Добавление функций определения поворотов (versor) между направлениями и базисами

basic-geometry-dev/main.c

@@ -53,12 +53,12 @@ structure_fp32_t* make_structures(const unsigned int amount)
 
 void print_versor_fp32(const BgcVersorFP32* versor)
 {
-    printf("Versor (%f, %f, %f, %f)\n", versor->s0, versor->x1, versor->x2, versor->x3);
+    printf("Versor (s0 = %0.12f, x1 = %0.12f, x2 = %0.12f, x3 = %0.12f)\n", versor->s0, versor->x1, versor->x2, versor->x3);
 }
 
 void print_versor_fp64(const BgcVersorFP64* versor)
 {
-    printf("Versor (%lf, %lf, %lf, %lf)\n", versor->s0, versor->x1, versor->x2, versor->x3);
+    printf("Versor (s0 = %0.20f, x1 = %0.20f, x2 = %0.20f, x3 = %0.20f)\n", versor->s0, versor->x1, versor->x2, versor->x3);
 }
 
 void print_vector_fp32(const BgcVector3FP32* vector)
@@ -149,7 +149,328 @@ int main() {
 }
 */
 
-int main() {
+void test_basis_difference_fp32()
+{
+
+    BgcVector3FP32 initial_primary, initial_auxiliary;
+    BgcVector3FP32 final_primary, final_auxiliary;
+    BgcVersorFP32 turn;
+
+    // No turn
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nNo turn:\n");
+    print_versor_fp32(&turn);
+
+    // Turn around (1, 1, 0) axis on 180 degrees
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nTurn around (1, 1, 0) axis on 180 degrees:\n");
+    print_versor_fp32(&turn);
+
+    // 180 degree turn
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp32(-1.0f, 0.0f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\n180 degree turn around (0, 1, 0):\n");
+    print_versor_fp32(&turn);
+
+    // 90 degree turn around x3 axis
+    bgc_vector3_set_values_fp32(2.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(0.0f, 3.1f, 0.0f, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp32(0.0f, 10.0f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(-1.0f, 0.0f, 0.0f, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\n90 degree turn around (0, 0, 1):\n");
+    print_versor_fp32(&turn);
+
+    // Unorthogonal pairs turn at 90 degrees around x3 axis
+    bgc_vector3_set_values_fp32(2.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(-2.0f, 3.1f, 0.0f, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp32(0.0f, 10.0f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(-1.0f, 5.0f, 0.0f, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nUnorthogonal pairs turn at 90 degrees around (0, 0, 1):\n");
+    print_versor_fp32(&turn);
+
+    // Zero vectors
+    bgc_vector3_set_values_fp32(0.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &initial_auxiliary);
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &final_auxiliary);
+
+    int code;
+
+    code = bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    if (code >= 0) {
+        printf("\nZero vectors: this cannot be!\n");
+        print_versor_fp32(&turn);
+    }
+    else {
+        printf("\nZero vector validation works fine\n");
+    }
+
+    // Parallel vectors
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(2.0f, 0.0f, 0.0f, &initial_auxiliary);
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &final_auxiliary);
+
+    code = bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    if (code >= 0) {
+        printf("\nParallel vectors: this cannot be!\n");
+        print_versor_fp32(&turn);
+    }
+    else {
+        printf("\nParallelism validation works fine\n");
+    }
+
+    // Small angle turn (about 1 degree):
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp32(0.999848f, 0.017452f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(-0.017452f, 0.999848f, 0.0f, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nSmall angle turn (about 1 degree):\n");
+    print_versor_fp32(&turn);
+
+    // About 179 degrees turn
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp32(-0.999848f, -0.017452f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(0.017452f, -0.999848f, 0.0f, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nAbout 179 degrees turn:\n");
+    print_versor_fp32(&turn);
+
+    // 120 degrees around (-1, -1, 1)
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(0.0f, 0.0f, -1.0f, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\n120 degees turn:\n");
+    print_versor_fp32(&turn);
+
+
+    // About 1 degree turn difference between initial_primary and initial_auxiliary directions
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(0.999848f, 0.017452f, 0.0f, &initial_auxiliary);
+    bgc_vector3_set_values_fp32(0.0f, 1.0f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(-1.0f, 0.0f, 0.0f, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nAbout 1 degree turn difference between initial_primary and initial_auxiliary directions:\n");
+    print_versor_fp32(&turn);
+
+    // About 0.01 degree turn difference between initial_primary and initial_auxiliary directions
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &initial_primary);
+    bgc_vector3_set_values_fp32(1.0f, 0.000001f, 0.0f, &initial_auxiliary);
+    bgc_vector3_set_values_fp32(0.0f, -1.0f, 0.0f, &final_primary);
+    bgc_vector3_set_values_fp32(1.0f, 0.0f, 0.0f, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp32(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nAbout 0.01 degree turn difference between initial_primary and initial_auxiliary directions:\n");
+    print_versor_fp32(&turn);
+}
+
+void test_basis_difference_fp64()
+{
+
+    BgcVector3FP64 initial_primary, initial_auxiliary;
+    BgcVector3FP64 final_primary, final_auxiliary;
+    BgcVersorFP64 turn;
+
+    // No turn
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &initial_auxiliary);
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nNo turn:\n");
+    print_versor_fp64(&turn);
+
+    // Turn around (1, 1, 0) axis on 180 degrees
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &initial_auxiliary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nTurn around (1, 1, 0) axis on 180 degrees:\n");
+    print_versor_fp64(&turn);
+
+    // 180 degree turn
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp64(-1.0, 0.0, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\n180 degree turn around (0, 1, 0):\n");
+    print_versor_fp64(&turn);
+
+    // 90 degree turn around x3 axis
+    bgc_vector3_set_values_fp64(2.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(0.0, 3.1, 0.0, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp64(0.0, 10.0, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(-1.0, 0.0, 0.0, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\n90 degree turn around (0, 0, 1):\n");
+    print_versor_fp64(&turn);
+
+    // Unorthogonal pairs turn at 90 degrees around x3 axis
+    bgc_vector3_set_values_fp64(2.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(-2.0, 3.1, 0.0, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp64(0.0, 10.0, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(-1.0, 5.0, 0.0, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nUnorthogonal pairs turn at 90 degrees around (0, 0, 1):\n");
+    print_versor_fp64(&turn);
+
+    // Zero vectors
+    bgc_vector3_set_values_fp64(0.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &initial_auxiliary);
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &final_auxiliary);
+
+    int code;
+
+    code = bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    if (code >= 0) {
+        printf("\nZero vectors: this cannot be!\n");
+        print_versor_fp64(&turn);
+    }
+    else {
+        printf("\nZero vector validation works fine\n");
+    }
+
+    // Parallel vectors
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(2.0, 0.0, 0.0, &initial_auxiliary);
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &final_auxiliary);
+
+    code = bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    if (code >= 0) {
+        printf("\nParallel vectors: this cannot be!\n");
+        print_versor_fp64(&turn);
+    }
+    else {
+        printf("\nParallelism validation works fine\n");
+    }
+
+    // Small angle turn (about 1 degree):
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp64(0.999848, 0.017452, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(-0.017452, 0.999848, 0.0, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nSmall angle turn (about 1 degree):\n");
+    print_versor_fp64(&turn);
+
+    // About 179 degrees turn
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp64(-0.999848, -0.017452, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(0.017452, -0.999848, 0.0, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nAbout 179 degrees turn:\n");
+    print_versor_fp64(&turn);
+
+    // 120 degrees around (-1, -1, 1)
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &initial_auxiliary);
+
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(0.0, 0.0, -1.0, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\n120 degees turn:\n");
+    print_versor_fp64(&turn);
+
+
+    // About 1 degree turn difference between initial_primary and initial_auxiliary directions
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(0.999848, 0.017452, 0.0, &initial_auxiliary);
+    bgc_vector3_set_values_fp64(0.0, 1.0, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(-1.0, 0.0, 0.0, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nAbout 1 degree turn difference between initial_primary and initial_auxiliary directions:\n");
+    print_versor_fp64(&turn);
+
+    // About 0.001 degree turn difference between initial_primary and initial_auxiliary directions
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &initial_primary);
+    bgc_vector3_set_values_fp64(1.0, 0.000001, 0.0, &initial_auxiliary);
+    bgc_vector3_set_values_fp64(0.0, -1.0, 0.0, &final_primary);
+    bgc_vector3_set_values_fp64(1.0, 0.0, 0.0, &final_auxiliary);
+
+    bgc_versor_make_basis_difference_fp64(&initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary, &turn);
+
+    printf("\nAbout 0.01 degree turn difference between initial_primary and initial_auxiliary directions:\n");
+    print_versor_fp64(&turn);
+}
+
+int main()
+{
     //BgcVersorFP32 start = { 1.0f, 0.0f, 0.0f, 0.0f };
     //BgcVersorFP32 end = { 0.0f, 1.0f, 0.0f, 0.0f };
     /*
@@ -162,12 +483,7 @@ int main() {
     printf("Result: %0.12f, %0.12f, %0.12f, %0.12f\n", result.s0, result.x1, result.x2, result.x3);
     */
 
-    BgcVersorFP64 start = { 1.0, 0.0, 0.0, 0.0 };
+    test_basis_difference_fp64();
-    BgcVersorFP64 end = { -0.707, 0.707, 0.0, 0.0 };
+
-    BgcVersorFP64 result;
-    BgcSlerpFP64 slerp;
-    bgc_slerp_make_full_fp64(&start, &end, &slerp);
-    bgc_slerp_get_turn_for_phase_fp64(&slerp, 0.5f, &result);
-    printf("Result: %0.15f, %0.15f, %0.15f, %0.15f\n", result.s0, result.x1, result.x2, result.x3);
     return 0;
 }

basic-geometry/basic-geometry.vcxproj

@@ -21,7 +21,6 @@
   <ItemGroup>
     <ClInclude Include="angle.h" />
     <ClInclude Include="basic-geometry.h" />
-    <ClInclude Include="basis3.h" />
     <ClInclude Include="complex.h" />
     <ClInclude Include="cotes-number.h" />
     <ClInclude Include="matrix2x2.h" />
@@ -41,7 +40,6 @@
     <ClCompile Include="angle.c" />
     <ClInclude Include="complex.c" />
     <ClInclude Include="cotes-number.c" />
-    <ClCompile Include="basis3.c" />
     <ClCompile Include="utilities.c" />
     <ClCompile Include="matrix2x2.c" />
     <ClCompile Include="matrix2x3.c" />

basic-geometry/basic-geometry.vcxproj.filters

@@ -69,9 +69,6 @@
     <ClInclude Include="slerp.h">
       <Filter>Файлы заголовков</Filter>
     </ClInclude>
-    <ClInclude Include="basis3.h">
-      <Filter>Файлы заголовков</Filter>
-    </ClInclude>
   </ItemGroup>
   <ItemGroup>
     <ClCompile Include="angle.c">
@@ -113,8 +110,5 @@
     <ClCompile Include="slerp.c">
       <Filter>Исходные файлы</Filter>
     </ClCompile>
-    <ClCompile Include="basis3.c">
-      <Filter>Исходные файлы</Filter>
-    </ClCompile>
   </ItemGroup>
 </Project>

basic-geometry/basis3.c

@@ -1,232 +0,0 @@
-#include <math.h>
-#include "./basis3.h"
-
-typedef struct {
-    int e1, e2, e3;
-} _BgcBasis3State;
-
-static inline void _bgc_basis3_state_reset(_BgcBasis3State* state)
-{
-    state->e1 = 0;
-    state->e2 = 0;
-    state->e3 = 0;
-}
-
-static inline int _bgc_basis3_validate_directions(const int primary_direction, const int auxiliary_direction)
-{
-    if (!bgc_is_correct_direction(primary_direction)) {
-        return BGC_ERROR_BASIS3_PRIMARY_DIRECTION_UNKNOWN;
-    }
-
-    if (!bgc_is_correct_direction(auxiliary_direction)) {
-        return BGC_ERROR_BASIS3_AUXILIARY_DIRECTION_UNKNOWN;
-    }
-
-    if (primary_direction == auxiliary_direction || primary_direction == -auxiliary_direction) {
-        return BGC_ERROR_BASIS3_PRIMARY_AUXILIARY_PARALLEL;
-    }
-
-    return BGC_SUCCESS;
-}
-
-static inline void _bgc_basis3_load_axis_fp32(const int direction, const BgcVector3FP32* axis, _BgcBasis3State* state, BgcBasis3FP32* basis)
-{
-    switch (direction) {
-    case BGC_DIRECTION_X1:
-        bgc_vector3_copy_fp32(axis, &basis->e1);
-        state->e1 = 1;
-        break;
-
-    case -BGC_DIRECTION_X1:
-        bgc_vector3_reverse_fp32(axis, &basis->e1);
-        state->e1 = 1;
-        break;
-
-    case BGC_DIRECTION_X2:
-        bgc_vector3_copy_fp32(axis, &basis->e2);
-        state->e2 = 1;
-        break;
-
-    case -BGC_DIRECTION_X2:
-        bgc_vector3_reverse_fp32(axis, &basis->e2);
-        state->e2 = 1;
-        break;
-
-    case BGC_DIRECTION_X3:
-        bgc_vector3_copy_fp32(axis, &basis->e3);
-        state->e3 = 1;
-        break;
-
-    case -BGC_DIRECTION_X3:
-        bgc_vector3_reverse_fp32(axis, &basis->e3);
-        state->e3 = 1;
-        break;
-    }
-}
-
-int bgc_basis3_make_from_directions_fp32(
-    const int primary_direction, const BgcVector3FP32* primary_vector,
-    const int auxiliary_direction, const BgcVector3FP32* auxiliary_vector,
-    BgcBasis3FP32* basis
-) {
-    const int direstion_validation_code = _bgc_basis3_validate_directions(primary_direction, auxiliary_direction);
-
-    if (direstion_validation_code != BGC_SUCCESS) {
-        return direstion_validation_code;
-    }
-
-    const float primary_square_modulus = bgc_vector3_get_square_modulus_fp32(primary_vector);
-
-    if (primary_square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
-        return BGC_ERROR_BASIS3_PRIMARY_VECTOR_IS_ZERO;
-    }
-
-    const float auxiliary_square_modulus = bgc_vector3_get_square_modulus_fp32(auxiliary_vector);
-
-    if (auxiliary_square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
-        return BGC_ERROR_BASIS3_AUXILIARY_VECTOR_IS_ZERO;
-    }
-
-    BgcVector3FP32 orthogonal;
-
-    bgc_vector3_get_cross_product_fp32(primary_vector, auxiliary_vector, &orthogonal);
-
-    const float orthogonal_square_modulus = bgc_vector3_get_square_modulus_fp32(&orthogonal);
-
-    if (orthogonal_square_modulus <= BGC_SQUARE_EPSYLON_FP32 * primary_square_modulus * auxiliary_square_modulus) {
-        return BGC_ERROR_BASIS3_PRIMARY_AUXILIARY_PARALLEL;
-    }
-
-    BgcVector3FP32 primary_axis, auxiliary_axis;
-
-    bgc_vector3_multiply_fp32(primary_vector, sqrtf(1.0f / primary_square_modulus), &primary_axis);
-
-    bgc_vector3_subtract_scaled_fp32(auxiliary_vector, &primary_axis, bgc_vector3_get_scalar_product_fp32(auxiliary_vector, &primary_axis), &auxiliary_axis);
-
-    bgc_vector3_multiply_fp32(&auxiliary_axis, sqrtf(1.0f / bgc_vector3_get_square_modulus_fp32(&auxiliary_axis)), &auxiliary_axis);
-
-    _BgcBasis3State state;
-
-    _bgc_basis3_state_reset(&state);
-
-    _bgc_basis3_load_axis_fp32(primary_direction, &primary_axis, &state, basis);
-    _bgc_basis3_load_axis_fp32(auxiliary_direction, &auxiliary_axis, &state, basis);
-
-    if (!state.e1) {
-        bgc_vector3_get_cross_product_fp32(&basis->e2, &basis->e3, &basis->e1);
-        bgc_vector3_normalize_fp32(&basis->e1);
-        return BGC_SUCCESS;
-    }
-
-    if (!state.e2) {
-        bgc_vector3_get_cross_product_fp32(&basis->e3, &basis->e1, &basis->e2);
-        bgc_vector3_normalize_fp32(&basis->e2);
-        return BGC_SUCCESS;
-    }
-
-    bgc_vector3_get_cross_product_fp32(&basis->e1, &basis->e2, &basis->e3);
-    bgc_vector3_normalize_fp32(&basis->e3);
-
-    return BGC_SUCCESS;
-}
-
-static inline void _bgc_basis3_load_axis_fp64(const int direction, const BgcVector3FP64* axis, _BgcBasis3State* state, BgcBasis3FP64* basis)
-{
-    switch (direction) {
-    case BGC_DIRECTION_X1:
-        bgc_vector3_copy_fp64(axis, &basis->e1);
-        state->e1 = 1;
-        break;
-
-    case -BGC_DIRECTION_X1:
-        bgc_vector3_reverse_fp64(axis, &basis->e1);
-        state->e1 = 1;
-        break;
-
-    case BGC_DIRECTION_X2:
-        bgc_vector3_copy_fp64(axis, &basis->e2);
-        state->e2 = 1;
-        break;
-
-    case -BGC_DIRECTION_X2:
-        bgc_vector3_reverse_fp64(axis, &basis->e2);
-        state->e2 = 1;
-        break;
-
-    case BGC_DIRECTION_X3:
-        bgc_vector3_copy_fp64(axis, &basis->e3);
-        state->e3 = 1;
-        break;
-
-    case -BGC_DIRECTION_X3:
-        bgc_vector3_reverse_fp64(axis, &basis->e3);
-        state->e3 = 1;
-        break;
-    }
-}
-
-int bgc_basis3_make_from_directions_fp64(
-    const int primary_direction, const BgcVector3FP64* primary_vector,
-    const int auxiliary_direction, const BgcVector3FP64* auxiliary_vector,
-    BgcBasis3FP64* basis
-) {
-    const int direstion_validation_code = _bgc_basis3_validate_directions(primary_direction, auxiliary_direction);
-
-    if (direstion_validation_code != BGC_SUCCESS) {
-        return direstion_validation_code;
-    }
-