highlight DLB files

README.md

@@ -1,7 +1,8 @@
 ##  DLB (Dual Quaternion Linear Blending)  
 
-- code/DLB.h: the c++ code of mapping the rigid transformation to the unit dual quaternion  
-- shaders/DLB.hlsli: the hlsl code of DLB (Dual quaternion Linear Blending) and mapping the unit dual quaternion to the rigid transformation  
+- [DLB.h](https://github.com/HanetakaChou/Dual-Quaternion-Linear-Blending/blob/master/code/DLB.h) the c++ code of mapping the rigid transformation to the unit dual quaternion  
+- [DLB.hlsli](https://github.com/HanetakaChou/Dual-Quaternion-Linear-Blending/blob/master/shaders/DLB.hlsli) the hlsl code of DLB (Dual quaternion Linear Blending) and mapping the unit dual quaternion to the rigid transformation  
+- [DLB.glsli](https://github.com/HanetakaChou/Dual-Quaternion-Linear-Blending/blob/master/shaders/DLB.hlsli) the glsl code of DLB (Dual quaternion Linear Blending) and mapping the unit dual quaternion to the rigid transformation  
 
 [![build windows](https://github.com/HanetakaChou/Dual-Quaternion-Linear-Blending/actions/workflows/build-windows.yml/badge.svg)](https://github.com/HanetakaChou/Dual-Quaternion-Linear-Blending/actions/workflows/build-windows.yml)  
 ![](README.png)  

code/DLB.h

@@ -1,6 +1,3 @@
-#ifndef _DLB_H_
-#define _DLB_H_ 1
-
 //
 // Copyright (C) YuqiaoZhang(HanetakaChou)
 //
@@ -18,6 +15,9 @@
 // along with this program.  If not, see <https://www.gnu.org/licenses/>.
 //
 
+#ifndef _DLB_H_
+#define _DLB_H_ 1
+
 //
 // Mapping the rigid transformation to the unit dual quaternion.
 //

shaders/DLB.glsli

@@ -0,0 +1,79 @@
+//
+// Copyright (C) YuqiaoZhang(HanetakaChou)
+//
+// This program is free software: you can redistribute it and/or modify
+// it under the terms of the GNU Lesser General Public License as published
+// by the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU Lesser General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public License
+// along with this program.  If not, see <https://www.gnu.org/licenses/>.
+//
+
+#ifndef _DLB_GLSLI_
+#define _DLB_GLSLI_ 1
+
+//
+// DLB (Dual quaternion Linear Blending)
+//
+mat2x4 dual_quaternion_linear_blending(in mat2x4 q_indices_x, in mat2x4 q_indices_y, in mat2x4 q_indices_z, in mat2x4 q_indices_w, in vec4 weights)
+{
+#if 1
+	// NOTE:
+	// The original DLB does NOT check the sign of the inner product of the unit quaternion q_x_0 and q_y_0(q_z_0 q_w_0).
+	// However, since the unit quaternion q and -q represent the same rotation transform, we may get the result of which the real part is zero.
+	mat2x4 b = weights.x * q_indices_x + weights.y * sign(dot(q_indices_x[0], q_indices_y[0])) * q_indices_y + weights.z * sign(dot(q_indices_x[0], q_indices_z[0])) * q_indices_z + weights.w * sign(dot(q_indices_x[0], q_indices_w[0])) * q_indices_w;
+#else
+	mat2x4 b = weights.x * q_indices_x + weights.y * q_indices_y + weights.z * q_indices_z + weights.w * q_indices_w;
+#endif
+
+	// "4 Implementation Notes" of [Ladislav Kavan, Steven Collins, Jiri Zara, Carol O'Sullivan. "Geometric Skinning with Approximate Dual Quaternion Blending." SIGGRAPH 2008.](http://www.cs.utah.edu/~ladislav/kavan08geometric/kavan08geometric.html)
+	// We do NOT need to calculate the exact dual part "\boldsymbol{q_\epsilon}", since the scalar part of the "\boldsymbol{q_\epsilon} {\boldsymbol{q_0}}^*" is ignored when we calculate the "\frac{1}{2}\overrightarrow{t}".
+	return (b / length(b[0]));
+}
+
+//
+// Mapping the rigid transformation to the unit dual quaternion.
+//
+// [in]  q: The unit dual quaternion of which the q[0] is the real part and the q[1] is the dual part.
+//
+// [out] r: The unit quaternion which represents the rotation transform of the rigid transformation.
+//
+// [out] t: The 3D vector which represnets the translation transform of the rigid transformation.
+//
+void unit_dual_quaternion_to_rigid_transform(in mat2x4 q, out vec4 r, out vec3 t)
+{
+	vec4 q_0 = q[0];
+	vec4 q_e = q[1];
+
+	// \boldsymbol{r_0} = \boldsymbol{q_0}
+	r = q_0;
+
+	// \overrightarrow{t} = 2 (- s_ϵ \overrightarrow{v_0} + s_0 \overrightarrow{v_ϵ} - \overrightarrow{v_ϵ} \times \overrightarrow{v_0}
+	// t = 2.0 * (- q_e.w * q_0.xyz + q_0.w * q_e.xyz - cross(q_e.xyz, q_0.xyz));
+	t = 2.0 * (q_0.w * q_e.xyz - q_e.w * q_0.xyz + cross(q_0.xyz, q_e.xyz));
+}
+
+//
+// Mapping the unit quaternion to the rotation transformation.
+//
+// [in]    q: The unit quaternion.
+//
+// [out]   p: The 3D vector which represents the position before the rotation transform.
+//
+// [return] : The 3D vector which represents the position after the rotation transform.
+//
+vec3 unit_quaternion_to_rotation_transform(in vec4 r, in vec3 p)
+{
+	// "Fig. 6.7" and "Fig. 6.8" of [Quaternions for Computer Graphics](https://link.springer.com/book/10.1007/978-1-4471-7509-4)
+	// "Lemma 4" of [Ladislav Kavan, Steven Collins, Jiri Zara, Carol O'Sullivan. "Geometric Skinning with Approximate Dual Quaternion Blending." SIGGRAPH 2008.](http://www.cs.utah.edu/~ladislav/kavan08geometric/kavan08geometric.html)
+
+	return (p + 2.0 * cross(r.xyz, cross(r.xyz, p) + r.w * p));
+}
+
+#endif

shaders/DLB.hlsli

@@ -1,6 +1,3 @@
-#ifndef _DLB_HLSLI_
-#define _DLB_HLSLI_ 1
-
 //
 // Copyright (C) YuqiaoZhang(HanetakaChou)
 //
@@ -18,6 +15,9 @@
 // along with this program.  If not, see <https://www.gnu.org/licenses/>.
 //
 
+#ifndef _DLB_HLSLI_
+#define _DLB_HLSLI_ 1
+
 //
 // DLB (Dual quaternion Linear Blending)
 //