diff --git a/basic-geometry/basic-geometry.vcxproj b/basic-geometry/basic-geometry.vcxproj
index 6c03bb8..5ae2c0c 100644
--- a/basic-geometry/basic-geometry.vcxproj
+++ b/basic-geometry/basic-geometry.vcxproj
@@ -137,6 +137,7 @@
       <PreprocessorDefinitions>WIN32;_DEBUG;_LIB;%(PreprocessorDefinitions)</PreprocessorDefinitions>
       <ConformanceMode>true</ConformanceMode>
       <PrecompiledHeader>NotUsing</PrecompiledHeader>
+      <LanguageStandard_C>stdc11</LanguageStandard_C>
     </ClCompile>
     <Link>
       <SubSystem>
@@ -153,6 +154,7 @@
       <PreprocessorDefinitions>WIN32;NDEBUG;_LIB;%(PreprocessorDefinitions)</PreprocessorDefinitions>
       <ConformanceMode>true</ConformanceMode>
       <PrecompiledHeader>NotUsing</PrecompiledHeader>
+      <LanguageStandard_C>stdc11</LanguageStandard_C>
     </ClCompile>
     <Link>
       <SubSystem>
@@ -169,6 +171,7 @@
       <PreprocessorDefinitions>_DEBUG;_LIB;%(PreprocessorDefinitions)</PreprocessorDefinitions>
       <ConformanceMode>true</ConformanceMode>
       <PrecompiledHeader>NotUsing</PrecompiledHeader>
+      <LanguageStandard_C>stdc11</LanguageStandard_C>
     </ClCompile>
     <Link>
       <SubSystem>
@@ -185,6 +188,7 @@
       <PreprocessorDefinitions>NDEBUG;_LIB;%(PreprocessorDefinitions)</PreprocessorDefinitions>
       <ConformanceMode>true</ConformanceMode>
       <PrecompiledHeader>NotUsing</PrecompiledHeader>
+      <LanguageStandard_C>stdc11</LanguageStandard_C>
     </ClCompile>
     <Link>
       <SubSystem>
diff --git a/basic-geometry/quaternion.c b/basic-geometry/quaternion.c
index 3de43c8..464880e 100644
--- a/basic-geometry/quaternion.c
+++ b/basic-geometry/quaternion.c
@@ -64,8 +64,8 @@ extern inline void _bgc_fp64_restrict_quaternion_multiply_by_quaternion(BGC_FP64
 extern inline void _bgc_fp32_restrict_quaternion_multiply_by_conjugate(BGC_FP32_Quaternion* restrict product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right);
 extern inline void _bgc_fp64_restrict_quaternion_multiply_by_conjugate(BGC_FP64_Quaternion* restrict product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right);
 
-extern inline int bgc_fp32_quaternion_divide_by_real(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* dividend, const float divisor);
-extern inline int bgc_fp64_quaternion_divide_by_real(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* dividend, const double divisor);
+extern inline int bgc_fp32_quaternion_divide_by_real_number(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* dividend, const float divisor);
+extern inline int bgc_fp64_quaternion_divide_by_real_number(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* dividend, const double divisor);
 
 extern inline int bgc_fp32_quaternion_divide_by_quaternion(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* divident, const BGC_FP32_Quaternion* divisor);
 extern inline int bgc_fp64_quaternion_divide_by_quaternion(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* divident, const BGC_FP64_Quaternion* divisor);
diff --git a/basic-geometry/quaternion.h b/basic-geometry/quaternion.h
index 8fab43a..4fec0f8 100644
--- a/basic-geometry/quaternion.h
+++ b/basic-geometry/quaternion.h
@@ -396,7 +396,7 @@ inline void bgc_fp64_quaternion_multiply_by_dual_quaternion(BGC_FP64_DualQuatern
 
 // ============== Divide By Number ============== //
 
-inline int bgc_fp32_quaternion_divide_by_real(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* dividend, const float divisor)
+inline int bgc_fp32_quaternion_divide_by_real_number(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* dividend, const float divisor)
 {
     if (bgc_fp32_is_zero(divisor) || isnan(divisor)) {
         return BGC_FAILURE;
@@ -407,7 +407,7 @@ inline int bgc_fp32_quaternion_divide_by_real(BGC_FP32_Quaternion* quotient, con
     return BGC_SUCCESS;
 }
 
-inline int bgc_fp64_quaternion_divide_by_real(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* dividend, const double divisor)
+inline int bgc_fp64_quaternion_divide_by_real_number(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* dividend, const double divisor)
 {
     if (bgc_fp64_is_zero(divisor) || isnan(divisor)) {
         return BGC_FAILURE;
diff --git a/basic-geometry/rigid-pose3.c b/basic-geometry/rigid-pose3.c
index abe7f05..e2613b3 100644
--- a/basic-geometry/rigid-pose3.c
+++ b/basic-geometry/rigid-pose3.c
@@ -27,6 +27,18 @@ extern inline void bgc_fp64_rigid_pose3_swap(BGC_FP64_RigidPose3* pose1, BGC_FP6
 extern inline void bgc_fp32_rigid_pose3_convert_to_fp64(BGC_FP64_RigidPose3* destination, const BGC_FP32_RigidPose3* source);
 extern inline void bgc_fp64_rigid_pose3_convert_to_fp32(BGC_FP32_RigidPose3* destination, const BGC_FP64_RigidPose3* source);
 
+extern inline void bgc_fp32_rigid_pose3_shorten(BGC_FP32_RigidPose3* pose);
+extern inline void bgc_fp64_rigid_pose3_shorten(BGC_FP64_RigidPose3* pose);
+
+extern inline void bgc_fp32_rigid_pose3_get_shortened(BGC_FP32_RigidPose3* shortened, const BGC_FP32_RigidPose3* pose);
+extern inline void bgc_fp64_rigid_pose3_get_shortened(BGC_FP64_RigidPose3* shortened, const BGC_FP64_RigidPose3* pose);
+
+extern inline void bgc_fp32_rigid_pose3_alternate(BGC_FP32_RigidPose3* pose);
+extern inline void bgc_fp64_rigid_pose3_alternate(BGC_FP64_RigidPose3* pose);
+
+extern inline void bgc_fp32_rigid_pose3_get_alternative(BGC_FP32_RigidPose3* alternative, const BGC_FP32_RigidPose3* pose);
+extern inline void bgc_fp64_rigid_pose3_get_alternative(BGC_FP64_RigidPose3* alternative, const BGC_FP64_RigidPose3* pose);
+
 extern inline void bgc_fp32_rigid_pose3_revert(BGC_FP32_RigidPose3* pose);
 extern inline void bgc_fp64_rigid_pose3_revert(BGC_FP64_RigidPose3* pose);
 
@@ -45,7 +57,14 @@ extern inline void bgc_fp64_rigid_pose3_get_outward_matrix(BGC_FP64_Matrix3x3* m
 extern inline void bgc_fp32_rigid_pose3_get_inward_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_RigidPose3* pose);
 extern inline void bgc_fp64_rigid_pose3_get_inward_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_RigidPose3* pose);
 
-extern inline void bgc_fp32_rigid_pose3_get_outward_affine3(BGC_FP32_Affine3* affine_map, const BGC_FP32_RigidPose3* pose);
-extern inline void bgc_fp64_rigid_pose3_get_outward_affine3(BGC_FP64_Affine3* affine_map, const BGC_FP64_RigidPose3* pose);
+extern inline void bgc_fp32_rigid_pose3_get_outer_shift(BGC_FP32_Vector3* shift, const BGC_FP32_RigidPose3* pose);
+extern inline void bgc_fp64_rigid_pose3_get_outer_shift(BGC_FP64_Vector3* shift, const BGC_FP64_RigidPose3* pose);
 
-extern inline void bgc_fp32_rigid_pose3_get_inward_affine3(BGC_FP32_Affine3* affine_map, const BGC_FP32_RigidPose3* pose);
+extern inline void bgc_fp32_rigid_pose3_get_inner_shift(BGC_FP32_Vector3* shift, const BGC_FP32_RigidPose3* pose);
+extern inline void bgc_fp64_rigid_pose3_get_inner_shift(BGC_FP64_Vector3* shift, const BGC_FP64_RigidPose3* pose);
+
+extern inline void bgc_fp32_rigid_pose3_get_outward_affine(BGC_FP32_Affine3* affine_map, const BGC_FP32_RigidPose3* pose);
+extern inline void bgc_fp64_rigid_pose3_get_outward_affine(BGC_FP64_Affine3* affine_map, const BGC_FP64_RigidPose3* pose);
+
+extern inline void bgc_fp32_rigid_pose3_get_inward_affine(BGC_FP32_Affine3* affine_map, const BGC_FP32_RigidPose3* pose);
+extern inline void bgc_fp64_rigid_pose3_get_inward_affine(BGC_FP64_Affine3* affine_map, const BGC_FP64_RigidPose3* pose);
diff --git a/basic-geometry/rigid-pose3.h b/basic-geometry/rigid-pose3.h
index 13e0ddd..80a4663 100644
--- a/basic-geometry/rigid-pose3.h
+++ b/basic-geometry/rigid-pose3.h
@@ -95,13 +95,13 @@ inline void bgc_fp64_rigid_pose3_get_dual_quaternion(BGC_FP64_DualQuaternion* qu
 inline void bgc_fp32_rigid_pose3_set_dual_quaternion(BGC_FP32_RigidPose3* pose, const BGC_FP32_DualQuaternion* quaternion)
 {
     bgc_fp32_dual_quaternion_copy(&pose->_versor, quaternion);
-    _bgc_fp32_rigid_pose3_normalize(destination);
+    _bgc_fp32_rigid_pose3_normalize(pose);
 }
 
 inline void bgc_fp64_rigid_pose3_set_dual_quaternion(BGC_FP64_RigidPose3* pose, const BGC_FP64_DualQuaternion* quaternion)
 {
     bgc_fp64_dual_quaternion_copy(&pose->_versor, quaternion);
-    _bgc_fp64_rigid_pose3_normalize(destination);
+    _bgc_fp64_rigid_pose3_normalize(pose);
 }
 
 // =============== Get Real Part ================ //
@@ -166,6 +166,78 @@ inline void bgc_fp64_rigid_pose3_convert_to_fp32(BGC_FP32_RigidPose3* destinatio
     _bgc_fp32_rigid_pose3_normalize(destination);
 }
 
+// ================== Shorten =================== //
+
+inline void bgc_fp32_rigid_pose3_shorten(BGC_FP32_RigidPose3* pose)
+{
+    if (pose->_versor.real_part.s0 < 0.0f) {
+        bgc_fp32_quaternion_revert(&pose->_versor.real_part);
+        bgc_fp32_quaternion_revert(&pose->_versor.dual_part);
+    }
+}
+
+inline void bgc_fp64_rigid_pose3_shorten(BGC_FP64_RigidPose3* pose)
+{
+    if (pose->_versor.real_part.s0 < 0.0) {
+        bgc_fp64_quaternion_revert(&pose->_versor.real_part);
+        bgc_fp64_quaternion_revert(&pose->_versor.dual_part);
+    }
+}
+
+// =============== Get Shortened ================ //
+
+inline void bgc_fp32_rigid_pose3_get_shortened(BGC_FP32_RigidPose3* shortened, const BGC_FP32_RigidPose3* pose)
+{
+    if (pose->_versor.real_part.s0 < 0.0f) {
+        bgc_fp32_quaternion_get_reverse(&shortened->_versor.real_part, &pose->_versor.real_part);
+        bgc_fp32_quaternion_get_reverse(&shortened->_versor.dual_part, &pose->_versor.dual_part);
+    }
+    else {
+        bgc_fp32_quaternion_copy(&shortened->_versor.real_part, &pose->_versor.real_part);
+        bgc_fp32_quaternion_copy(&shortened->_versor.dual_part, &pose->_versor.dual_part);
+    }
+}
+
+inline void bgc_fp64_rigid_pose3_get_shortened(BGC_FP64_RigidPose3* shortened, const BGC_FP64_RigidPose3* pose)
+{
+    if (pose->_versor.real_part.s0 < 0.0) {
+        bgc_fp64_quaternion_get_reverse(&shortened->_versor.real_part, &pose->_versor.real_part);
+        bgc_fp64_quaternion_get_reverse(&shortened->_versor.dual_part, &pose->_versor.dual_part);
+    }
+    else {
+        bgc_fp64_quaternion_copy(&shortened->_versor.real_part, &pose->_versor.real_part);
+        bgc_fp64_quaternion_copy(&shortened->_versor.dual_part, &pose->_versor.dual_part);
+    }
+}
+
+// ================= Alternate ================== //
+
+inline void bgc_fp32_rigid_pose3_alternate(BGC_FP32_RigidPose3* pose)
+{
+    bgc_fp32_quaternion_revert(&pose->_versor.real_part);
+    bgc_fp32_quaternion_revert(&pose->_versor.dual_part);
+}
+
+inline void bgc_fp64_rigid_pose3_alternate(BGC_FP64_RigidPose3* pose)
+{
+    bgc_fp64_quaternion_revert(&pose->_versor.real_part);
+    bgc_fp64_quaternion_revert(&pose->_versor.dual_part);
+}
+
+// ============== Get Alternative =============== //
+
+inline void bgc_fp32_rigid_pose3_get_alternative(BGC_FP32_RigidPose3* alternative, const BGC_FP32_RigidPose3* pose)
+{
+    bgc_fp32_quaternion_get_reverse(&alternative->_versor.real_part, &pose->_versor.real_part);
+    bgc_fp32_quaternion_get_reverse(&alternative->_versor.dual_part, &pose->_versor.dual_part);
+}
+
+inline void bgc_fp64_rigid_pose3_get_alternative(BGC_FP64_RigidPose3* alternative, const BGC_FP64_RigidPose3* pose)
+{
+    bgc_fp64_quaternion_get_reverse(&alternative->_versor.real_part, &pose->_versor.real_part);
+    bgc_fp64_quaternion_get_reverse(&alternative->_versor.dual_part, &pose->_versor.dual_part);
+}
+
 // =================== Revert =================== //
 
 inline void bgc_fp32_rigid_pose3_revert(BGC_FP32_RigidPose3* pose)
@@ -260,42 +332,76 @@ inline void bgc_fp64_rigid_pose3_get_inward_matrix(BGC_FP64_Matrix3x3* matrix, c
     _bgc_fp64_versor_get_reverse_matrix(matrix, &pose->_versor.real_part);
 }
 
-// ============ Get Outward Affine3 ============= //
+// ============== Get Outer Shift =============== //
 
-inline void bgc_fp32_rigid_pose3_get_outward_affine3(BGC_FP32_Affine3* affine_map, const BGC_FP32_RigidPose3* pose)
+inline void bgc_fp32_rigid_pose3_get_outer_shift(BGC_FP32_Vector3* shift, const BGC_FP32_RigidPose3* pose)
 {
-    _bgc_fp32_versor_get_rotation_matrix(&affine_map->distortion, &pose->_versor.real_part);
+    const BGC_FP32_Quaternion* const real = &pose->_versor.real_part;
+    const BGC_FP32_Quaternion* const dual = &pose->_versor.dual_part;
 
-    const BGC_FP32_Quaternion * real = &pose->_versor.real_part;
-    const BGC_FP32_Quaternion * dual = &pose->_versor.dual_part;
-
-    affine_map->shift.x1 = (dual->x1 * real->s0 + dual->x3 * real->x2) - (dual->s0 * real->x1 + dual->x2 * real->x3);
-    affine_map->shift.x2 = (dual->x2 * real->s0 + dual->x1 * real->x3) - (dual->s0 * real->x2 + dual->x3 * real->x1);
-    affine_map->shift.x3 = (dual->x3 * real->s0 + dual->x2 * real->x1) - (dual->s0 * real->x3 + dual->x1 * real->x2);
+    shift->x1 = 2.0f * ((dual->x1 * real->s0 + dual->x3 * real->x2) - (dual->s0 * real->x1 + dual->x2 * real->x3));
+    shift->x2 = 2.0f * ((dual->x2 * real->s0 + dual->x1 * real->x3) - (dual->s0 * real->x2 + dual->x3 * real->x1));
+    shift->x3 = 2.0f * ((dual->x3 * real->s0 + dual->x2 * real->x1) - (dual->s0 * real->x3 + dual->x1 * real->x2));
 }
 
-inline void bgc_fp64_rigid_pose3_get_outward_affine3(BGC_FP64_Affine3* affine_map, const BGC_FP64_RigidPose3* pose)
+inline void bgc_fp64_rigid_pose3_get_outer_shift(BGC_FP64_Vector3* shift, const BGC_FP64_RigidPose3* pose)
+{
+    const BGC_FP64_Quaternion* const real = &pose->_versor.real_part;
+    const BGC_FP64_Quaternion* const dual = &pose->_versor.dual_part;
+
+    shift->x1 = 2.0 * ((dual->x1 * real->s0 + dual->x3 * real->x2) - (dual->s0 * real->x1 + dual->x2 * real->x3));
+    shift->x2 = 2.0 * ((dual->x2 * real->s0 + dual->x1 * real->x3) - (dual->s0 * real->x2 + dual->x3 * real->x1));
+    shift->x3 = 2.0 * ((dual->x3 * real->s0 + dual->x2 * real->x1) - (dual->s0 * real->x3 + dual->x1 * real->x2));
+}
+
+// ============== Get Inner Shift ============== //
+
+inline void bgc_fp32_rigid_pose3_get_inner_shift(BGC_FP32_Vector3* shift, const BGC_FP32_RigidPose3* pose)
+{
+    const BGC_FP32_Quaternion* const real = &pose->_versor.real_part;
+    const BGC_FP32_Quaternion* const dual = &pose->_versor.dual_part;
+
+    shift->x1 = 2.0f * ((dual->s0 * real->x1 - dual->x1 * real->s0) + (dual->x3 * real->x2 - dual->x2 * real->x3));
+    shift->x2 = 2.0f * ((dual->s0 * real->x2 - dual->x2 * real->s0) + (dual->x1 * real->x3 - dual->x3 * real->x1));
+    shift->x3 = 2.0f * ((dual->s0 * real->x3 - dual->x3 * real->s0) + (dual->x2 * real->x1 - dual->x1 * real->x2));
+}
+
+inline void bgc_fp64_rigid_pose3_get_inner_shift(BGC_FP64_Vector3* shift, const BGC_FP64_RigidPose3* pose)
+{
+    const BGC_FP64_Quaternion* const real = &pose->_versor.real_part;
+    const BGC_FP64_Quaternion* const dual = &pose->_versor.dual_part;
+
+    shift->x1 = 2.0 * ((dual->s0 * real->x1 - dual->x1 * real->s0) + (dual->x3 * real->x2 - dual->x2 * real->x3));
+    shift->x2 = 2.0 * ((dual->s0 * real->x2 - dual->x2 * real->s0) + (dual->x1 * real->x3 - dual->x3 * real->x1));
+    shift->x3 = 2.0 * ((dual->s0 * real->x3 - dual->x3 * real->s0) + (dual->x2 * real->x1 - dual->x1 * real->x2));
+}
+
+// ============ Get Outward Affine3 ============= //
+
+inline void bgc_fp32_rigid_pose3_get_outward_affine(BGC_FP32_Affine3* affine_map, const BGC_FP32_RigidPose3* pose)
+{
+    _bgc_fp32_versor_get_rotation_matrix(&affine_map->distortion, &pose->_versor.real_part);
+    bgc_fp32_rigid_pose3_get_outer_shift(&affine_map->shift, pose);
+}
+
+inline void bgc_fp64_rigid_pose3_get_outward_affine(BGC_FP64_Affine3* affine_map, const BGC_FP64_RigidPose3* pose)
 {
     _bgc_fp64_versor_get_rotation_matrix(&affine_map->distortion, &pose->_versor.real_part);
-
-    const BGC_FP64_Quaternion * real = &pose->_versor.real_part;
-    const BGC_FP64_Quaternion * dual = &pose->_versor.dual_part;
-
-    affine_map->shift.x1 = (dual->x1 * real->s0 + dual->x3 * real->x2) - (dual->s0 * real->x1 + dual->x2 * real->x3);
-    affine_map->shift.x2 = (dual->x2 * real->s0 + dual->x1 * real->x3) - (dual->s0 * real->x2 + dual->x3 * real->x1);
-    affine_map->shift.x3 = (dual->x3 * real->s0 + dual->x2 * real->x1) - (dual->s0 * real->x3 + dual->x1 * real->x2);
+    bgc_fp64_rigid_pose3_get_outer_shift(&affine_map->shift, pose);
 }
 
 // ============= Get Inward Affine3 ============= //
 
-inline void bgc_fp32_rigid_pose3_get_inward_affine3(BGC_FP32_Affine3* affine_map, const BGC_FP32_RigidPose3* pose)
+inline void bgc_fp32_rigid_pose3_get_inward_affine(BGC_FP32_Affine3* affine_map, const BGC_FP32_RigidPose3* pose)
 {
     _bgc_fp32_versor_get_reverse_matrix(&affine_map->distortion, &pose->_versor.real_part);
+    bgc_fp32_rigid_pose3_get_inner_shift(&affine_map->shift, pose);
+}
 
-    const BGC_FP32_Quaternion * real = &pose->_versor.real_part;
-    const BGC_FP32_Quaternion * dual = &pose->_versor.dual_part;
-
-    //TODO: set the shift in the affine map
+inline void bgc_fp64_rigid_pose3_get_inward_affine(BGC_FP64_Affine3* affine_map, const BGC_FP64_RigidPose3* pose)
+{
+    _bgc_fp64_versor_get_reverse_matrix(&affine_map->distortion, &pose->_versor.real_part);
+    bgc_fp64_rigid_pose3_get_inner_shift(&affine_map->shift, pose);
 }
 
 #endif
diff --git a/basic-geometry/vector3.c b/basic-geometry/vector3.c
index 828b6cd..a0da396 100644
--- a/basic-geometry/vector3.c
+++ b/basic-geometry/vector3.c
@@ -77,9 +77,9 @@ extern inline double bgc_fp64_vector3_get_dot_product(const BGC_FP64_Vector3* ve
 
 extern inline float bgc_fp32_vector3_get_triple_product(const BGC_FP32_Vector3* vector1, const BGC_FP32_Vector3* vector2, const BGC_FP32_Vector3* vector3);
 extern inline double bgc_fp64_vector3_get_triple_product(const BGC_FP64_Vector3* vector1, const BGC_FP64_Vector3* vector2, const BGC_FP64_Vector3* vector3);
-
-extern inline void _bgc_fp32_restrict_vector3_get_cross_product(BGC_FP32_Vector3* restrict product, const BGC_FP32_Vector3* vector1, const BGC_FP32_Vector3* vector2);
-extern inline void _bgc_fp64_restrict_vector3_get_cross_product(BGC_FP64_Vector3* restrict product, const BGC_FP64_Vector3* vector1, const BGC_FP64_Vector3* vector2);
+
+extern inline void _bgc_fp32_restrict_vector3_get_cross_product(BGC_FP32_Vector3* restrict product, const BGC_FP32_Vector3* vector1, const BGC_FP32_Vector3* vector2);
+extern inline void _bgc_fp64_restrict_vector3_get_cross_product(BGC_FP64_Vector3* restrict product, const BGC_FP64_Vector3* vector1, const BGC_FP64_Vector3* vector2);
 
 extern inline void bgc_fp32_vector3_get_cross_product(BGC_FP32_Vector3* product, const BGC_FP32_Vector3* vector1, const BGC_FP32_Vector3* vector2);
 extern inline void bgc_fp64_vector3_get_cross_product(BGC_FP64_Vector3* product, const BGC_FP64_Vector3* vector1, const BGC_FP64_Vector3* vector2);