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-///////////////////////////////////////////////////////////////////////////////////
-/// OpenGL Mathematics (glm.g-truc.net)
-///
-/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
-/// Permission is hereby granted, free of charge, to any person obtaining a copy
-/// of this software and associated documentation files (the "Software"), to deal
-/// in the Software without restriction, including without limitation the rights
-/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-/// copies of the Software, and to permit persons to whom the Software is
-/// furnished to do so, subject to the following conditions:
-///
-/// The above copyright notice and this permission notice shall be included in
-/// all copies or substantial portions of the Software.
-///
-/// Restrictions:
-/// By making use of the Software for military purposes, you choose to make
-/// a Bunny unhappy.
-///
-/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
-/// THE SOFTWARE.
-///
-/// @ref gtx_matrix_decompose
-/// @file glm/gtx/matrix_decompose.inl
-/// @date 2014-08-29 / 2014-08-29
-/// @author Christophe Riccio
-///////////////////////////////////////////////////////////////////////////////////
-
-namespace glm
-{
- /// Make a linear combination of two vectors and return the result.
- // result = (a * ascl) + (b * bscl)
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tvec3<T, P> combine(
- tvec3<T, P> const & a,
- tvec3<T, P> const & b,
- T ascl, T bscl)
- {
- return (a * ascl) + (b * bscl);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER void v3Scale(tvec3<T, P> & v, T desiredLength)
- {
- T len = glm::length(v);
- if(len != 0)
- {
- T l = desiredLength / len;
- v[0] *= l;
- v[1] *= l;
- v[2] *= l;
- }
- }
-
- /**
- * Matrix decompose
- * http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
- * Decomposes the mode matrix to translations,rotation scale components
- *
- */
-
- template <typename T, precision P>
- 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)
- {
- tmat4x4<T, P> LocalMatrix(ModelMatrix);
-
- // Normalize the matrix.
- if(LocalMatrix[3][3] == static_cast<T>(0))
- return false;
-
- for(length_t i = 0; i < 4; ++i)
- for(length_t j = 0; j < 4; ++j)
- LocalMatrix[i][j] /= LocalMatrix[3][3];
-
- // perspectiveMatrix is used to solve for perspective, but it also provides
- // an easy way to test for singularity of the upper 3x3 component.
- tmat4x4<T, P> PerspectiveMatrix(LocalMatrix);
-
- for(length_t i = 0; i < 3; i++)
- PerspectiveMatrix[i][3] = 0;
- PerspectiveMatrix[3][3] = 1;
-
- /// TODO: Fixme!
- if(determinant(PerspectiveMatrix) == static_cast<T>(0))
- return false;
-
- // First, isolate perspective. This is the messiest.
- if(LocalMatrix[0][3] != 0 || LocalMatrix[1][3] != 0 || LocalMatrix[2][3] != 0)
- {
- // rightHandSide is the right hand side of the equation.
- tvec4<T, P> RightHandSide;
- RightHandSide[0] = LocalMatrix[0][3];
- RightHandSide[1] = LocalMatrix[1][3];
- RightHandSide[2] = LocalMatrix[2][3];
- RightHandSide[3] = LocalMatrix[3][3];
-
- // Solve the equation by inverting PerspectiveMatrix and multiplying
- // rightHandSide by the inverse. (This is the easiest way, not
- // necessarily the best.)
- tmat4x4<T, P> InversePerspectiveMatrix = glm::inverse(PerspectiveMatrix);// inverse(PerspectiveMatrix, inversePerspectiveMatrix);
- tmat4x4<T, P> TransposedInversePerspectiveMatrix = glm::transpose(InversePerspectiveMatrix);// transposeMatrix4(inversePerspectiveMatrix, transposedInversePerspectiveMatrix);
-
- Perspective = TransposedInversePerspectiveMatrix * RightHandSide;
- // v4MulPointByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspectivePoint);
-
- // Clear the perspective partition
- LocalMatrix[0][3] = LocalMatrix[1][3] = LocalMatrix[2][3] = 0;
- LocalMatrix[3][3] = 1;
- }
- else
- {
- // No perspective.
- Perspective = tvec4<T, P>(0, 0, 0, 1);
- }
-
- // Next take care of translation (easy).
- Translation = tvec3<T, P>(LocalMatrix[3]);
- LocalMatrix[3] = tvec4<T, P>(0, 0, 0, LocalMatrix[3].w);
-
- tvec3<T, P> Row[3], Pdum3;
-
- // Now get scale and shear.
- for(length_t i = 0; i < 3; ++i)
- for(int j = 0; j < 3; ++j)
- Row[i][j] = LocalMatrix[i][j];
-
- // Compute X scale factor and normalize first row.
- Scale.x = length(Row[0]);// v3Length(Row[0]);
-
- v3Scale(Row[0], static_cast<T>(1));
-
- // Compute XY shear factor and make 2nd row orthogonal to 1st.
- Skew.z = dot(Row[0], Row[1]);
- Row[1] = combine(Row[1], Row[0], static_cast<T>(1), -Skew.z);
-
- // Now, compute Y scale and normalize 2nd row.
- Scale.y = length(Row[1]);
- v3Scale(Row[1], static_cast<T>(1));
- Skew.z /= Scale.y;
-
- // Compute XZ and YZ shears, orthogonalize 3rd row.
- Skew.y = glm::dot(Row[0], Row[2]);
- Row[2] = combine(Row[2], Row[0], static_cast<T>(1), -Skew.y);
- Skew.x = glm::dot(Row[1], Row[2]);
- Row[2] = combine(Row[2], Row[1], static_cast<T>(1), -Skew.x);
-
- // Next, get Z scale and normalize 3rd row.
- Scale.z = length(Row[2]);
- v3Scale(Row[2], static_cast<T>(1));
- Skew.y /= Scale.z;
- Skew.x /= Scale.z;
-
- // At this point, the matrix (in rows[]) is orthonormal.
- // Check for a coordinate system flip. If the determinant
- // is -1, then negate the matrix and the scaling factors.
- Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3);
- if(dot(Row[0], Pdum3) < 0)
- {
- for(length_t i = 0; i < 3; i++)
- {
- Scale.x *= static_cast<T>(-1);
- Row[i] *= static_cast<T>(-1);
- }
- }
-
- // Now, get the rotations out, as described in the gem.
-
- // FIXME - Add the ability to return either quaternions (which are
- // easier to recompose with) or Euler angles (rx, ry, rz), which
- // are easier for authors to deal with. The latter will only be useful
- // when we fix https://bugs.webkit.org/show_bug.cgi?id=23799, so I
- // will leave the Euler angle code here for now.
-
- // ret.rotateY = asin(-Row[0][2]);
- // if (cos(ret.rotateY) != 0) {
- // ret.rotateX = atan2(Row[1][2], Row[2][2]);
- // ret.rotateZ = atan2(Row[0][1], Row[0][0]);
- // } else {
- // ret.rotateX = atan2(-Row[2][0], Row[1][1]);
- // ret.rotateZ = 0;
- // }
-
- T s, t, x, y, z, w;
-
- t = Row[0][0] + Row[1][1] + Row[2][2] + 1.0;
-
- if(t > 1e-4)
- {
- s = 0.5 / sqrt(t);
- w = 0.25 / s;
- x = (Row[2][1] - Row[1][2]) * s;
- y = (Row[0][2] - Row[2][0]) * s;
- z = (Row[1][0] - Row[0][1]) * s;
- }
- else if(Row[0][0] > Row[1][1] && Row[0][0] > Row[2][2])
- {
- s = sqrt (1.0 + Row[0][0] - Row[1][1] - Row[2][2]) * 2.0; // S=4*qx
- x = 0.25 * s;
- y = (Row[0][1] + Row[1][0]) / s;
- z = (Row[0][2] + Row[2][0]) / s;
- w = (Row[2][1] - Row[1][2]) / s;
- }
- else if(Row[1][1] > Row[2][2])
- {
- s = sqrt (1.0 + Row[1][1] - Row[0][0] - Row[2][2]) * 2.0; // S=4*qy
- x = (Row[0][1] + Row[1][0]) / s;
- y = 0.25 * s;
- z = (Row[1][2] + Row[2][1]) / s;
- w = (Row[0][2] - Row[2][0]) / s;
- }
- else
- {
- s = sqrt(1.0 + Row[2][2] - Row[0][0] - Row[1][1]) * 2.0; // S=4*qz
- x = (Row[0][2] + Row[2][0]) / s;
- y = (Row[1][2] + Row[2][1]) / s;
- z = 0.25 * s;
- w = (Row[1][0] - Row[0][1]) / s;
- }
-
- Orientation.x = x;
- Orientation.y = y;
- Orientation.z = z;
- Orientation.w = w;
-
- return true;
- }
-}//namespace glm