1 | //All of these functions are based on dqs.cg from http://isg.cs.tcd.ie/kavanl/dq/ |
---|
2 | /* dqs.cg |
---|
3 | |
---|
4 | Dual quaternion skinning vertex shaders (no shading computations) |
---|
5 | |
---|
6 | Version 1.0.3, November 1st, 2007 |
---|
7 | |
---|
8 | Copyright (C) 2006-2007 University of Dublin, Trinity College, All Rights |
---|
9 | Reserved |
---|
10 | |
---|
11 | This software is provided 'as-is', without any express or implied |
---|
12 | warranty. In no event will the author(s) be held liable for any damages |
---|
13 | arising from the use of this software. |
---|
14 | |
---|
15 | Permission is granted to anyone to use this software for any purpose, |
---|
16 | including commercial applications, and to alter it and redistribute it |
---|
17 | freely, subject to the following restrictions: |
---|
18 | |
---|
19 | 1. The origin of this software must not be misrepresented; you must not |
---|
20 | claim that you wrote the original software. If you use this software |
---|
21 | in a product, an acknowledgment in the product documentation would be |
---|
22 | appreciated but is not required. |
---|
23 | 2. Altered source versions must be plainly marked as such, and must not be |
---|
24 | misrepresented as being the original software. |
---|
25 | 3. This notice may not be removed or altered from any source distribution. |
---|
26 | |
---|
27 | Author: Ladislav Kavan, kavanl@cs.tcd.ie |
---|
28 | |
---|
29 | */ |
---|
30 | |
---|
31 | float2x4 blendTwoWeights(float4 blendWgt, float4 blendIdx, float2x4 dualQuaternions[24]) |
---|
32 | { |
---|
33 | float2x4 blendDQ = blendWgt.x*dualQuaternions[blendIdx.x]; |
---|
34 | blendDQ += blendWgt.y*dualQuaternions[blendIdx.y]; |
---|
35 | |
---|
36 | return blendDQ; |
---|
37 | } |
---|
38 | |
---|
39 | float2x4 blendTwoWeightsAntipod(float4 blendWgt, float4 blendIdx, float2x4 dualQuaternions[24]) |
---|
40 | { |
---|
41 | float2x4 dq0 = dualQuaternions[blendIdx.x]; |
---|
42 | float2x4 dq1 = dualQuaternions[blendIdx.y]; |
---|
43 | |
---|
44 | //Accurate antipodality handling. For speed increase, remove the following line, |
---|
45 | //though, the results will only be valid for rotations less than 180 degrees. |
---|
46 | if (dot(dq0[0], dq1[0]) < 0.0) dq1 *= -1.0; |
---|
47 | |
---|
48 | float2x4 blendDQ = blendWgt.x*dq0; |
---|
49 | blendDQ += blendWgt.y*dq1; |
---|
50 | |
---|
51 | return blendDQ; |
---|
52 | } |
---|
53 | |
---|
54 | float3 calculateBlendPosition(float3 position, float2x4 blendDQ) |
---|
55 | { |
---|
56 | float3 blendPosition = position + 2.0*cross(blendDQ[0].yzw, cross(blendDQ[0].yzw, position.xyz) + blendDQ[0].x*position); |
---|
57 | float3 trans = 2.0*(blendDQ[0].x*blendDQ[1].yzw - blendDQ[1].x*blendDQ[0].yzw + cross(blendDQ[0].yzw, blendDQ[1].yzw)); |
---|
58 | blendPosition += trans; |
---|
59 | |
---|
60 | return blendPosition; |
---|
61 | } |
---|
62 | |
---|
63 | float3 calculateBlendNormal(float3 normal, float2x4 blendDQ) |
---|
64 | { |
---|
65 | return normal + 2.0*cross(blendDQ[0].yzw, cross(blendDQ[0].yzw, normal) + blendDQ[0].x*normal); |
---|
66 | } |
---|
67 | |
---|
68 | float3x3 adjointTransposeMatrix(float3x3 M) |
---|
69 | { |
---|
70 | float3x3 atM; |
---|
71 | atM._m00 = M._m22 * M._m11 - M._m12 * M._m21; |
---|
72 | atM._m01 = M._m12 * M._m20 - M._m10 * M._m22; |
---|
73 | atM._m02 = M._m10 * M._m21 - M._m20 * M._m11; |
---|
74 | |
---|
75 | atM._m10 = M._m02 * M._m21 - M._m22 * M._m01; |
---|
76 | atM._m11 = M._m22 * M._m00 - M._m02 * M._m20; |
---|
77 | atM._m12 = M._m20 * M._m01 - M._m00 * M._m21; |
---|
78 | |
---|
79 | atM._m20 = M._m12 * M._m01 - M._m02 * M._m11; |
---|
80 | atM._m21 = M._m10 * M._m02 - M._m12 * M._m00; |
---|
81 | atM._m22 = M._m00 * M._m11 - M._m10 * M._m01; |
---|
82 | |
---|
83 | return atM; |
---|
84 | } |
---|
85 | |
---|