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