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@ -6,40 +6,38 @@ |
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namespace glm |
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{ |
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template<typename T, precision P> |
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GLM_FUNC_QUALIFIER void axisAngle |
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( |
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mat<4, 4, T, P> const& mat, |
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vec<3, T, P> & axis, |
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T & angle |
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) |
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GLM_FUNC_QUALIFIER void axisAngle(mat<4, 4, T, P> const& mat, vec<3, T, P> & axis, T & angle) |
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{ |
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T epsilon = (T)0.01; |
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T epsilon2 = (T)0.1; |
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T epsilon = static_cast<T>(0.01); |
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T epsilon2 = static_cast<T>(0.1); |
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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)) |
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{ |
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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)) |
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{ |
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angle = (T)0.0; |
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axis.x = (T)1.0; |
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axis.y = (T)0.0; |
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axis.z = (T)0.0; |
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angle = static_cast<T>(0.0); |
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axis.x = static_cast<T>(1.0); |
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axis.y = static_cast<T>(0.0); |
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axis.z = static_cast<T>(0.0); |
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return; |
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} |
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angle = static_cast<T>(3.1415926535897932384626433832795); |
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T xx = (mat[0][0] + (T)1.0) * (T)0.5; |
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T yy = (mat[1][1] + (T)1.0) * (T)0.5; |
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T zz = (mat[2][2] + (T)1.0) * (T)0.5; |
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T xy = (mat[1][0] + mat[0][1]) * (T)0.25; |
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T xz = (mat[2][0] + mat[0][2]) * (T)0.25; |
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T yz = (mat[2][1] + mat[1][2]) * (T)0.25; |
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T xx = (mat[0][0] + static_cast<T>(1.0)) * static_cast<T>(0.5); |
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T yy = (mat[1][1] + static_cast<T>(1.0)) * static_cast<T>(0.5); |
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T zz = (mat[2][2] + static_cast<T>(1.0)) * static_cast<T>(0.5); |
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T xy = (mat[1][0] + mat[0][1]) * static_cast<T>(0.25); |
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T xz = (mat[2][0] + mat[0][2]) * static_cast<T>(0.25); |
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T yz = (mat[2][1] + mat[1][2]) * static_cast<T>(0.25); |
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if((xx > yy) && (xx > zz)) |
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{ |
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if (xx < epsilon) { |
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axis.x = (T)0.0; |
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axis.y = (T)0.7071; |
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axis.z = (T)0.7071; |
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} else { |
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if(xx < epsilon) |
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{ |
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axis.x = static_cast<T>(0.0); |
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axis.y = static_cast<T>(0.7071); |
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axis.z = static_cast<T>(0.7071); |
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} |
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else |
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{ |
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axis.x = sqrt(xx); |
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axis.y = xy / axis.x; |
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axis.z = xz / axis.x; |
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@ -47,11 +45,14 @@ namespace glm |
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} |
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else if (yy > zz) |
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{ |
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if (yy < epsilon) { |
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axis.x = (T)0.7071; |
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axis.y = (T)0.0; |
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axis.z = (T)0.7071; |
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} else { |
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if(yy < epsilon) |
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{ |
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axis.x = static_cast<T>(0.7071); |
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axis.y = static_cast<T>(0.0); |
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axis.z = static_cast<T>(0.7071); |
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} |
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else |
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{ |
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axis.y = sqrt(yy); |
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axis.x = xy / axis.y; |
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axis.z = yz / axis.y; |
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@ -59,11 +60,14 @@ namespace glm |
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} |
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else |
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{ |
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if (zz < epsilon) { |
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axis.x = (T)0.7071; |
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axis.y = (T)0.7071; |
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axis.z = (T)0.0; |
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} else { |
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if (zz < epsilon) |
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{ |
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axis.x = static_cast<T>(0.7071); |
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axis.y = static_cast<T>(0.7071); |
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axis.z = static_cast<T>(0.0); |
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} |
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else |
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{ |
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axis.z = sqrt(zz); |
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axis.x = xz / axis.z; |
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axis.y = yz / axis.z; |
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@ -73,9 +77,9 @@ namespace glm |
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} |
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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])); |
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if (glm::abs(s) < T(0.001)) |
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s = (T)1.0; |
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T const angleCos = (mat[0][0] + mat[1][1] + mat[2][2] - (T)1.0) * (T)0.5; |
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if (angleCos - static_cast<T>(1) < epsilon) |
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s = static_cast<T>(1); |
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T const angleCos = (mat[0][0] + mat[1][1] + mat[2][2] - static_cast<T>(1)) * static_cast<T>(0.5); |
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if(angleCos - static_cast<T>(1) < epsilon) |
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angle = pi<T>() * static_cast<T>(0.25); |
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else |
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angle = acos(angleCos); |
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@ -85,11 +89,7 @@ namespace glm |
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} |
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template<typename T, precision P> |
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GLM_FUNC_QUALIFIER mat<4, 4, T, P> axisAngleMatrix |
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( |
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vec<3, T, P> const & axis, |
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T const angle |
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) |
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GLM_FUNC_QUALIFIER mat<4, 4, T, P> axisAngleMatrix(vec<3, T, P> const & axis, T const angle) |
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{ |
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T c = cos(angle); |
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T s = sin(angle); |
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@ -97,32 +97,24 @@ namespace glm |
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vec<3, T, P> n = normalize(axis); |
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return mat<4, 4, T, P>( |
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t * n.x * n.x + c, t * n.x * n.y + n.z * s, t * n.x * n.z - n.y * s, T(0), |
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t * n.x * n.y - n.z * s, t * n.y * n.y + c, t * n.y * n.z + n.x * s, T(0), |
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t * n.x * n.z + n.y * s, t * n.y * n.z - n.x * s, t * n.z * n.z + c, T(0), |
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T(0), T(0), T(0), T(1)); |
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t * n.x * n.x + c, t * n.x * n.y + n.z * s, t * n.x * n.z - n.y * s, static_cast<T>(0.0), |
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t * n.x * n.y - n.z * s, t * n.y * n.y + c, t * n.y * n.z + n.x * s, static_cast<T>(0.0), |
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t * n.x * n.z + n.y * s, t * n.y * n.z - n.x * s, t * n.z * n.z + c, static_cast<T>(0.0), |
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static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(1.0)); |
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} |
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template<typename T, precision P> |
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GLM_FUNC_QUALIFIER mat<4, 4, T, P> extractMatrixRotation |
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( |
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mat<4, 4, T, P> const& m |
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) |
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GLM_FUNC_QUALIFIER mat<4, 4, T, P> extractMatrixRotation(mat<4, 4, T, P> const& m) |
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{ |
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return mat<4, 4, T, P>( |
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m[0][0], m[0][1], m[0][2], 0.0, |
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m[1][0], m[1][1], m[1][2], 0.0, |
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m[2][0], m[2][1], m[2][2], 0.0, |
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0.0, 0.0, 0.0, 1.0); |
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m[0][0], m[0][1], m[0][2], static_cast<T>(0.0), |
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m[1][0], m[1][1], m[1][2], static_cast<T>(0.0), |
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m[2][0], m[2][1], m[2][2], static_cast<T>(0.0), |
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static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(1.0)); |
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} |
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template<typename T, precision P> |
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GLM_FUNC_QUALIFIER mat<4, 4, T, P> interpolate |
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( |
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mat<4, 4, T, P> const& m1, |
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mat<4, 4, T, P> const& m2, |
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T const delta |
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) |
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GLM_FUNC_QUALIFIER mat<4, 4, T, P> interpolate(mat<4, 4, T, P> const& m1, mat<4, 4, T, P> const& m2, T const delta) |
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{ |
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mat<4, 4, T, P> m1rot = extractMatrixRotation(m1); |
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mat<4, 4, T, P> dltRotation = m2 * transpose(m1rot); |
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