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226 lines
7.4 KiB
226 lines
7.4 KiB
/////////////////////////////////////////////////////////////////////////////////// |
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/// OpenGL Mathematics (glm.g-truc.net) |
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/// |
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/// Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net) |
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/// Permission is hereby granted, free of charge, to any person obtaining a copy |
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/// of this software and associated documentation files (the "Software"), to deal |
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/// in the Software without restriction, including without limitation the rights |
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/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
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/// copies of the Software, and to permit persons to whom the Software is |
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/// furnished to do so, subject to the following conditions: |
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/// |
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/// The above copyright notice and this permission notice shall be included in |
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/// all copies or substantial portions of the Software. |
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/// |
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/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
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/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
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/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
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/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
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/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
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/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
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/// THE SOFTWARE. |
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/// |
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/// @ref gtx_decomposition |
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/// @file glm/gtx/decomposition.inl |
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/// @date 2014-08-29 / 2014-08-29 |
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/// @author Christophe Riccio |
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/////////////////////////////////////////////////////////////////////////////////// |
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namespace glm |
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{ |
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/// Make a linear combination of two vectors and return the result. |
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// result = (a * ascl) + (b * bscl) |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tvec3<T, P> combine( |
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tvec3<T, P> const & a, |
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tvec3<T, P> const & b, |
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T ascl, T bscl) |
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{ |
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return (a * ascl) + (b * bscl); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER void v3Scale(tvec3<T, P> & v, T desiredLength) |
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{ |
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T len = glm::length(v); |
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if(len != 0) |
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{ |
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T l = desiredLength / len; |
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v[0] *= l; |
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v[1] *= l; |
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v[2] *= l; |
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} |
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} |
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/** |
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* Matrix decompose |
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* http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp |
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* Decomposes the mode matrix to translations,rotation scale components |
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* |
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*/ |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER bool decompose(tmat4x4<T, P> const & ModelMatrix, tvec3<T, P> & Scale, tquat<T, P> & Orientation, tvec3<T, P> & Translation, tvec3<T, P> & Skew, tvec4<T, P> & Perspective) |
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{ |
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tmat4x4<T, P> LocalMatrix(ModelMatrix); |
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// Normalize the matrix. |
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if(LocalMatrix[3][3] == static_cast<T>(0)) |
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return false; |
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for(length_t i = 0; i < 4; ++i) |
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for(length_t j = 0; j < 4; ++j) |
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LocalMatrix[i][j] /= LocalMatrix[3][3]; |
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// perspectiveMatrix is used to solve for perspective, but it also provides |
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// an easy way to test for singularity of the upper 3x3 component. |
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tmat4x4<T, P> PerspectiveMatrix(LocalMatrix); |
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for(length_t i = 0; i < 3; i++) |
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PerspectiveMatrix[i][3] = 0; |
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PerspectiveMatrix[3][3] = 1; |
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/// TODO: Fixme! |
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if(determinant(PerspectiveMatrix) == static_cast<T>(0)) |
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return false; |
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// First, isolate perspective. This is the messiest. |
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if(LocalMatrix[0][3] != 0 || LocalMatrix[1][3] != 0 || LocalMatrix[2][3] != 0) |
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{ |
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// rightHandSide is the right hand side of the equation. |
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tvec4<T, P> RightHandSide; |
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RightHandSide[0] = LocalMatrix[0][3]; |
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RightHandSide[1] = LocalMatrix[1][3]; |
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RightHandSide[2] = LocalMatrix[2][3]; |
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RightHandSide[3] = LocalMatrix[3][3]; |
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// Solve the equation by inverting PerspectiveMatrix and multiplying |
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// rightHandSide by the inverse. (This is the easiest way, not |
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// necessarily the best.) |
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tmat4x4<T, P> InversePerspectiveMatrix = glm::inverse(PerspectiveMatrix);// inverse(PerspectiveMatrix, inversePerspectiveMatrix); |
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tmat4x4<T, P> TransposedInversePerspectiveMatrix = glm::transpose(InversePerspectiveMatrix);// transposeMatrix4(inversePerspectiveMatrix, transposedInversePerspectiveMatrix); |
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Perspective = TransposedInversePerspectiveMatrix * RightHandSide; |
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// v4MulPointByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspectivePoint); |
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// Clear the perspective partition |
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LocalMatrix[0][3] = LocalMatrix[1][3] = LocalMatrix[2][3] = 0; |
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LocalMatrix[3][3] = 1; |
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} |
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else |
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{ |
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// No perspective. |
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Perspective = tvec4<T, P>(0, 0, 0, 1); |
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} |
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// Next take care of translation (easy). |
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Translation = tvec3<T, P>(LocalMatrix[3]); |
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LocalMatrix[3] = tvec4<T, P>(0, 0, 0, LocalMatrix[3].w); |
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tvec3<T, P> Row[3], Pdum3; |
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// Now get scale and shear. |
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for(length_t i = 0; i < 3; ++i) |
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Row[i] = LocalMatrix[i]; |
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// Compute X scale factor and normalize first row. |
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Scale.x = length(Row[0]);// v3Length(Row[0]); |
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v3Scale(Row[0], 1.0); |
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// Compute XY shear factor and make 2nd row orthogonal to 1st. |
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Skew.z = dot(Row[0], Row[1]); |
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Row[1] = combine(Row[1], Row[0], 1.0, -Skew.z); |
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// Now, compute Y scale and normalize 2nd row. |
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Scale.y = length(Row[1]); |
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v3Scale(Row[1], 1.0); |
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Skew.z /= Scale.y; |
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// Compute XZ and YZ shears, orthogonalize 3rd row. |
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Skew.y = glm::dot(Row[0], Row[2]); |
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Row[2] = combine(Row[2], Row[0], 1.0, -Skew.y); |
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Skew.x = glm::dot(Row[1], Row[2]); |
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Row[2] = combine(Row[2], Row[1], 1.0, -Skew.x); |
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// Next, get Z scale and normalize 3rd row. |
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Scale.z = length(Row[2]); |
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v3Scale(Row[2], 1.0); |
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Skew.y /= Scale.z; |
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Skew.x /= Scale.z; |
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// At this point, the matrix (in rows[]) is orthonormal. |
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// Check for a coordinate system flip. If the determinant |
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// is -1, then negate the matrix and the scaling factors. |
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Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3); |
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if(dot(Row[0], Pdum3) < 0) |
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{ |
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for(length_t i = 0; i < 3; i++) |
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{ |
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Scale.x *= static_cast<T>(-1); |
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Row[i] *= static_cast<T>(-1); |
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} |
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} |
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// Now, get the rotations out, as described in the gem. |
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// FIXME - Add the ability to return either quaternions (which are |
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// easier to recompose with) or Euler angles (rx, ry, rz), which |
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// are easier for authors to deal with. The latter will only be useful |
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// when we fix https://bugs.webkit.org/show_bug.cgi?id=23799, so I |
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// will leave the Euler angle code here for now. |
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// ret.rotateY = asin(-Row[0][2]); |
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// if (cos(ret.rotateY) != 0) { |
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// ret.rotateX = atan2(Row[1][2], Row[2][2]); |
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// ret.rotateZ = atan2(Row[0][1], Row[0][0]); |
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// } else { |
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// ret.rotateX = atan2(-Row[2][0], Row[1][1]); |
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// ret.rotateZ = 0; |
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// } |
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T s, t, x, y, z, w; |
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t = Row[0][0] + Row[1][1] + Row[2][2] + 1.0; |
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if(t > 1e-4) |
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{ |
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s = 0.5 / sqrt(t); |
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w = 0.25 / s; |
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x = (Row[2][1] - Row[1][2]) * s; |
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y = (Row[0][2] - Row[2][0]) * s; |
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z = (Row[1][0] - Row[0][1]) * s; |
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} |
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else if(Row[0][0] > Row[1][1] && Row[0][0] > Row[2][2]) |
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{ |
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s = sqrt (1.0 + Row[0][0] - Row[1][1] - Row[2][2]) * 2.0; // S=4*qx |
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x = 0.25 * s; |
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y = (Row[0][1] + Row[1][0]) / s; |
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z = (Row[0][2] + Row[2][0]) / s; |
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w = (Row[2][1] - Row[1][2]) / s; |
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} |
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else if(Row[1][1] > Row[2][2]) |
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{ |
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s = sqrt (1.0 + Row[1][1] - Row[0][0] - Row[2][2]) * 2.0; // S=4*qy |
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x = (Row[0][1] + Row[1][0]) / s; |
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y = 0.25 * s; |
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z = (Row[1][2] + Row[2][1]) / s; |
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w = (Row[0][2] - Row[2][0]) / s; |
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} |
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else |
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{ |
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s = sqrt(1.0 + Row[2][2] - Row[0][0] - Row[1][1]) * 2.0; // S=4*qz |
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x = (Row[0][2] + Row[2][0]) / s; |
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y = (Row[1][2] + Row[2][1]) / s; |
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z = 0.25 * s; |
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w = (Row[1][0] - Row[0][1]) / s; |
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} |
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Orientation.x = x; |
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Orientation.y = y; |
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Orientation.z = z; |
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Orientation.w = w; |
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return true; |
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} |
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}//namespace glm
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