From d8347656c7a69013b73482d5755921c83b24221b Mon Sep 17 00:00:00 2001
From: andrey <9942846+Morgend@users.noreply.github.com>
Date: Mon, 26 Jan 2026 20:00:12 +0700
Subject: [PATCH] =?UTF-8?q?=D0=94=D0=BE=D0=B1=D0=B0=D0=B2=D0=BB=D0=B5?=
 =?UTF-8?q?=D0=BD=D0=B8=D0=B5=20position3=20=D0=B8=20a=D1=84=D1=84=D0=B8?=
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---
 basic-geometry/affine3.c          |  13 ++
 basic-geometry/affine3.h          | 197 ++++++++++++++++++++++++++++++
 basic-geometry/basic-geometry.cbp |   4 +
 basic-geometry/basic-geometry.h   |   4 +
 basic-geometry/position3.c        |  13 ++
 basic-geometry/position3.h        | 140 +++++++++++++++++++++
 basic-geometry/utilities.h        |   4 +
 7 files changed, 375 insertions(+)
 create mode 100644 basic-geometry/affine3.c
 create mode 100644 basic-geometry/affine3.h
 create mode 100644 basic-geometry/position3.c
 create mode 100644 basic-geometry/position3.h

diff --git a/basic-geometry/affine3.c b/basic-geometry/affine3.c
new file mode 100644
index 0000000..89b9970
--- /dev/null
+++ b/basic-geometry/affine3.c
@@ -0,0 +1,13 @@
+#include "affine3.h"
+
+extern inline void bgc_affine3_reset_fp32(BgcAffine3FP32 * affine);
+extern inline void bgc_affine3_reset_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_transform_point_fp32(const BgcAffine3FP32 * affine, const BgcVector3FP32 * initial_point, BgcVector3FP32 * transformed_point);
+extern inline void bgc_affine3_transform_point_fp64(const BgcAffine3FP64 * affine, const BgcVector3FP64 * initial_point, BgcVector3FP64 * transformed_point);
+
+extern inline void bgc_affine3_transform_vector_fp32(const BgcAffine3FP32 * affine, const BgcVector3FP32 * initial_vector, BgcVector3FP32 * transformed_vector);
+extern inline void bgc_affine3_transform_vector_fp64(const BgcAffine3FP64 * affine, const BgcVector3FP64 * initial_vector, BgcVector3FP64 * transformed_vector);
diff --git a/basic-geometry/affine3.h b/basic-geometry/affine3.h
new file mode 100644
index 0000000..8fbcd3a
--- /dev/null
+++ b/basic-geometry/affine3.h
@@ -0,0 +1,197 @@
+#ifndef _BGC_AFFINE3_H_INCLUDED_
+#define _BGC_AFFINE3_H_INCLUDED_
+
+#include "utilities.h"
+#include "vector3.h"
+#include "matrixes.h"
+#include "matrix3x3.h"
+
+// ==================== 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
+}
+
+// ==================== 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;
+    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
+}
+
+// =============== 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_
diff --git a/basic-geometry/basic-geometry.cbp b/basic-geometry/basic-geometry.cbp
index 1dadfea..b906c16 100644
--- a/basic-geometry/basic-geometry.cbp
+++ b/basic-geometry/basic-geometry.cbp
@@ -76,6 +76,10 @@
 			<Option compilerVar="CC" />
 		</Unit>
 		<Unit filename="matrixes.h" />
+		<Unit filename="position.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="position.h" />
 		<Unit filename="quaternion.c">
 			<Option compilerVar="CC" />
 		</Unit>
diff --git a/basic-geometry/basic-geometry.h b/basic-geometry/basic-geometry.h
index fcaf5bb..3da01a8 100644
--- a/basic-geometry/basic-geometry.h
+++ b/basic-geometry/basic-geometry.h
@@ -13,6 +13,8 @@
 #include "./matrix2x3.h"
 #include "./matrix3x2.h"
 #include "./matrix3x3.h"
+
+#include "./affine3.h"
 
 #include "./complex.h"
 #include "./cotes-number.h"
@@ -22,5 +24,7 @@
 #include "./quaternion.h"
 #include "./versor.h"
 #include "./slerp.h"
+
+#include "./position3.h"
 
 #endif
diff --git a/basic-geometry/position3.c b/basic-geometry/position3.c
new file mode 100644
index 0000000..07e1b72
--- /dev/null
+++ b/basic-geometry/position3.c
@@ -0,0 +1,13 @@
+#include "position3.h"
+
+extern inline void bgc_position3_reset_fp32(BgcPosition3FP32 * node);
+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_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_affine3_map_fp64(const BgcPosition3FP64 * position, BgcAffine3FP64 * affine_map);
diff --git a/basic-geometry/position3.h b/basic-geometry/position3.h
new file mode 100644
index 0000000..edfe45c
--- /dev/null
+++ b/basic-geometry/position3.h
@@ -0,0 +1,140 @@
+#ifndef _BGC_POSITION3_H_INCLUDED_
+#define _BGC_POSITION3_H_INCLUDED_
+
+#include "vector3.h"
+#include "affine3.h"
+#include "versor.h"
+
+// ==================== Types ==================== //
+
+typedef struct {
+    BgcVersorFP32 turn;
+    BgcVector3FP32 shift;
+} BgcPosition3FP32;
+
+typedef struct {
+    BgcVersorFP64 turn;
+    BgcVector3FP64 shift;
+} BgcPosition3FP64;
+
+// ==================== Reset ==================== //
+
+inline void bgc_position3_reset_fp32(BgcPosition3FP32 * position)
+{
+    bgc_versor_reset_fp32(&position->turn);
+    bgc_vector3_reset_fp32(&position->shift);
+}
+
+inline void bgc_position3_reset_fp64(BgcPosition3FP64 * position)
+{
+    bgc_versor_reset_fp64(&position->turn);
+    bgc_vector3_reset_fp64(&position->shift);
+}
+
+// ==================== Make ===================== //
+
+inline void bgc_position3_make_fp32(const BgcVersorFP32 * turn, const BgcVector3FP32 * shift, BgcPosition3FP32 * position)
+{
+    bgc_versor_copy_fp32(turn, &position->turn);
+    bgc_vector3_copy_fp32(shift, &position->shift);
+}
+
+inline void bgc_position3_make_fp64(const BgcVersorFP64 * turn, const BgcVector3FP64 * shift, BgcPosition3FP64 * position)
+{
+    bgc_versor_copy_fp64(turn, &position->turn);
+    bgc_vector3_copy_fp64(shift, &position->shift);
+}
+
+// =================== Combine =================== //
+
+inline void bgc_position3_combine_fp32(const BgcPosition3FP32 * parent, const BgcPosition3FP32 * child, BgcPosition3FP32 * combination)
+{
+    BgcVector3FP32 relative_shift;
+    bgc_versor_turn_vector_fp32(&parent->turn, &child->shift, &relative_shift);
+    bgc_versor_combine_fp32(&child->turn, &parent->turn, &combination->turn);
+    bgc_vector3_add_fp32(&parent->shift, &relative_shift, &combination->shift);
+}
+
+inline void bgc_position3_combine_fp64(const BgcPosition3FP64 * parent, const BgcPosition3FP64 * child, BgcPosition3FP64 * combination)
+{
+    BgcVector3FP64 relative_shift;
+    bgc_versor_turn_vector_fp64(&parent->turn, &child->shift, &relative_shift);
+    bgc_versor_combine_fp64(&child->turn, &parent->turn, &combination->turn);
+    bgc_vector3_add_fp64(&parent->shift, &relative_shift, &combination->shift);
+}
+
+// ================= Get Affine ================== //
+
+inline void bgc_position3_get_affine3_map_fp32(const BgcPosition3FP32 * position, BgcAffine3FP32 * affine_map)
+{
+#if BGC_AFFINE_USE_MATRIX
+    bgc_versor_get_rotation_matrix_fp32(&position->turn, &affine_map->distortion);
+    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)
+{
+#if BGC_AFFINE_USE_MATRIX
+    bgc_versor_get_rotation_matrix_fp64(&position->turn, &affine_map->distortion);
+    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;
+    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);
+    affine_map->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
+    affine_map->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
+
+    affine_map->r1c2 = 2.0 * (x1x2 - s0x3);
+    affine_map->r2c3 = 2.0 * (x2x3 - s0x1);
+    affine_map->r3c1 = 2.0 * (x1x3 - s0x2);
+
+    affine_map->r2c1 = 2.0 * (x1x2 + s0x3);
+    affine_map->r3c2 = 2.0 * (x2x3 + s0x1);
+    affine_map->r1c3 = 2.0 * (x1x3 + s0x2);
+
+    affine_map->shift1 = position->shift.x1;
+    affine_map->shift2 = position->shift.x2;
+    affine_map->shift3 = position->shift.x3;
+#endif
+}
+
+#endif // _BGC_POSITION_H_INCLUDED_
diff --git a/basic-geometry/utilities.h b/basic-geometry/utilities.h
index 25ae143..03ad443 100644
--- a/basic-geometry/utilities.h
+++ b/basic-geometry/utilities.h
@@ -46,6 +46,10 @@
 #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