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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_interpolation
-/// @file glm/gtx/matrix_interpolation.hpp
-/// @date 2011-03-05 / 2011-03-05
-/// @author Christophe Riccio
-///////////////////////////////////////////////////////////////////////////////////
-
-namespace glm
-{
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER void axisAngle
- (
- tmat4x4<T, P> const & mat,
- tvec3<T, P> & axis,
- T & angle
- )
- {
- T epsilon = (T)0.01;
- T epsilon2 = (T)0.1;
-
- if((abs(mat[1][0] - mat[0][1]) < epsilon) && (abs(mat[2][0] - mat[0][2]) < epsilon) && (abs(mat[2][1] - mat[1][2]) < epsilon))
- {
- if ((abs(mat[1][0] + mat[0][1]) < epsilon2) && (abs(mat[2][0] + mat[0][2]) < epsilon2) && (abs(mat[2][1] + mat[1][2]) < epsilon2) && (abs(mat[0][0] + mat[1][1] + mat[2][2] - (T)3.0) < epsilon2))
- {
- angle = (T)0.0;
- axis.x = (T)1.0;
- axis.y = (T)0.0;
- axis.z = (T)0.0;
- return;
- }
- angle = static_cast<T>(3.1415926535897932384626433832795);
- T xx = (mat[0][0] + (T)1.0) / (T)2.0;
- T yy = (mat[1][1] + (T)1.0) / (T)2.0;
- T zz = (mat[2][2] + (T)1.0) / (T)2.0;
- T xy = (mat[1][0] + mat[0][1]) / (T)4.0;
- T xz = (mat[2][0] + mat[0][2]) / (T)4.0;
- T yz = (mat[2][1] + mat[1][2]) / (T)4.0;
- if((xx > yy) && (xx > zz))
- {
- if (xx < epsilon) {
- axis.x = (T)0.0;
- axis.y = (T)0.7071;
- axis.z = (T)0.7071;
- } else {
- axis.x = sqrt(xx);
- axis.y = xy / axis.x;
- axis.z = xz / axis.x;
- }
- }
- else if (yy > zz)
- {
- if (yy < epsilon) {
- axis.x = (T)0.7071;
- axis.y = (T)0.0;
- axis.z = (T)0.7071;
- } else {
- axis.y = sqrt(yy);
- axis.x = xy / axis.y;
- axis.z = yz / axis.y;
- }
- }
- else
- {
- if (zz < epsilon) {
- axis.x = (T)0.7071;
- axis.y = (T)0.7071;
- axis.z = (T)0.0;
- } else {
- axis.z = sqrt(zz);
- axis.x = xz / axis.z;
- axis.y = yz / axis.z;
- }
- }
- return;
- }
- T s = sqrt((mat[2][1] - mat[1][2]) * (mat[2][1] - mat[1][2]) + (mat[2][0] - mat[0][2]) * (mat[2][0] - mat[0][2]) + (mat[1][0] - mat[0][1]) * (mat[1][0] - mat[0][1]));
- if (glm::abs(s) < T(0.001))
- s = (T)1.0;
- angle = acos((mat[0][0] + mat[1][1] + mat[2][2] - (T)1.0) / (T)2.0);
- axis.x = (mat[1][2] - mat[2][1]) / s;
- axis.y = (mat[2][0] - mat[0][2]) / s;
- axis.z = (mat[0][1] - mat[1][0]) / s;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tmat4x4<T, P> axisAngleMatrix
- (
- tvec3<T, P> const & axis,
- T const angle
- )
- {
- T c = cos(angle);
- T s = sin(angle);
- T t = static_cast<T>(1) - c;
- tvec3<T, P> n = normalize(axis);
-
- return tmat4x4<T, P>(
- t * n.x * n.x + c, t * n.x * n.y + n.z * s, t * n.x * n.z - n.y * s, T(0),
- t * n.x * n.y - n.z * s, t * n.y * n.y + c, t * n.y * n.z + n.x * s, T(0),
- t * n.x * n.z + n.y * s, t * n.y * n.z - n.x * s, t * n.z * n.z + c, T(0),
- T(0), T(0), T(0), T(1)
- );
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tmat4x4<T, P> extractMatrixRotation
- (
- tmat4x4<T, P> const & mat
- )
- {
- return tmat4x4<T, P>(
- mat[0][0], mat[0][1], mat[0][2], 0.0,
- mat[1][0], mat[1][1], mat[1][2], 0.0,
- mat[2][0], mat[2][1], mat[2][2], 0.0,
- 0.0, 0.0, 0.0, 1.0
- );
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tmat4x4<T, P> interpolate
- (
- tmat4x4<T, P> const & m1,
- tmat4x4<T, P> const & m2,
- T const delta
- )
- {
- tmat4x4<T, P> m1rot = extractMatrixRotation(m1);
- tmat4x4<T, P> dltRotation = m2 * transpose(m1rot);
- tvec3<T, P> dltAxis;
- T dltAngle;
- axisAngle(dltRotation, dltAxis, dltAngle);
- tmat4x4<T, P> out = axisAngleMatrix(dltAxis, dltAngle * delta) * m1rot;
- out[3][0] = m1[3][0] + delta * (m2[3][0] - m1[3][0]);
- out[3][1] = m1[3][1] + delta * (m2[3][1] - m1[3][1]);
- out[3][2] = m1[3][2] + delta * (m2[3][2] - m1[3][2]);
- return out;
- }
-}//namespace glm