    combination->shift2 = shift2;
-
-    combination->r3c1 = r3c1;
-    combination->r3c2 = r3c2;
-    combination->r3c3 = r3c3;
-    combination->shift3 = shift3;
-#endif
 }
 
 inline void bgc_affine3_combine_fp64(const BgcAffine3FP64 * parent, const BgcAffine3FP64 * child, BgcAffine3FP64 * combination)
 {
-#if BGC_AFFINE_USE_MATRIX
     BgcVector3FP64 child_shift;
     bgc_matrix3x3_get_right_product_fp64(&parent->distortion, &child->shift, &child_shift);
     bgc_matrix_product_3x3_at_3x3_fp64(&parent->distortion, &child->distortion, &combination->distortion);
     bgc_vector3_add_fp64(&parent->shift, &child_shift, &combination->shift);
-#else
-    const double r1c1 = parent->r1c1 * child->r1c1 + parent->r1c2 * child->r2c1 + parent->r1c3 * child->r3c1;
-    const double r1c2 = parent->r1c1 * child->r1c2 + parent->r1c2 * child->r2c2 + parent->r1c3 * child->r3c2;
-    const double r1c3 = parent->r1c1 * child->r1c3 + parent->r1c2 * child->r2c3 + parent->r1c3 * child->r3c3;
-
-    const double r2c1 = parent->r2c1 * child->r1c1 + parent->r2c2 * child->r2c1 + parent->r2c3 * child->r3c1;
-    const double r2c2 = parent->r2c1 * child->r1c2 + parent->r2c2 * child->r2c2 + parent->r2c3 * child->r3c2;
-    const double r2c3 = parent->r2c1 * child->r1c3 + parent->r2c2 * child->r2c3 + parent->r2c3 * child->r3c3;
-
-    const double r3c1 = parent->r3c1 * child->r1c1 + parent->r3c2 * child->r2c1 + parent->r3c3 * child->r3c1;
-    const double r3c2 = parent->r3c1 * child->r1c2 + parent->r3c2 * child->r2c2 + parent->r3c3 * child->r3c2;
-    const double r3c3 = parent->r3c1 * child->r1c3 + parent->r3c2 * child->r2c3 + parent->r3c3 * child->r3c3;
-
-    const double shift1 = parent->r1c1 * child->shift1 + parent->r1c2 * child->shift2 + parent->r1c3 * child->shift3;
-    const double shift2 = parent->r2c1 * child->shift1 + parent->r2c2 * child->shift2 + parent->r2c3 * child->shift3;
-    const double shift3 = parent->r3c1 * child->shift1 + parent->r3c2 * child->shift2 + parent->r3c3 * child->shift3;
-
-    combination->r1c1 = r1c1;
-    combination->r1c2 = r1c2;
-    combination->r1c3 = r1c3;
-    combination->shift1 = shift1;
-
-    combination->r2c1 = r2c1;
-    combination->r2c2 = r2c2;
-    combination->r2c3 = r2c3;
-    combination->shift2 = shift2;
-
-    combination->r3c1 = r3c1;
-    combination->r3c2 = r3c2;
-    combination->r3c3 = r3c3;
-    combination->shift3 = shift3;
-#endif
 }
 
 // =============== Transform Point =============== //
 
 inline void bgc_affine3_transform_point_fp32(const BgcAffine3FP32 * affine, const BgcVector3FP32 * initial_point, BgcVector3FP32 * transformed_point)
 {
-#if BGC_AFFINE_USE_MATRIX
     BgcVector3FP32 distorted;
     bgc_matrix3x3_get_right_product_fp32(&affine->distortion, initial_point, &distorted);
     bgc_vector3_add_fp32(&affine->shift, &distorted, transformed_point);
-#else
-    const float x1 = (affine->r1c1 * initial_point->x1 + affine->r1c2 * initial_point->x2) + (affine->r1c3 * initial_point->x3 + affine->shift1);
-    const float x2 = (affine->r2c1 * initial_point->x1 + affine->r2c2 * initial_point->x2) + (affine->r2c3 * initial_point->x3 + affine->shift2);
-    const float x3 = (affine->r3c1 * initial_point->x1 + affine->r3c2 * initial_point->x2) + (affine->r3c3 * initial_point->x3 + affine->shift3);
-
-    transformed_point->x1 = x1;
-    transformed_point->x2 = x2;
-    transformed_point->x3 = x3;
-#endif
 }
 
 inline void bgc_affine3_transform_point_fp64(const BgcAffine3FP64 * affine, const BgcVector3FP64 * initial_point, BgcVector3FP64 * transformed_point)
 {
-#if BGC_AFFINE_USE_MATRIX
     BgcVector3FP64 distorted;
     bgc_matrix3x3_get_right_product_fp64(&affine->distortion, initial_point, &distorted);
     bgc_vector3_add_fp64(&affine->shift, &distorted, transformed_point);
-#else
-    const double x1 = affine->r1c1 * initial_point->x1 + affine->r1c2 * initial_point->x2 + affine->r1c3 * initial_point->x3 + affine->shift1;
-    const double x2 = affine->r2c1 * initial_point->x1 + affine->r2c2 * initial_point->x2 + affine->r2c3 * initial_point->x3 + affine->shift2;
-    const double x3 = affine->r3c1 * initial_point->x1 + affine->r3c2 * initial_point->x2 + affine->r3c3 * initial_point->x3 + affine->shift3;
-
-    transformed_point->x1 = x1;
-    transformed_point->x2 = x2;
-    transformed_point->x3 = x3;
-#endif
 }
 
 // ============== Transform Vector =============== //
 
 inline void bgc_affine3_transform_vector_fp32(const BgcAffine3FP32 * affine, const BgcVector3FP32 * initial_vector, BgcVector3FP32 * transformed_vector)
 {
-#if BGC_AFFINE_USE_MATRIX
     bgc_matrix3x3_get_right_product_fp32(&affine->distortion, initial_vector, transformed_vector);
-#else
-    const float x1 = affine->r1c1 * initial_vector->x1 + affine->r1c2 * initial_vector->x2 + affine->r1c3 * initial_vector->x3;
-    const float x2 = affine->r2c1 * initial_vector->x1 + affine->r2c2 * initial_vector->x2 + affine->r2c3 * initial_vector->x3;
-    const float x3 = affine->r3c1 * initial_vector->x1 + affine->r3c2 * initial_vector->x2 + affine->r3c3 * initial_vector->x3;
-
-    transformed_vector->x1 = x1;
-    transformed_vector->x2 = x2;
-    transformed_vector->x3 = x3;
-#endif
 }
 
 inline void bgc_affine3_transform_vector_fp64(const BgcAffine3FP64 * affine, const BgcVector3FP64 * initial_vector, BgcVector3FP64 * transformed_vector)
 {
-#if BGC_AFFINE_USE_MATRIX
     bgc_matrix3x3_get_right_product_fp64(&affine->distortion, initial_vector, transformed_vector);
-#else
-    const double x1 = affine->r1c1 * initial_vector->x1 + affine->r1c2 * initial_vector->x2 + affine->r1c3 * initial_vector->x3;
-    const double x2 = affine->r2c1 * initial_vector->x1 + affine->r2c2 * initial_vector->x2 + affine->r2c3 * initial_vector->x3;
-    const double x3 = affine->r3c1 * initial_vector->x1 + affine->r3c2 * initial_vector->x2 + affine->r3c3 * initial_vector->x3;
-
-    transformed_vector->x1 = x1;
-    transformed_vector->x2 = x2;
-    transformed_vector->x3 = x3;
-#endif
 }
 
-#endif // _BGC_AFFINE3_H_INCLUDED_
+#endif

basic-geometry/basic-geometry.cbp

@@ -43,6 +43,14 @@
 				</Linker>
 			</Target>
 		</Build>
+		<Unit filename="affine2.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="affine2.h" />
+		<Unit filename="affine3.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="affine3.h" />
 		<Unit filename="angle.c">
 			<Option compilerVar="CC" />
 		</Unit>
@@ -76,10 +84,14 @@
 			<Option compilerVar="CC" />
 		</Unit>
 		<Unit filename="matrixes.h" />
-		<Unit filename="position.c">
+		<Unit filename="position2.c">
 			<Option compilerVar="CC" />
 		</Unit>
-		<Unit filename="position.h" />
+		<Unit filename="position2.h" />
+		<Unit filename="position3.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="position3.h" />
 		<Unit filename="quaternion.c">
 			<Option compilerVar="CC" />
 		</Unit>

basic-geometry/basic-geometry.h

@@ -14,6 +14,7 @@
 #include "./matrix3x2.h"
 #include "./matrix3x3.h"
 
+#include "./affine2.h"
 #include "./affine3.h"
 
 #include "./complex.h"
@@ -25,6 +26,7 @@
 #include "./versor.h"
 #include "./slerp.h"
 
+#include "./position2.h"
 #include "./position3.h"
 
 #endif

basic-geometry/position2.c

@@ -0,0 +1,40 @@
+#include "position2.h"
+
+extern inline void bgc_position2_reset_fp32(BgcPosition2FP32 * node);
+extern inline void bgc_position2_reset_fp64(BgcPosition2FP64 * node);
+
+extern inline void bgc_position2_make_fp32(const BgcCotesNumberFP32 * turn, const BgcVector2FP32 * shift, BgcPosition2FP32 * position);
+extern inline void bgc_position2_make_fp64(const BgcCotesNumberFP64 * turn, const BgcVector2FP64 * shift, BgcPosition2FP64 * position);
+
+extern inline void bgc_position2_copy_fp32(const BgcPosition2FP32 * source, BgcPosition2FP32 * destination);
+extern inline void bgc_position2_copy_fp64(const BgcPosition2FP64 * source, BgcPosition2FP64 * destination);
+
+extern inline void bgc_position2_convert_fp64_to_fp32(const BgcPosition2FP64 * source, BgcPosition2FP32 * destination);
+extern inline void bgc_position2_convert_fp32_to_fp64(const BgcPosition2FP32 * source, BgcPosition2FP64 * destination);
+
+extern inline void bgc_position2_invert_fp32(BgcPosition2FP32 * position);
+extern inline void bgc_position2_invert_fp64(BgcPosition2FP64 * position);
+
+extern inline void bgc_position2_get_inverse_fp32(const BgcPosition2FP32 * position, BgcPosition2FP32 * inverted);
+extern inline void bgc_position2_get_inverse_fp64(const BgcPosition2FP64 * position, BgcPosition2FP64 * inverted);
+
+extern inline void bgc_position2_combine_fp32(const BgcPosition2FP32 * parent, const BgcPosition2FP32 * child, BgcPosition2FP32 * combination);
+extern inline void bgc_position2_combine_fp64(const BgcPosition2FP64 * parent, const BgcPosition2FP64 * child, BgcPosition2FP64 * combination);
+
+extern inline void bgc_position2_get_outward_affine_fp32(const BgcPosition2FP32 * position, BgcAffine2FP32 * outward_affine_map);
+extern inline void bgc_position2_get_outward_affine_fp64(const BgcPosition2FP64 * position, BgcAffine2FP64 * outward_affine_map);
+
+extern inline void bgc_position2_get_inward_affine_fp32(const BgcPosition2FP32 * position, BgcAffine2FP32 * inward_affine_map);
+extern inline void bgc_position2_get_inward_affine_fp64(const BgcPosition2FP64 * position, BgcAffine2FP64 * inward_affine_map);
+
+extern inline void bgc_position2_transform_point_outwards_fp32(const BgcPosition2FP32 * position, const BgcVector2FP32 * inner_point, BgcVector2FP32 * outer_point);
+extern inline void bgc_position2_transform_point_outwards_fp64(const BgcPosition2FP64 * position, const BgcVector2FP64 * inner_point, BgcVector2FP64 * outer_point);
+
+extern inline void bgc_position2_transform_point_inwards_fp32(const BgcPosition2FP32 * position, const BgcVector2FP32 * outer_point, BgcVector2FP32 * inner_point);
+extern inline void bgc_position2_transform_point_inwards_fp64(const BgcPosition2FP64 * position, const BgcVector2FP64 * outer_point, BgcVector2FP64 * inner_point);
+
+extern inline void bgc_position2_transform_vector_outwards_fp32(const BgcPosition2FP32 * position, const BgcVector2FP32 * inner_vector, BgcVector2FP32 * outer_vector);
+extern inline void bgc_position2_transform_vector_outwards_fp64(const BgcPosition2FP64 * position, const BgcVector2FP64 * inner_vector, BgcVector2FP64 * outer_vector);
+
+extern inline void bgc_position2_transform_vector_inward_fp32(const BgcPosition2FP32 * position, const BgcVector2FP32 * outer_vector, BgcVector2FP32 * inner_vector);
+extern inline void bgc_position2_transform_vector_inward_fp64(const BgcPosition2FP64 * position, const BgcVector2FP64 * outer_vector, BgcVector2FP64 * inner_vector);

basic-geometry/position2.h

@@ -0,0 +1,215 @@
+#ifndef _BGC_POSITION2_H_INCLUDED_
+#define _BGC_POSITION2_H_INCLUDED_
+
+#include "vector2.h"
+#include "affine2.h"
+#include "cotes-number.h"
+
+// ==================== Types ==================== //
+
+typedef struct {
+    BgcCotesNumberFP32 turn;
+    BgcVector2FP32 shift;
+} BgcPosition2FP32;
+
+typedef struct {
+    BgcCotesNumberFP64 turn;
+    BgcVector2FP64 shift;
+} BgcPosition2FP64;
+
+// ==================== Reset ==================== //
+
+inline void bgc_position2_reset_fp32(BgcPosition2FP32 * position)
+{
+    bgc_cotes_number_reset_fp32(&position->turn);
+    bgc_vector2_reset_fp32(&position->shift);
+}
+
+inline void bgc_position2_reset_fp64(BgcPosition2FP64 * position)
+{
+    bgc_cotes_number_reset_fp64(&position->turn);
+    bgc_vector2_reset_fp64(&position->shift);
+}
+
+// ==================== Make ===================== //
+
+inline void bgc_position2_make_fp32(const BgcCotesNumberFP32 * turn, const BgcVector2FP32 * shift, BgcPosition2FP32 * position)
+{
+    bgc_cotes_number_copy_fp32(turn, &position->turn);
+    bgc_vector2_copy_fp32(shift, &position->shift);
+}
+
+inline void bgc_position2_make_fp64(const BgcCotesNumberFP64 * turn, const BgcVector2FP64 * shift, BgcPosition2FP64 * position)
+{
+    bgc_cotes_number_copy_fp64(turn, &position->turn);
+    bgc_vector2_copy_fp64(shift, &position->shift);
+}
+
+
+// ==================== Copy ===================== //
+
+inline void bgc_position2_copy_fp32(const BgcPosition2FP32 * source, BgcPosition2FP32 * destination)
+{
+    bgc_cotes_number_copy_fp32(&source->turn, &destination->turn);
+    bgc_vector2_copy_fp32(&source->shift, &destination->shift);
+}
+
+inline void bgc_position2_copy_fp64(const BgcPosition2FP64 * source, BgcPosition2FP64 * destination)
+{
+    bgc_cotes_number_copy_fp64(&source->turn, &destination->turn);
+    bgc_vector2_copy_fp64(&source->shift, &destination->shift);
+}
+
+// =================== Convert =================== //
+
+inline void bgc_position2_convert_fp64_to_fp32(const BgcPosition2FP64 * source, BgcPosition2FP32 * destination)
+{
+    bgc_cotes_number_convert_fp64_to_fp32(&source->turn, &destination->turn);
+    bgc_vector2_convert_fp64_to_fp32(&source->shift, &destination->shift);
+}
+
+inline void bgc_position2_convert_fp32_to_fp64(const BgcPosition2FP32 * source, BgcPosition2FP64 * destination)
+{
+    bgc_cotes_number_convert_fp32_to_fp64(&source->turn, &destination->turn);
+    bgc_vector2_convert_fp32_to_fp64(&source->shift, &destination->shift);
+}
+
+// =================== Invert ==================== //
+
+inline void bgc_position2_invert_fp32(BgcPosition2FP32 * position)
+{
+    bgc_cotes_number_turn_vector_back_fp32(&position->turn, &position->shift, &position->shift);
+    bgc_cotes_number_invert_fp32(&position->turn);
+    bgc_vector2_make_opposite_fp32(&position->shift);
+}
+
+inline void bgc_position2_invert_fp64(BgcPosition2FP64 * position)
+{
+    bgc_cotes_number_turn_vector_back_fp64(&position->turn, &position->shift, &position->shift);
+    bgc_cotes_number_invert_fp64(&position->turn);
+    bgc_vector2_make_opposite_fp64(&position->shift);
+}
+
+// ================= Get Inverse ================= //
+
+inline void bgc_position2_get_inverse_fp32(const BgcPosition2FP32 * position, BgcPosition2FP32 * inverted)
+{
+    bgc_cotes_number_turn_vector_back_fp32(&position->turn, &position->shift, &inverted->shift);
+    bgc_cotes_number_get_inverse_fp32(&position->turn, &inverted->turn);
+    bgc_vector2_make_opposite_fp32(&inverted->shift);
+}
+
+inline void bgc_position2_get_inverse_fp64(const BgcPosition2FP64 * position, BgcPosition2FP64 * inverted)
+{
+    bgc_cotes_number_turn_vector_back_fp64(&position->turn, &position->shift, &inverted->shift);
+    bgc_cotes_number_get_inverse_fp64(&position->turn, &inverted->turn);
+    bgc_vector2_make_opposite_fp64(&inverted->shift);
+}
+
+// =================== Combine =================== //
+
+inline void bgc_position2_combine_fp32(const BgcPosition2FP32 * parent, const BgcPosition2FP32 * child, BgcPosition2FP32 * combination)
+{
+    BgcVector2FP32 relative_shift;
+    bgc_cotes_number_turn_vector_fp32(&parent->turn, &child->shift, &relative_shift);
+    bgc_cotes_number_combine_fp32(&child->turn, &parent->turn, &combination->turn);
+    bgc_vector2_add_fp32(&parent->shift, &relative_shift, &combination->shift);
+}
+
+inline void bgc_position2_combine_fp64(const BgcPosition2FP64 * parent, const BgcPosition2FP64 * child, BgcPosition2FP64 * combination)
+{
+    BgcVector2FP64 relative_shift;
+    bgc_cotes_number_turn_vector_fp64(&parent->turn, &child->shift, &relative_shift);
+    bgc_cotes_number_combine_fp64(&child->turn, &parent->turn, &combination->turn);
+    bgc_vector2_add_fp64(&parent->shift, &relative_shift, &combination->shift);
+}
+
+// ============= Get Outward Affine ============== //
+
+inline void bgc_position2_get_outward_affine_fp32(const BgcPosition2FP32 * position, BgcAffine2FP32 * outward_affine_map)
+{
+    bgc_cotes_number_get_rotation_matrix_fp32(&position->turn, &outward_affine_map->distortion);
+    bgc_vector2_copy_fp32(&position->shift, &outward_affine_map->shift);
+}
+
+inline void bgc_position2_get_outward_affine_fp64(const BgcPosition2FP64 * position, BgcAffine2FP64 * outward_affine_map)
+{
+    bgc_cotes_number_get_rotation_matrix_fp64(&position->turn, &outward_affine_map->distortion);
+    bgc_vector2_copy_fp64(&position->shift, &outward_affine_map->shift);
+}
+
+// ============== Get Inward Affine ============== //
+
+inline void bgc_position2_get_inward_affine_fp32(const BgcPosition2FP32 * position, BgcAffine2FP32 * inward_affine_map)
+{
+    bgc_cotes_number_get_reverse_matrix_fp32(&position->turn, &inward_affine_map->distortion);
+    bgc_matrix2x2_get_right_product_fp32(&inward_affine_map->distortion, &position->shift, &inward_affine_map->shift);
+    bgc_vector2_make_opposite_fp32(&inward_affine_map->shift);
+}
+
+inline void bgc_position2_get_inward_affine_fp64(const BgcPosition2FP64 * position, BgcAffine2FP64 * inward_affine_map)
+{
+    bgc_cotes_number_get_reverse_matrix_fp64(&position->turn, &inward_affine_map->distortion);
+    bgc_matrix2x2_get_right_product_fp64(&inward_affine_map->distortion, &position->shift, &inward_affine_map->shift);
+    bgc_vector2_make_opposite_fp64(&inward_affine_map->shift);
+}
+
+// ========== Transform Point Outwards =========== //
+
+inline void bgc_position2_transform_point_outwards_fp32(const BgcPosition2FP32 * position, const BgcVector2FP32 * inner_point, BgcVector2FP32 * outer_point)
+{
+    BgcVector2FP32 turned_point;
+    bgc_cotes_number_turn_vector_fp32(&position->turn, inner_point, &turned_point);
+    bgc_vector2_add_fp32(&position->shift, &turned_point, outer_point);
+}
+
+inline void bgc_position2_transform_point_outwards_fp64(const BgcPosition2FP64 * position, const BgcVector2FP64 * inner_point, BgcVector2FP64 * outer_point)
+{
+    BgcVector2FP64 turned_point;
+    bgc_cotes_number_turn_vector_fp64(&position->turn, inner_point, &turned_point);
+    bgc_vector2_add_fp64(&position->shift, &turned_point, outer_point);
+}
+
+// =========== Transform Point Inwards =========== //
+
+inline void bgc_position2_transform_point_inwards_fp32(const BgcPosition2FP32 * position, const BgcVector2FP32 * outer_point, BgcVector2FP32 * inner_point)
+{
+    BgcVector2FP32 relative_point;
+    bgc_vector2_subtract_fp32(outer_point, &position->shift, &relative_point);
+    bgc_cotes_number_turn_vector_back_fp32(&position->turn, &relative_point, inner_point);
+
+}
+
+inline void bgc_position2_transform_point_inwards_fp64(const BgcPosition2FP64 * position, const BgcVector2FP64 * outer_point, BgcVector2FP64 * inner_point)
+{
+    BgcVector2FP64 relative_point;
+    bgc_vector2_subtract_fp64(outer_point, &position->shift, &relative_point);
+    bgc_cotes_number_turn_vector_back_fp64(&position->turn, &relative_point, inner_point);
+
+}
+
+// ========== Transform Vector Outwards ========== //
+
+inline void bgc_position2_transform_vector_outwards_fp32(const BgcPosition2FP32 * position, const BgcVector2FP32 * inner_vector, BgcVector2FP32 * outer_vector)
+{
+    bgc_cotes_number_turn_vector_fp32(&position->turn, inner_vector, outer_vector);
+}
+
+inline void bgc_position2_transform_vector_outwards_fp64(const BgcPosition2FP64 * position, const BgcVector2FP64 * inner_vector, BgcVector2FP64 * outer_vector)
+{
+    bgc_cotes_number_turn_vector_fp64(&position->turn, inner_vector, outer_vector);
+}
+
+// ========== Transform Vector Inwards =========== //
+
+inline void bgc_position2_transform_vector_inward_fp32(const BgcPosition2FP32 * position, const BgcVector2FP32 * outer_vector, BgcVector2FP32 * inner_vector)
+{
+    bgc_cotes_number_turn_vector_back_fp32(&position->turn, outer_vector, inner_vector);
+}
+
+inline void bgc_position2_transform_vector_inward_fp64(const BgcPosition2FP64 * position, const BgcVector2FP64 * outer_vector, BgcVector2FP64 * inner_vector)
+{
+    bgc_cotes_number_turn_vector_back_fp64(&position->turn, outer_vector, inner_vector);
+}
+
+#endif

basic-geometry/position3.c

@@ -6,8 +6,35 @@ extern inline void bgc_position3_reset_fp64(BgcPosition3FP64 * node);
 extern inline void bgc_position3_make_fp32(const BgcVersorFP32 * turn, const BgcVector3FP32 * shift, BgcPosition3FP32 * position);
 extern inline void bgc_position3_make_fp64(const BgcVersorFP64 * turn, const BgcVector3FP64 * shift, BgcPosition3FP64 * position);
 
+extern inline void bgc_position3_copy_fp32(const BgcPosition3FP32 * source, BgcPosition3FP32 * destination);
+extern inline void bgc_position3_copy_fp64(const BgcPosition3FP64 * source, BgcPosition3FP64 * destination);
+
+extern inline void bgc_position3_convert_fp64_to_fp32(const BgcPosition3FP64 * source, BgcPosition3FP32 * destination);
+extern inline void bgc_position3_convert_fp32_to_fp64(const BgcPosition3FP32 * source, BgcPosition3FP64 * destination);
+
+extern inline void bgc_position3_invert_fp32(BgcPosition3FP32 * position);
+extern inline void bgc_position3_invert_fp64(BgcPosition3FP64 * position);
+
+extern inline void bgc_position3_get_inverse_fp32(const BgcPosition3FP32 * position, BgcPosition3FP32 * inverted);
+extern inline void bgc_position3_get_inverse_fp64(const BgcPosition3FP64 * position, BgcPosition3FP64 * inverted);
+
 extern inline void bgc_position3_combine_fp32(const BgcPosition3FP32 * parent, const BgcPosition3FP32 * child, BgcPosition3FP32 * combination);
 extern inline void bgc_position3_combine_fp64(const BgcPosition3FP64 * parent, const BgcPosition3FP64 * child, BgcPosition3FP64 * combination);
 
-extern inline void bgc_position3_get_affine3_map_fp32(const BgcPosition3FP32 * position, BgcAffine3FP32 * affine_map);
+extern inline void bgc_position3_get_outward_affine_fp32(const BgcPosition3FP32 * position, BgcAffine3FP32 * outward_affine_map);
-extern inline void bgc_position3_get_affine3_map_fp64(const BgcPosition3FP64 * position, BgcAffine3FP64 * affine_map);
+extern inline void bgc_position3_get_outward_affine_fp64(const BgcPosition3FP64 * position, BgcAffine3FP64 * outward_affine_map);
+
+extern inline void bgc_position3_get_inward_affine_fp32(const BgcPosition3FP32 * position, BgcAffine3FP32 * inward_affine_map);
+extern inline void bgc_position3_get_inward_affine_fp64(const BgcPosition3FP64 * position, BgcAffine3FP64 * inward_affine_map);
+
+extern inline void bgc_position3_transform_point_outwards_fp32(const BgcPosition3FP32 * position, const BgcVector3FP32 * inner_point, BgcVector3FP32 * outer_point);
+extern inline void bgc_position3_transform_point_outwards_fp64(const BgcPosition3FP64 * position, const BgcVector3FP64 * inner_point, BgcVector3FP64 * outer_point);
+
+extern inline void bgc_position3_transform_point_inwards_fp32(const BgcPosition3FP32 * position, const BgcVector3FP32 * outer_point, BgcVector3FP32 * inner_point);
+extern inline void bgc_position3_transform_point_inwards_fp64(const BgcPosition3FP64 * position, const BgcVector3FP64 * outer_point, BgcVector3FP64 * inner_point);
+
+extern inline void bgc_position3_transform_vector_outwards_fp32(const BgcPosition3FP32 * position, const BgcVector3FP32 * inner_vector, BgcVector3FP32 * outer_vector);
+extern inline void bgc_position3_transform_vector_outwards_fp64(const BgcPosition3FP64 * position, const BgcVector3FP64 * inner_vector, BgcVector3FP64 * outer_vector);
+
+extern inline void bgc_position3_transform_vector_inward_fp32(const BgcPosition3FP32 * position, const BgcVector3FP32 * outer_vector, BgcVector3FP32 * inner_vector);
+extern inline void bgc_position3_transform_vector_inward_fp64(const BgcPosition3FP64 * position, const BgcVector3FP64 * outer_vector, BgcVector3FP64 * inner_vector);

basic-geometry/position3.h

@@ -45,6 +45,66 @@ inline void bgc_position3_make_fp64(const BgcVersorFP64 * turn, const BgcVector3
     bgc_vector3_copy_fp64(shift, &position->shift);
 }
 
+// ==================== Copy ===================== //
+
+inline void bgc_position3_copy_fp32(const BgcPosition3FP32 * source, BgcPosition3FP32 * destination)
+{
+    bgc_versor_copy_fp32(&source->turn, &destination->turn);
+    bgc_vector3_copy_fp32(&source->shift, &destination->shift);
+}
+
+inline void bgc_position3_copy_fp64(const BgcPosition3FP64 * source, BgcPosition3FP64 * destination)
+{
+    bgc_versor_copy_fp64(&source->turn, &destination->turn);
+    bgc_vector3_copy_fp64(&source->shift, &destination->shift);
+}
+
+// =================== Convert =================== //
+
+inline void bgc_position3_convert_fp64_to_fp32(const BgcPosition3FP64 * source, BgcPosition3FP32 * destination)
+{
+    bgc_versor_convert_fp64_to_fp32(&source->turn, &destination->turn);
+    bgc_vector3_convert_fp64_to_fp32(&source->shift, &destination->shift);
+}
+
+inline void bgc_position3_convert_fp32_to_fp64(const BgcPosition3FP32 * source, BgcPosition3FP64 * destination)
+{
+    bgc_versor_convert_fp32_to_fp64(&source->turn, &destination->turn);
+    bgc_vector3_convert_fp32_to_fp64(&source->shift, &destination->shift);
+}
+
+// =================== Invert ==================== //
+
+inline void bgc_position3_invert_fp32(BgcPosition3FP32 * position)
+{
+    bgc_versor_turn_vector_back_fp32(&position->turn, &position->shift, &position->shift);
+    bgc_versor_invert_fp32(&position->turn);
+    bgc_vector3_make_opposite_fp32(&position->shift);
+}
+
+inline void bgc_position3_invert_fp64(BgcPosition3FP64 * position)
+{
+    bgc_versor_turn_vector_back_fp64(&position->turn, &position->shift, &position->shift);
+    bgc_versor_invert_fp64(&position->turn);
+    bgc_vector3_make_opposite_fp64(&position->shift);
+}
+
+// ================= Get Inverse ================= //
+
+inline void bgc_position3_get_inverse_fp32(const BgcPosition3FP32 * position, BgcPosition3FP32 * inverted)
+{
+    bgc_versor_turn_vector_back_fp32(&position->turn, &position->shift, &inverted->shift);
+    bgc_versor_get_inverse_fp32(&position->turn, &inverted->turn);
+    bgc_vector3_make_opposite_fp32(&inverted->shift);
+}
+
+inline void bgc_position3_get_inverse_fp64(const BgcPosition3FP64 * position, BgcPosition3FP64 * inverted)
+{
+    bgc_versor_turn_vector_back_fp64(&position->turn, &position->shift, &inverted->shift);
+    bgc_versor_get_inverse_fp64(&position->turn, &inverted->turn);
+    bgc_vector3_make_opposite_fp64(&inverted->shift);
+}
+
 // =================== Combine =================== //
 
 inline void bgc_position3_combine_fp32(const BgcPosition3FP32 * parent, const BgcPosition3FP32 * child, BgcPosition3FP32 * combination)
@@ -63,78 +123,92 @@ inline void bgc_position3_combine_fp64(const BgcPosition3FP64 * parent, const Bg
     bgc_vector3_add_fp64(&parent->shift, &relative_shift, &combination->shift);
 }
 
-// ================= Get Affine ================== //
+// ============= Get Outward Affine ============== //
 
-inline void bgc_position3_get_affine3_map_fp32(const BgcPosition3FP32 * position, BgcAffine3FP32 * affine_map)
+inline void bgc_position3_get_outward_affine_fp32(const BgcPosition3FP32 * position, BgcAffine3FP32 * outward_affine_map)
 {
-#if BGC_AFFINE_USE_MATRIX
+    bgc_versor_get_rotation_matrix_fp32(&position->turn, &outward_affine_map->distortion);
-    bgc_versor_get_rotation_matrix_fp32(&position->turn, &affine_map->distortion);
+    bgc_vector3_copy_fp32(&position->shift, &outward_affine_map->shift);
-    bgc_vector3_copy_fp32(&position->shift, &affine_map->shift);
-#else
-    const float s0s0 = position->turn._s0 * position->turn._s0;
-    const float x1x1 = position->turn._x1 * position->turn._x1;
-    const float x2x2 = position->turn._x2 * position->turn._x2;
-    const float x3x3 = position->turn._x3 * position->turn._x3;
-
-    const float s0x1 = position->turn._s0 * position->turn._x1;
-    const float s0x2 = position->turn._s0 * position->turn._x2;
-    const float s0x3 = position->turn._s0 * position->turn._x3;
-    const float x1x2 = position->turn._x1 * position->turn._x2;
-    const float x1x3 = position->turn._x1 * position->turn._x3;
-    const float x2x3 = position->turn._x2 * position->turn._x3;
-
-    affine_map->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
-    affine_map->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
-    affine_map->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
-
-    affine_map->r1c2 = 2.0f * (x1x2 - s0x3);
-    affine_map->r2c3 = 2.0f * (x2x3 - s0x1);
-    affine_map->r3c1 = 2.0f * (x1x3 - s0x2);
-
-    affine_map->r2c1 = 2.0f * (x1x2 + s0x3);
-    affine_map->r3c2 = 2.0f * (x2x3 + s0x1);
-    affine_map->r1c3 = 2.0f * (x1x3 + s0x2);
-
-    affine_map->shift1 = position->shift.x1;
-    affine_map->shift2 = position->shift.x2;
-    affine_map->shift3 = position->shift.x3;
-#endif
 }
 
-inline void bgc_position3_get_affine3_map_fp64(const BgcPosition3FP64 * position, BgcAffine3FP64 * affine_map)
+inline void bgc_position3_get_outward_affine_fp64(const BgcPosition3FP64 * position, BgcAffine3FP64 * outward_affine_map)
 {
-#if BGC_AFFINE_USE_MATRIX
+    bgc_versor_get_rotation_matrix_fp64(&position->turn, &outward_affine_map->distortion);
-    bgc_versor_get_rotation_matrix_fp64(&position->turn, &affine_map->distortion);
+    bgc_vector3_copy_fp64(&position->shift, &outward_affine_map->shift);
-    bgc_vector3_copy_fp64(&position->shift, &affine_map->shift);
+}
-#else
-    const double s0s0 = position->turn._s0 * position->turn._s0;
-    const double x1x1 = position->turn._x1 * position->turn._x1;
-    const double x2x2 = position->turn._x2 * position->turn._x2;
-    const double x3x3 = position->turn._x3 * position->turn._x3;
 
-    const double s0x1 = position->turn._s0 * position->turn._x1;
+// ============== Get Inward Affine ============== //
-    const double s0x2 = position->turn._s0 * position->turn._x2;
-    const double s0x3 = position->turn._s0 * position->turn._x3;
-    const double x1x2 = position->turn._x1 * position->turn._x2;
-    const double x1x3 = position->turn._x1 * position->turn._x3;
-    const double x2x3 = position->turn._x2 * position->turn._x3;
 
-    affine_map->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
+inline void bgc_position3_get_inward_affine_fp32(const BgcPosition3FP32 * position, BgcAffine3FP32 * inward_affine_map)
-    affine_map->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
+{
-    affine_map->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
+    bgc_versor_get_reverse_matrix_fp32(&position->turn, &inward_affine_map->distortion);
+    bgc_matrix3x3_get_right_product_fp32(&inward_affine_map->distortion, &position->shift, &inward_affine_map->shift);
+    bgc_vector3_make_opposite_fp32(&inward_affine_map->shift);
+}
 
-    affine_map->r1c2 = 2.0 * (x1x2 - s0x3);
+inline void bgc_position3_get_inward_affine_fp64(const BgcPosition3FP64 * position, BgcAffine3FP64 * inward_affine_map)
-    affine_map->r2c3 = 2.0 * (x2x3 - s0x1);
+{
-    affine_map->r3c1 = 2.0 * (x1x3 - s0x2);
+    bgc_versor_get_reverse_matrix_fp64(&position->turn, &inward_affine_map->distortion);
+    bgc_matrix3x3_get_right_product_fp64(&inward_affine_map->distortion, &position->shift, &inward_affine_map->shift);
+    bgc_vector3_make_opposite_fp64(&inward_affine_map->shift);
+}
 
-    affine_map->r2c1 = 2.0 * (x1x2 + s0x3);
+// ========== Transform Point Outwards =========== //
-    affine_map->r3c2 = 2.0 * (x2x3 + s0x1);
-    affine_map->r1c3 = 2.0 * (x1x3 + s0x2);
 
-    affine_map->shift1 = position->shift.x1;
+inline void bgc_position3_transform_point_outwards_fp32(const BgcPosition3FP32 * position, const BgcVector3FP32 * inner_point, BgcVector3FP32 * outer_point)
-    affine_map->shift2 = position->shift.x2;
+{
-    affine_map->shift3 = position->shift.x3;
+    BgcVector3FP32 turned_point;
-#endif
+    bgc_versor_turn_vector_fp32(&position->turn, inner_point, &turned_point);
+    bgc_vector3_add_fp32(&position->shift, &turned_point, outer_point);
+}
+
+inline void bgc_position3_transform_point_outwards_fp64(const BgcPosition3FP64 * position, const BgcVector3FP64 * inner_point, BgcVector3FP64 * outer_point)
+{
+    BgcVector3FP64 turned_point;
+    bgc_versor_turn_vector_fp64(&position->turn, inner_point, &turned_point);
+    bgc_vector3_add_fp64(&position->shift, &turned_point, outer_point);
+}
+
+// =========== Transform Point Inwards =========== //
+
+inline void bgc_position3_transform_point_inwards_fp32(const BgcPosition3FP32 * position, const BgcVector3FP32 * outer_point, BgcVector3FP32 * inner_point)
+{
+    BgcVector3FP32 relative_point;
+    bgc_vector3_subtract_fp32(outer_point, &position->shift, &relative_point);
+    bgc_versor_turn_vector_back_fp32(&position->turn, &relative_point, inner_point);
+
+}
+
+inline void bgc_position3_transform_point_inwards_fp64(const BgcPosition3FP64 * position, const BgcVector3FP64 * outer_point, BgcVector3FP64 * inner_point)
+{
+    BgcVector3FP64 relative_point;
+    bgc_vector3_subtract_fp64(outer_point, &position->shift, &relative_point);
+    bgc_versor_turn_vector_back_fp64(&position->turn, &relative_point, inner_point);
+
+}
+
+// ========== Transform Vector Outwards ========== //
+
+inline void bgc_position3_transform_vector_outwards_fp32(const BgcPosition3FP32 * position, const BgcVector3FP32 * inner_vector, BgcVector3FP32 * outer_vector)
+{
+    bgc_versor_turn_vector_fp32(&position->turn, inner_vector, outer_vector);
+}
+
+inline void bgc_position3_transform_vector_outwards_fp64(const BgcPosition3FP64 * position, const BgcVector3FP64 * inner_vector, BgcVector3FP64 * outer_vector)
+{
+    bgc_versor_turn_vector_fp64(&position->turn, inner_vector, outer_vector);
+}
+
+// ========== Transform Vector Inwards =========== //
+
+inline void bgc_position3_transform_vector_inward_fp32(const BgcPosition3FP32 * position, const BgcVector3FP32 * outer_vector, BgcVector3FP32 * inner_vector)
+{
+    bgc_versor_turn_vector_back_fp32(&position->turn, outer_vector, inner_vector);
+}
+
+inline void bgc_position3_transform_vector_inward_fp64(const BgcPosition3FP64 * position, const BgcVector3FP64 * outer_vector, BgcVector3FP64 * inner_vector)
+{
+    bgc_versor_turn_vector_back_fp64(&position->turn, outer_vector, inner_vector);
 }
 
 #endif // _BGC_POSITION_H_INCLUDED_

basic-geometry/utilities.h

@@ -46,10 +46,6 @@
 #define BGC_AXIS_REVERSE_X2 -2
 #define BGC_AXIS_REVERSE_X3 -3
 
-#if !defined(BGC_AFFINE_USE_MATRIX)
-#define BGC_AFFINE_USE_MATRIX 1
-#endif
-
 inline int bgc_is_correct_axis(const int axis)
 {
     return axis == BGC_AXIS_X1 || axis == BGC_AXIS_REVERSE_X1