From b0b064de5a83bc20a9084188b5acd4f0c67ae1c7 Mon Sep 17 00:00:00 2001
From: Andrey Pokidov <andrey.pokidov@gmail.com>
Date: Thu, 5 Feb 2026 01:47:52 +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=20=D0=B0=D1=80=D0=B8=D1=84=D0=BC=D0=B5=D1=82?=
 =?UTF-8?q?=D0=B8=D1=87=D0=B5=D1=81=D0=BA=D0=B8=D1=85=20=D0=BE=D0=BF=D0=B5?=
 =?UTF-8?q?=D1=80=D0=B0=D1=86=D0=B8=D0=B9=20=D0=B4=D0=BB=D1=8F=20=D0=B4?=
 =?UTF-8?q?=D1=83=D0=B0=D0=BB=D1=8C=D0=BD=D1=8B=D1=85=20=D0=BA=D0=B2=D0=B0?=
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Content-Transfer-Encoding: 8bit

---
 basic-geometry/angle.h                        |  4 +-
 basic-geometry/basic-geometry.h               | 16 ++---
 basic-geometry/basic-geometry.vcxproj         | 11 ++-
 basic-geometry/basic-geometry.vcxproj.filters | 33 ++++-----
 basic-geometry/complex.h                      |  4 +-
 basic-geometry/dual-number.h                  |  4 +-
 basic-geometry/dual-quaternion.c              | 15 ++++
 basic-geometry/dual-quaternion.h              | 72 ++++++++++++++++++-
 basic-geometry/dual-vector3.c                 |  9 +++
 basic-geometry/dual-vector3.h                 | 18 ++++-
 basic-geometry/matrices.h                     |  4 +-
 basic-geometry/matrix2x2.h                    |  4 +-
 basic-geometry/matrix2x3.h                    |  4 +-
 basic-geometry/matrix3x2.h                    |  4 +-
 basic-geometry/matrix3x3.h                    |  4 +-
 basic-geometry/quaternion.h                   |  4 +-
 basic-geometry/slerp.h                        |  4 +-
 basic-geometry/turn2.h                        |  4 +-
 basic-geometry/turn3.c                        | 23 ++----
 basic-geometry/turn3.h                        |  4 +-
 basic-geometry/types.h                        | 16 -----
 basic-geometry/utilities.h                    |  4 +-
 basic-geometry/vector2.h                      |  4 +-
 basic-geometry/vector3.h                      |  4 +-
 24 files changed, 171 insertions(+), 102 deletions(-)
 delete mode 100644 basic-geometry/types.h

diff --git a/basic-geometry/angle.h b/basic-geometry/angle.h
index a50b599..81bc004 100644
--- a/basic-geometry/angle.h
+++ b/basic-geometry/angle.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_ANGLE_H_
-#define _BGC_ANGLE_H_
+#ifndef _BGC_ANGLE_H_INCLUDED_
+#define _BGC_ANGLE_H_INCLUDED_
 
 #include <math.h>
 #include "utilities.h"
diff --git a/basic-geometry/basic-geometry.h b/basic-geometry/basic-geometry.h
index 2f9726f..e8c4598 100644
--- a/basic-geometry/basic-geometry.h
+++ b/basic-geometry/basic-geometry.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_H_
-#define _BGC_H_
+#ifndef _BGC_H_INCLUDED_
+#define _BGC_H_INCLUDED_
 
 #include "./utilities.h"
 
@@ -18,14 +18,14 @@
 #include "./affine3.h"
 
 #include "./complex.h"
-#include "./quaternion.h"
+#include "./quaternion.h"
 
-#include "./turn2.h"
-#include "./turn3.h"
+#include "./turn2.h"
+#include "./turn3.h"
+
+#include "./position2.h"
+#include "./position3.h"
 
-#include "./position2.h"
-#include "./position3.h"
-
 #include "./slerp.h"
 
 #endif
diff --git a/basic-geometry/basic-geometry.vcxproj b/basic-geometry/basic-geometry.vcxproj
index 8984b17..f392d21 100644
--- a/basic-geometry/basic-geometry.vcxproj
+++ b/basic-geometry/basic-geometry.vcxproj
@@ -24,7 +24,6 @@
     <ClInclude Include="angle.h" />
     <ClInclude Include="basic-geometry.h" />
     <ClInclude Include="complex.h" />
-    <ClInclude Include="cotes-number.h" />
     <ClInclude Include="dual-number.h" />
     <ClInclude Include="dual-quaternion.h" />
     <ClInclude Include="dual-vector3.h" />
@@ -38,11 +37,10 @@
     <ClInclude Include="position2.h" />
     <ClInclude Include="position3.h" />
     <ClInclude Include="quaternion.h" />
-    <ClInclude Include="rotation3.h" />
-    <ClInclude Include="types.h" />
+    <ClInclude Include="turn2.h" />
+    <ClInclude Include="turn3.h" />
     <ClInclude Include="utilities.h" />
     <ClInclude Include="slerp.h" />
-    <ClInclude Include="versor.h" />
     <ClInclude Include="vector2.h" />
     <ClInclude Include="vector3.h" />
   </ItemGroup>
@@ -51,7 +49,6 @@
     <ClCompile Include="affine3.c" />
     <ClCompile Include="angle.c" />
     <ClInclude Include="complex.c" />
-    <ClInclude Include="cotes-number.c" />
     <ClCompile Include="dual-number.c" />
     <ClCompile Include="dual-quaternion.c" />
     <ClCompile Include="dual-vector3.c" />
@@ -59,6 +56,8 @@
     <ClCompile Include="hg-vector3.c" />
     <ClCompile Include="position2.c" />
     <ClCompile Include="position3.c" />
+    <ClCompile Include="turn2.c" />
+    <ClCompile Include="turn3.c" />
     <ClCompile Include="utilities.c" />
     <ClCompile Include="matrix2x2.c" />
     <ClCompile Include="matrix2x3.c" />
@@ -66,9 +65,7 @@
     <ClCompile Include="matrix3x3.c" />
     <ClCompile Include="matrices.c" />
     <ClCompile Include="quaternion.c" />
-    <ClCompile Include="rotation3.c" />
     <ClCompile Include="slerp.c" />
-    <ClCompile Include="versor.c" />
     <ClCompile Include="vector2.c" />
     <ClCompile Include="vector3.c" />
   </ItemGroup>
diff --git a/basic-geometry/basic-geometry.vcxproj.filters b/basic-geometry/basic-geometry.vcxproj.filters
index b855491..1163028 100644
--- a/basic-geometry/basic-geometry.vcxproj.filters
+++ b/basic-geometry/basic-geometry.vcxproj.filters
@@ -21,9 +21,6 @@
     <ClInclude Include="complex.h">
       <Filter>Файлы заголовков</Filter>
     </ClInclude>
-    <ClInclude Include="cotes-number.h">
-      <Filter>Файлы заголовков</Filter>
-    </ClInclude>
     <ClInclude Include="utilities.h">
       <Filter>Файлы заголовков</Filter>
     </ClInclude>
@@ -36,12 +33,6 @@
     <ClInclude Include="matrix3x3.h">
       <Filter>Файлы заголовков</Filter>
     </ClInclude>
-    <ClInclude Include="rotation3.h">
-      <Filter>Файлы заголовков</Filter>
-    </ClInclude>
-    <ClInclude Include="versor.h">
-      <Filter>Файлы заголовков</Filter>
-    </ClInclude>
     <ClInclude Include="vector2.h">
       <Filter>Файлы заголовков</Filter>
     </ClInclude>
@@ -63,15 +54,9 @@
     <ClInclude Include="complex.c">
       <Filter>Исходные файлы</Filter>
     </ClInclude>
-    <ClInclude Include="cotes-number.c">
-      <Filter>Исходные файлы</Filter>
-    </ClInclude>
     <ClInclude Include="slerp.h">
       <Filter>Файлы заголовков</Filter>
     </ClInclude>
-    <ClInclude Include="types.h">
-      <Filter>Файлы заголовков</Filter>
-    </ClInclude>
     <ClInclude Include="affine3.h">
       <Filter>Файлы заголовков</Filter>
     </ClInclude>
@@ -99,6 +84,12 @@
     <ClInclude Include="hg-matrix3x3.h">
       <Filter>Файлы заголовков</Filter>
     </ClInclude>
+    <ClInclude Include="turn2.h">
+      <Filter>Файлы заголовков</Filter>
+    </ClInclude>
+    <ClInclude Include="turn3.h">
+      <Filter>Файлы заголовков</Filter>
+    </ClInclude>
   </ItemGroup>
   <ItemGroup>
     <ClCompile Include="angle.c">
@@ -113,18 +104,12 @@
     <ClCompile Include="matrix3x3.c">
       <Filter>Исходные файлы</Filter>
     </ClCompile>
-    <ClCompile Include="versor.c">
-      <Filter>Исходные файлы</Filter>
-    </ClCompile>
     <ClCompile Include="vector2.c">
       <Filter>Исходные файлы</Filter>
     </ClCompile>
     <ClCompile Include="vector3.c">
       <Filter>Исходные файлы</Filter>
     </ClCompile>
-    <ClCompile Include="rotation3.c">
-      <Filter>Исходные файлы</Filter>
-    </ClCompile>
     <ClCompile Include="quaternion.c">
       <Filter>Исходные файлы</Filter>
     </ClCompile>
@@ -167,5 +152,11 @@
     <ClCompile Include="hg-matrix3x3.c">
       <Filter>Исходные файлы</Filter>
     </ClCompile>
+    <ClCompile Include="turn2.c">
+      <Filter>Исходные файлы</Filter>
+    </ClCompile>
+    <ClCompile Include="turn3.c">
+      <Filter>Исходные файлы</Filter>
+    </ClCompile>
   </ItemGroup>
 </Project>
\ No newline at end of file
diff --git a/basic-geometry/complex.h b/basic-geometry/complex.h
index d1e3587..3209dcb 100644
--- a/basic-geometry/complex.h
+++ b/basic-geometry/complex.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_COMPLEX_H_
-#define _BGC_COMPLEX_H_
+#ifndef _BGC_COMPLEX_H_INCLUDED_
+#define _BGC_COMPLEX_H_INCLUDED_
 
 #include "utilities.h"
 #include "angle.h"
diff --git a/basic-geometry/dual-number.h b/basic-geometry/dual-number.h
index e33169e..98a961a 100644
--- a/basic-geometry/dual-number.h
+++ b/basic-geometry/dual-number.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_DUAL_NUMBER_H_
-#define _BGC_DUAL_NUMBER_H_
+#ifndef _BGC_DUAL_NUMBER_H_INCLUDED_
+#define _BGC_DUAL_NUMBER_H_INCLUDED_
 
 #include "utilities.h"
 
diff --git a/basic-geometry/dual-quaternion.c b/basic-geometry/dual-quaternion.c
index e0362c3..74d8b4c 100644
--- a/basic-geometry/dual-quaternion.c
+++ b/basic-geometry/dual-quaternion.c
@@ -20,3 +20,18 @@ extern inline void bgc_fp64_dual_quaternion_add_scaled(BGC_FP64_DualQuaternion*
 
 extern inline void bgc_fp32_dual_quaternion_subtract(BGC_FP32_DualQuaternion* difference, const BGC_FP32_DualQuaternion* minuend, const BGC_FP32_DualQuaternion* subtrahend);
 extern inline void bgc_fp64_dual_quaternion_subtract(BGC_FP64_DualQuaternion* difference, const BGC_FP64_DualQuaternion* minuend, const BGC_FP64_DualQuaternion* subtrahend);
+
+extern inline void bgc_fp32_dual_quaternion_multiply(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const float multipier);
+extern inline void bgc_fp64_dual_quaternion_multiply(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const double multipier);
+
+extern inline void bgc_fp32_dual_quaternion_divide(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* divident, const float divisor);
+extern inline void bgc_fp64_dual_quaternion_divide(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* divident, const double divisor);
+
+extern inline void bgc_fp32_dual_quaternion_get_mean2(BGC_FP32_DualQuaternion* mean, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2);
+extern inline void bgc_fp64_dual_quaternion_get_mean2(BGC_FP64_DualQuaternion* mean, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2);
+
+extern inline void bgc_fp32_dual_quaternion_get_mean3(BGC_FP32_DualQuaternion* mean, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2, const BGC_FP32_DualQuaternion* quaternion3);
+extern inline void bgc_fp64_dual_quaternion_get_mean3(BGC_FP64_DualQuaternion* mean, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2, const BGC_FP64_DualQuaternion* quaternion3);
+
+extern inline void bgc_fp32_dual_quaternion_interpolate(BGC_FP32_DualQuaternion* interpolation, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2, const float phase);
+extern inline void bgc_fp64_dual_quaternion_interpolate(BGC_FP64_DualQuaternion* interpolation, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2, const double phase);
diff --git a/basic-geometry/dual-quaternion.h b/basic-geometry/dual-quaternion.h
index 6fad794..97784b6 100644
--- a/basic-geometry/dual-quaternion.h
+++ b/basic-geometry/dual-quaternion.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_DUAL_QUATERNION_H_
-#define _BGC_DUAL_QUATERNION_H_
+#ifndef _BGC_DUAL_QUATERNION_H_INCLUDED_
+#define _BGC_DUAL_QUATERNION_H_INCLUDED_
 
 #include "quaternion.h"
 
@@ -111,4 +111,72 @@ inline void bgc_fp64_dual_quaternion_subtract(BGC_FP64_DualQuaternion* differenc
     bgc_fp64_quaternion_subtract(&difference->dual, &minuend->dual, &subtrahend->dual);
 }
 
+// ================== Multiply ================== //
+
+inline void bgc_fp32_dual_quaternion_multiply(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const float multipier)
+{
+    bgc_fp32_quaternion_multiply(&product->real, &multiplicand->real, multipier);
+    bgc_fp32_quaternion_multiply(&product->dual, &multiplicand->dual, multipier);
+}
+
+inline void bgc_fp64_dual_quaternion_multiply(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const double multipier)
+{
+    bgc_fp64_quaternion_multiply(&product->real, &multiplicand->real, multipier);
+    bgc_fp64_quaternion_multiply(&product->dual, &multiplicand->dual, multipier);
+}
+
+// =================== Divide =================== //
+
+inline void bgc_fp32_dual_quaternion_divide(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* divident, const float divisor)
+{
+    bgc_fp32_dual_quaternion_multiply(quotient, divident, 1.0f / divisor);
+}
+
+inline void bgc_fp64_dual_quaternion_divide(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* divident, const double divisor)
+{
+    bgc_fp64_dual_quaternion_multiply(quotient, divident, 1.0 / divisor);
+}
+
+// ================ Mean of Two ================= //
+
+inline void bgc_fp32_dual_quaternion_get_mean2(BGC_FP32_DualQuaternion* mean, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2)
+{
+    bgc_fp32_quaternion_get_mean2(&mean->real, &quaternion1->real, &quaternion2->real);
+    bgc_fp32_quaternion_get_mean2(&mean->dual, &quaternion1->dual, &quaternion2->dual);
+}
+
+inline void bgc_fp64_dual_quaternion_get_mean2(BGC_FP64_DualQuaternion* mean, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2)
+{
+    bgc_fp64_quaternion_get_mean2(&mean->real, &quaternion1->real, &quaternion2->real);
+    bgc_fp64_quaternion_get_mean2(&mean->dual, &quaternion1->dual, &quaternion2->dual);
+}
+
+// =============== Mean of Three ================ //
+
+inline void bgc_fp32_dual_quaternion_get_mean3(BGC_FP32_DualQuaternion* mean, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2, const BGC_FP32_DualQuaternion* quaternion3)
+{
+    bgc_fp32_quaternion_get_mean3(&mean->real, &quaternion1->real, &quaternion2->real, &quaternion3->real);
+    bgc_fp32_quaternion_get_mean3(&mean->dual, &quaternion1->dual, &quaternion2->dual, &quaternion3->dual);
+}
+
+inline void bgc_fp64_dual_quaternion_get_mean3(BGC_FP64_DualQuaternion* mean, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2, const BGC_FP64_DualQuaternion* quaternion3)
+{
+    bgc_fp64_quaternion_get_mean3(&mean->real, &quaternion1->real, &quaternion2->real, &quaternion3->real);
+    bgc_fp64_quaternion_get_mean3(&mean->dual, &quaternion1->dual, &quaternion2->dual, &quaternion3->dual);
+}
+
+// ============ Linear Interpolation ============ //
+
+inline void bgc_fp32_dual_quaternion_interpolate(BGC_FP32_DualQuaternion* interpolation, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2, const float phase)
+{
+    bgc_fp32_quaternion_interpolate(&interpolation->real, &quaternion1->real, &quaternion2->real, phase);
+    bgc_fp32_quaternion_interpolate(&interpolation->dual, &quaternion1->dual, &quaternion2->dual, phase);
+}
+
+inline void bgc_fp64_dual_quaternion_interpolate(BGC_FP64_DualQuaternion* interpolation, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2, const double phase)
+{
+    bgc_fp64_quaternion_interpolate(&interpolation->real, &quaternion1->real, &quaternion2->real, phase);
+    bgc_fp64_quaternion_interpolate(&interpolation->dual, &quaternion1->dual, &quaternion2->dual, phase);
+}
+
 #endif
diff --git a/basic-geometry/dual-vector3.c b/basic-geometry/dual-vector3.c
index 44c5ee3..7e5d379 100644
--- a/basic-geometry/dual-vector3.c
+++ b/basic-geometry/dual-vector3.c
@@ -32,3 +32,12 @@ extern inline void bgc_fp64_dual_vector3_multiply(BGC_FP64_DualVector3* product,
 
 extern inline void bgc_fp32_dual_vector3_divide(BGC_FP32_DualVector3* quotient, const BGC_FP32_DualVector3* dividend, const float divisor);
 extern inline void bgc_fp64_dual_vector3_divide(BGC_FP64_DualVector3* quotient, const BGC_FP64_DualVector3* dividend, const double divisor);
+
+extern inline void bgc_fp32_dual_vector3_get_mean2(BGC_FP32_DualVector3* mean, const BGC_FP32_DualVector3* vector1, const BGC_FP32_DualVector3* vector2);
+extern inline void bgc_fp64_dual_vector3_get_mean2(BGC_FP64_DualVector3* mean, const BGC_FP64_DualVector3* vector1, const BGC_FP64_DualVector3* vector2);
+
+extern inline void bgc_fp32_dual_vector3_get_mean3(BGC_FP32_DualVector3* mean, const BGC_FP32_DualVector3* vector1, const BGC_FP32_DualVector3* vector2, const BGC_FP32_DualVector3* vector3);
+extern inline void bgc_fp64_dual_vector3_get_mean3(BGC_FP64_DualVector3* mean, const BGC_FP64_DualVector3* vector1, const BGC_FP64_DualVector3* vector2, const BGC_FP64_DualVector3* vector3);
+
+extern inline void bgc_fp32_dual_vector3_interpolate(BGC_FP32_DualVector3* interpolation, const BGC_FP32_DualVector3* quaternion1, const BGC_FP32_DualVector3* quaternion2, const float phase);
+extern inline void bgc_fp64_dual_vector3_interpolate(BGC_FP64_DualVector3* interpolation, const BGC_FP64_DualVector3* quaternion1, const BGC_FP64_DualVector3* quaternion2, const double phase);
diff --git a/basic-geometry/dual-vector3.h b/basic-geometry/dual-vector3.h
index 7f3d4bf..b62efaa 100644
--- a/basic-geometry/dual-vector3.h
+++ b/basic-geometry/dual-vector3.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_DUAL_VECTOR3_H_INCLUDE_
-#define _BGC_DUAL_VECTOR3_H_INCLUDE_
+#ifndef _BGC_DUAL_VECTOR3_H_INCLUDED_
+#define _BGC_DUAL_VECTOR3_H_INCLUDED_
 
 #include "./vector3.h"
 
@@ -197,4 +197,18 @@ inline void bgc_fp64_dual_vector3_get_mean3(BGC_FP64_DualVector3* mean, const BG
     bgc_fp64_vector3_get_mean3(&mean->dual, &vector1->dual, &vector2->dual, &vector3->dual);
 }
 
+// ============ Linear Interpolation ============ //
+
+inline void bgc_fp32_dual_vector3_interpolate(BGC_FP32_DualVector3* interpolation, const BGC_FP32_DualVector3* quaternion1, const BGC_FP32_DualVector3* quaternion2, const float phase)
+{
+    bgc_fp32_vector3_interpolate(&interpolation->real, &quaternion1->real, &quaternion2->real, phase);
+    bgc_fp32_vector3_interpolate(&interpolation->dual, &quaternion1->dual, &quaternion2->dual, phase);
+}
+
+inline void bgc_fp64_dual_vector3_interpolate(BGC_FP64_DualVector3* interpolation, const BGC_FP64_DualVector3* quaternion1, const BGC_FP64_DualVector3* quaternion2, const double phase)
+{
+    bgc_fp64_vector3_interpolate(&interpolation->real, &quaternion1->real, &quaternion2->real, phase);
+    bgc_fp64_vector3_interpolate(&interpolation->dual, &quaternion1->dual, &quaternion2->dual, phase);
+}
+
 #endif
diff --git a/basic-geometry/matrices.h b/basic-geometry/matrices.h
index 3f2180e..d500a33 100644
--- a/basic-geometry/matrices.h
+++ b/basic-geometry/matrices.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_MATRICES_H_
-#define _BGC_MATRICES_H_
+#ifndef _BGC_MATRICES_H_INCLUDED_
+#define _BGC_MATRICES_H_INCLUDED_
 
 // ================== Matrix2x2 ================= //
 
diff --git a/basic-geometry/matrix2x2.h b/basic-geometry/matrix2x2.h
index 5a92417..9d7d8e7 100644
--- a/basic-geometry/matrix2x2.h
+++ b/basic-geometry/matrix2x2.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_MATRIX2X2_H_
-#define _BGC_MATRIX2X2_H_
+#ifndef _BGC_MATRIX2X2_H_INCLUDED_
+#define _BGC_MATRIX2X2_H_INCLUDED_
 
 #include "angle.h"
 #include "vector2.h"
diff --git a/basic-geometry/matrix2x3.h b/basic-geometry/matrix2x3.h
index 7093a94..906dfe8 100644
--- a/basic-geometry/matrix2x3.h
+++ b/basic-geometry/matrix2x3.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_MATRIX2X3_H_
-#define _BGC_MATRIX2X3_H_
+#ifndef _BGC_MATRIX2X3_H_INCLUDED_
+#define _BGC_MATRIX2X3_H_INCLUDED_
 
 #include "vector2.h"
 #include "vector3.h"
diff --git a/basic-geometry/matrix3x2.h b/basic-geometry/matrix3x2.h
index b219ddd..693ccfd 100644
--- a/basic-geometry/matrix3x2.h
+++ b/basic-geometry/matrix3x2.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_MATRIX3X2_H_
-#define _BGC_MATRIX3X2_H_
+#ifndef _BGC_MATRIX3X2_H_INCLUDED_
+#define _BGC_MATRIX3X2_H_INCLUDED_
 
 #include "vector2.h"
 #include "vector3.h"
diff --git a/basic-geometry/matrix3x3.h b/basic-geometry/matrix3x3.h
index 18568bd..26450b2 100644
--- a/basic-geometry/matrix3x3.h
+++ b/basic-geometry/matrix3x3.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_MATRIX3X3_H_
-#define _BGC_MATRIX3X3_H_
+#ifndef _BGC_MATRIX3X3_H_INCLUDED_
+#define _BGC_MATRIX3X3_H_INCLUDED_
 
 #include "vector3.h"
 #include "matrices.h"
diff --git a/basic-geometry/quaternion.h b/basic-geometry/quaternion.h
index 87521f1..8de1ccc 100644
--- a/basic-geometry/quaternion.h
+++ b/basic-geometry/quaternion.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_QUATERNION_H_
-#define _BGC_QUATERNION_H_
+#ifndef _BGC_QUATERNION_H_INCLUDED_
+#define _BGC_QUATERNION_H_INCLUDED_
 
 #include <math.h>
 
diff --git a/basic-geometry/slerp.h b/basic-geometry/slerp.h
index ba26246..91dae68 100644
--- a/basic-geometry/slerp.h
+++ b/basic-geometry/slerp.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_VERSOR_SLERP_H_
-#define _BGC_VERSOR_SLERP_H_
+#ifndef _BGC_SLERP_H_INCLUDED_
+#define _BGC_SLERP_H_INCLUDED_
 
 #include "./turn3.h"
 
diff --git a/basic-geometry/turn2.h b/basic-geometry/turn2.h
index fd1e1e6..667d2fc 100644
--- a/basic-geometry/turn2.h
+++ b/basic-geometry/turn2.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_COTES_NUMBER_H_
-#define _BGC_COTES_NUMBER_H_
+#ifndef _BGC_TURN2_H_INCLUDED_
+#define _BGC_TURN2_H_INCLUDED_
 
 #include <math.h>
 
diff --git a/basic-geometry/turn3.c b/basic-geometry/turn3.c
index 64250c4..21570f1 100644
--- a/basic-geometry/turn3.c
+++ b/basic-geometry/turn3.c
@@ -192,7 +192,7 @@ void bgc_fp64_turn3_set_rotation(BGC_FP64_Turn3* turn, const double x1, const do
 
     const double multiplier = sine / sqrt(square_vector);
 
-    bgc_fp64_quaternion_make(&turn->_versor, cosf(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier);
+    bgc_fp64_quaternion_make(&turn->_versor, cos(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier);
 
     const double square_modulus = bgc_fp64_quaternion_get_square_modulus(&turn->_versor);
 
@@ -203,7 +203,7 @@ void bgc_fp64_turn3_set_rotation(BGC_FP64_Turn3* turn, const double x1, const do
 
 // ========= Make Direction Difference ========== //
 
-static int _bgc_fp32_turn3_make_direction_turn(BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* start, const BGC_FP32_Vector3* end, const float square_modulus)
+static int _bgc_fp32_turn3_make_direction_turn(BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* start, const BGC_FP32_Vector3* end, const float square_modulus_product)
 {
     BGC_FP32_Vector3 orthogonal_axis;
 
@@ -213,13 +213,13 @@ static int _bgc_fp32_turn3_make_direction_turn(BGC_FP32_Turn3* turn, const BGC_F
     const float square_modulus = bgc_fp32_vector3_get_square_modulus(&orthogonal_axis);
     const float square_sine = square_modulus / square_modulus_product;
 
-    if (square_sine > BGC_FP64_SQUARE_EPSILON) {
+    if (square_sine > BGC_FP32_SQUARE_EPSILON) {
         const float cosine = scalar_product / sqrtf(square_modulus_product);
-        const float angle = 0.5 * atan2f(sqrtf(square_sine), cosine);
+        const float angle = 0.5f * atan2f(sqrtf(square_sine), cosine);
 
-        const float multiplier = sin(angle) * sqrtf(1.0f / square_modulus);
+        const float multiplier = sinf(angle) * sqrtf(1.0f / square_modulus);
 
-        bgc_fp32_turn3_set_raw_values(versor, cosf(angle), orthogonal_axis.x1 * multiplier, orthogonal_axis.x2 * multiplier, orthogonal_axis.x3 * multiplier);
+        bgc_fp32_turn3_set_raw_values(turn, cosf(angle), orthogonal_axis.x1 * multiplier, orthogonal_axis.x2 * multiplier, orthogonal_axis.x3 * multiplier);
         return BGC_SOME_TURN;
     }
 
@@ -227,7 +227,7 @@ static int _bgc_fp32_turn3_make_direction_turn(BGC_FP32_Turn3* turn, const BGC_F
         return BGC_OPPOSITE;
     }
 
-    bgc_fp32_turn3_reset(versor);
+    bgc_fp32_turn3_reset(turn);
 
     return BGC_ZERO_TURN;
 }
@@ -273,15 +273,6 @@ int bgc_fp32_turn3_find_direction_difference(BGC_FP32_Turn3* difference, const B
         return BGC_ZERO_TURN;
     }
 
-    const double scalar_product = bgc_fp64_vector3_get_dot_product(start, end);
-
-    if () {
-    }
-
-    BGC_FP64_Vector3 orthogonal_axis;
-
-    bgc_fp64_vector3_get_cross_product(&orthogonal_axis, start, end);
-
     return _bgc_fp32_turn3_make_direction_turn(difference, start, end, start_square_modulus * end_square_modulus);
 }
 
diff --git a/basic-geometry/turn3.h b/basic-geometry/turn3.h
index d354054..13d02fe 100644
--- a/basic-geometry/turn3.h
+++ b/basic-geometry/turn3.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_VERSOR_H_
-#define _BGC_VERSOR_H_
+#ifndef _BGC_TURN3_H_INCLUDED_
+#define _BGC_TURN3_H_INCLUDED_
 
 #include <stdint.h>
 
diff --git a/basic-geometry/types.h b/basic-geometry/types.h
deleted file mode 100644
index 7ad6d7f..0000000
--- a/basic-geometry/types.h
+++ /dev/null
@@ -1,16 +0,0 @@
-#ifndef _BGC_TYPES_H_
-#define _BGC_TYPES_H_
-
-// ================== Complex =================== //
-
-typedef struct
-{
-    float real, imaginary;
-} BgcComplexFP32;
-
-typedef struct
-{
-    double real, imaginary;
-} BgcComplexFP64;
-
-#endif
diff --git a/basic-geometry/utilities.h b/basic-geometry/utilities.h
index 9e0a3a9..c315fa6 100644
--- a/basic-geometry/utilities.h
+++ b/basic-geometry/utilities.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_UTILITIES_H_
-#define _BGC_UTILITIES_H_
+#ifndef _BGC_UTILITIES_H_INCLUDED_
+#define _BGC_UTILITIES_H_INCLUDED_
 
 #define BGC_FP32_EPSILON_EFFECTIVENESS_LIMIT 1.0f
 
diff --git a/basic-geometry/vector2.h b/basic-geometry/vector2.h
index 7d7ad2f..7b1b38a 100644
--- a/basic-geometry/vector2.h
+++ b/basic-geometry/vector2.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_VECTOR2_H_
-#define _BGC_VECTOR2_H_
+#ifndef _BGC_VECTOR2_H_INCLUDED_
+#define _BGC_VECTOR2_H_INCLUDED_
 
 #include "utilities.h"
 #include "angle.h"
diff --git a/basic-geometry/vector3.h b/basic-geometry/vector3.h
index 4888d56..3ed50c5 100644
--- a/basic-geometry/vector3.h
+++ b/basic-geometry/vector3.h
@@ -1,5 +1,5 @@
-#ifndef _BGC_VECTOR3_H_
-#define _BGC_VECTOR3_H_
+#ifndef _BGC_VECTOR3_H_INCLUDED_
+#define _BGC_VECTOR3_H_INCLUDED_
 
 #include "utilities.h"
 #include "angle.h"