900 lines
23 KiB
Plaintext
900 lines
23 KiB
Plaintext
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/// @ref gtx_euler_angles
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#include "compatibility.hpp" // glm::atan2
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namespace glm
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{
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleX
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(
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T const& angleX
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)
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{
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T cosX = glm::cos(angleX);
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T sinX = glm::sin(angleX);
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return mat<4, 4, T, defaultp>(
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T(1), T(0), T(0), T(0),
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T(0), cosX, sinX, T(0),
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T(0),-sinX, cosX, T(0),
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T(0), T(0), T(0), T(1));
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}
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleY
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(
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T const& angleY
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)
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{
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T cosY = glm::cos(angleY);
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T sinY = glm::sin(angleY);
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return mat<4, 4, T, defaultp>(
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cosY, T(0), -sinY, T(0),
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T(0), T(1), T(0), T(0),
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sinY, T(0), cosY, T(0),
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T(0), T(0), T(0), T(1));
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}
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleZ
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(
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T const& angleZ
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)
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{
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T cosZ = glm::cos(angleZ);
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T sinZ = glm::sin(angleZ);
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return mat<4, 4, T, defaultp>(
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cosZ, sinZ, T(0), T(0),
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-sinZ, cosZ, T(0), T(0),
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T(0), T(0), T(1), T(0),
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T(0), T(0), T(0), T(1));
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}
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template <typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> derivedEulerAngleX
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(
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T const & angleX,
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T const & angularVelocityX
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)
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{
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T cosX = glm::cos(angleX) * angularVelocityX;
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T sinX = glm::sin(angleX) * angularVelocityX;
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return mat<4, 4, T, defaultp>(
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T(0), T(0), T(0), T(0),
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T(0),-sinX, cosX, T(0),
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T(0),-cosX,-sinX, T(0),
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T(0), T(0), T(0), T(0));
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}
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template <typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> derivedEulerAngleY
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(
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T const & angleY,
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T const & angularVelocityY
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)
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{
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T cosY = glm::cos(angleY) * angularVelocityY;
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T sinY = glm::sin(angleY) * angularVelocityY;
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return mat<4, 4, T, defaultp>(
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-sinY, T(0), -cosY, T(0),
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T(0), T(0), T(0), T(0),
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cosY, T(0), -sinY, T(0),
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T(0), T(0), T(0), T(0));
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}
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template <typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> derivedEulerAngleZ
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(
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T const & angleZ,
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T const & angularVelocityZ
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)
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{
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T cosZ = glm::cos(angleZ) * angularVelocityZ;
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T sinZ = glm::sin(angleZ) * angularVelocityZ;
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return mat<4, 4, T, defaultp>(
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-sinZ, cosZ, T(0), T(0),
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-cosZ, -sinZ, T(0), T(0),
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T(0), T(0), T(0), T(0),
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T(0), T(0), T(0), T(0));
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}
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleXY
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(
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T const& angleX,
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T const& angleY
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)
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{
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T cosX = glm::cos(angleX);
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T sinX = glm::sin(angleX);
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T cosY = glm::cos(angleY);
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T sinY = glm::sin(angleY);
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return mat<4, 4, T, defaultp>(
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cosY, -sinX * -sinY, cosX * -sinY, T(0),
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T(0), cosX, sinX, T(0),
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sinY, -sinX * cosY, cosX * cosY, T(0),
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T(0), T(0), T(0), T(1));
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}
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleYX
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(
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T const& angleY,
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T const& angleX
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)
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{
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T cosX = glm::cos(angleX);
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T sinX = glm::sin(angleX);
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T cosY = glm::cos(angleY);
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T sinY = glm::sin(angleY);
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return mat<4, 4, T, defaultp>(
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cosY, 0, -sinY, T(0),
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sinY * sinX, cosX, cosY * sinX, T(0),
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sinY * cosX, -sinX, cosY * cosX, T(0),
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T(0), T(0), T(0), T(1));
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}
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleXZ
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(
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T const& angleX,
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T const& angleZ
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)
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{
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return eulerAngleX(angleX) * eulerAngleZ(angleZ);
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}
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleZX
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(
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T const& angleZ,
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T const& angleX
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)
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{
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return eulerAngleZ(angleZ) * eulerAngleX(angleX);
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}
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleYZ
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(
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T const& angleY,
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T const& angleZ
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)
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{
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return eulerAngleY(angleY) * eulerAngleZ(angleZ);
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}
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleZY
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(
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T const& angleZ,
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T const& angleY
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)
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{
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return eulerAngleZ(angleZ) * eulerAngleY(angleY);
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}
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleXYZ
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(
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T const& t1,
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T const& t2,
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T const& t3
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)
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{
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T c1 = glm::cos(-t1);
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T c2 = glm::cos(-t2);
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T c3 = glm::cos(-t3);
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T s1 = glm::sin(-t1);
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T s2 = glm::sin(-t2);
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T s3 = glm::sin(-t3);
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mat<4, 4, T, defaultp> Result;
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Result[0][0] = c2 * c3;
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Result[0][1] =-c1 * s3 + s1 * s2 * c3;
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Result[0][2] = s1 * s3 + c1 * s2 * c3;
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Result[0][3] = static_cast<T>(0);
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Result[1][0] = c2 * s3;
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Result[1][1] = c1 * c3 + s1 * s2 * s3;
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Result[1][2] =-s1 * c3 + c1 * s2 * s3;
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Result[1][3] = static_cast<T>(0);
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Result[2][0] =-s2;
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Result[2][1] = s1 * c2;
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Result[2][2] = c1 * c2;
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Result[2][3] = static_cast<T>(0);
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Result[3][0] = static_cast<T>(0);
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Result[3][1] = static_cast<T>(0);
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Result[3][2] = static_cast<T>(0);
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Result[3][3] = static_cast<T>(1);
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return Result;
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}
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template<typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleYXZ
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(
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T const& yaw,
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T const& pitch,
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T const& roll
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)
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{
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T tmp_ch = glm::cos(yaw);
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T tmp_sh = glm::sin(yaw);
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T tmp_cp = glm::cos(pitch);
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T tmp_sp = glm::sin(pitch);
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T tmp_cb = glm::cos(roll);
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T tmp_sb = glm::sin(roll);
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mat<4, 4, T, defaultp> Result;
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Result[0][0] = tmp_ch * tmp_cb + tmp_sh * tmp_sp * tmp_sb;
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Result[0][1] = tmp_sb * tmp_cp;
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Result[0][2] = -tmp_sh * tmp_cb + tmp_ch * tmp_sp * tmp_sb;
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Result[0][3] = static_cast<T>(0);
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Result[1][0] = -tmp_ch * tmp_sb + tmp_sh * tmp_sp * tmp_cb;
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Result[1][1] = tmp_cb * tmp_cp;
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Result[1][2] = tmp_sb * tmp_sh + tmp_ch * tmp_sp * tmp_cb;
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Result[1][3] = static_cast<T>(0);
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Result[2][0] = tmp_sh * tmp_cp;
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Result[2][1] = -tmp_sp;
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Result[2][2] = tmp_ch * tmp_cp;
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Result[2][3] = static_cast<T>(0);
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Result[3][0] = static_cast<T>(0);
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Result[3][1] = static_cast<T>(0);
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Result[3][2] = static_cast<T>(0);
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Result[3][3] = static_cast<T>(1);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleXZX
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(
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T const & t1,
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T const & t2,
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T const & t3
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)
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{
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T c1 = glm::cos(t1);
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T s1 = glm::sin(t1);
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T c2 = glm::cos(t2);
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T s2 = glm::sin(t2);
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T c3 = glm::cos(t3);
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T s3 = glm::sin(t3);
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mat<4, 4, T, defaultp> Result;
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Result[0][0] = c2;
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Result[0][1] = c1 * s2;
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Result[0][2] = s1 * s2;
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Result[0][3] = static_cast<T>(0);
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Result[1][0] =-c3 * s2;
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Result[1][1] = c1 * c2 * c3 - s1 * s3;
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Result[1][2] = c1 * s3 + c2 * c3 * s1;
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Result[1][3] = static_cast<T>(0);
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Result[2][0] = s2 * s3;
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Result[2][1] =-c3 * s1 - c1 * c2 * s3;
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Result[2][2] = c1 * c3 - c2 * s1 * s3;
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Result[2][3] = static_cast<T>(0);
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Result[3][0] = static_cast<T>(0);
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Result[3][1] = static_cast<T>(0);
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Result[3][2] = static_cast<T>(0);
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Result[3][3] = static_cast<T>(1);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleXYX
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(
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T const & t1,
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T const & t2,
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T const & t3
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)
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{
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T c1 = glm::cos(t1);
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T s1 = glm::sin(t1);
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T c2 = glm::cos(t2);
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T s2 = glm::sin(t2);
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T c3 = glm::cos(t3);
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T s3 = glm::sin(t3);
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mat<4, 4, T, defaultp> Result;
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Result[0][0] = c2;
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Result[0][1] = s1 * s2;
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Result[0][2] =-c1 * s2;
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Result[0][3] = static_cast<T>(0);
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Result[1][0] = s2 * s3;
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Result[1][1] = c1 * c3 - c2 * s1 * s3;
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Result[1][2] = c3 * s1 + c1 * c2 * s3;
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Result[1][3] = static_cast<T>(0);
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Result[2][0] = c3 * s2;
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Result[2][1] =-c1 * s3 - c2 * c3 * s1;
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Result[2][2] = c1 * c2 * c3 - s1 * s3;
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Result[2][3] = static_cast<T>(0);
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Result[3][0] = static_cast<T>(0);
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Result[3][1] = static_cast<T>(0);
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Result[3][2] = static_cast<T>(0);
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Result[3][3] = static_cast<T>(1);
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleYXY
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(
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T const & t1,
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T const & t2,
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T const & t3
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)
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{
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T c1 = glm::cos(t1);
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T s1 = glm::sin(t1);
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T c2 = glm::cos(t2);
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T s2 = glm::sin(t2);
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T c3 = glm::cos(t3);
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T s3 = glm::sin(t3);
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mat<4, 4, T, defaultp> Result;
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Result[0][0] = c1 * c3 - c2 * s1 * s3;
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Result[0][1] = s2* s3;
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Result[0][2] =-c3 * s1 - c1 * c2 * s3;
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Result[0][3] = static_cast<T>(0);
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Result[1][0] = s1 * s2;
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Result[1][1] = c2;
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Result[1][2] = c1 * s2;
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Result[1][3] = static_cast<T>(0);
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||
|
|
Result[2][0] = c1 * s3 + c2 * c3 * s1;
|
||
|
|
Result[2][1] =-c3 * s2;
|
||
|
|
Result[2][2] = c1 * c2 * c3 - s1 * s3;
|
||
|
|
Result[2][3] = static_cast<T>(0);
|
||
|
|
Result[3][0] = static_cast<T>(0);
|
||
|
|
Result[3][1] = static_cast<T>(0);
|
||
|
|
Result[3][2] = static_cast<T>(0);
|
||
|
|
Result[3][3] = static_cast<T>(1);
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleYZY
|
||
|
|
(
|
||
|
|
T const & t1,
|
||
|
|
T const & t2,
|
||
|
|
T const & t3
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T c1 = glm::cos(t1);
|
||
|
|
T s1 = glm::sin(t1);
|
||
|
|
T c2 = glm::cos(t2);
|
||
|
|
T s2 = glm::sin(t2);
|
||
|
|
T c3 = glm::cos(t3);
|
||
|
|
T s3 = glm::sin(t3);
|
||
|
|
|
||
|
|
mat<4, 4, T, defaultp> Result;
|
||
|
|
Result[0][0] = c1 * c2 * c3 - s1 * s3;
|
||
|
|
Result[0][1] = c3 * s2;
|
||
|
|
Result[0][2] =-c1 * s3 - c2 * c3 * s1;
|
||
|
|
Result[0][3] = static_cast<T>(0);
|
||
|
|
Result[1][0] =-c1 * s2;
|
||
|
|
Result[1][1] = c2;
|
||
|
|
Result[1][2] = s1 * s2;
|
||
|
|
Result[1][3] = static_cast<T>(0);
|
||
|
|
Result[2][0] = c3 * s1 + c1 * c2 * s3;
|
||
|
|
Result[2][1] = s2 * s3;
|
||
|
|
Result[2][2] = c1 * c3 - c2 * s1 * s3;
|
||
|
|
Result[2][3] = static_cast<T>(0);
|
||
|
|
Result[3][0] = static_cast<T>(0);
|
||
|
|
Result[3][1] = static_cast<T>(0);
|
||
|
|
Result[3][2] = static_cast<T>(0);
|
||
|
|
Result[3][3] = static_cast<T>(1);
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleZYZ
|
||
|
|
(
|
||
|
|
T const & t1,
|
||
|
|
T const & t2,
|
||
|
|
T const & t3
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T c1 = glm::cos(t1);
|
||
|
|
T s1 = glm::sin(t1);
|
||
|
|
T c2 = glm::cos(t2);
|
||
|
|
T s2 = glm::sin(t2);
|
||
|
|
T c3 = glm::cos(t3);
|
||
|
|
T s3 = glm::sin(t3);
|
||
|
|
|
||
|
|
mat<4, 4, T, defaultp> Result;
|
||
|
|
Result[0][0] = c1 * c2 * c3 - s1 * s3;
|
||
|
|
Result[0][1] = c1 * s3 + c2 * c3 * s1;
|
||
|
|
Result[0][2] =-c3 * s2;
|
||
|
|
Result[0][3] = static_cast<T>(0);
|
||
|
|
Result[1][0] =-c3 * s1 - c1 * c2 * s3;
|
||
|
|
Result[1][1] = c1 * c3 - c2 * s1 * s3;
|
||
|
|
Result[1][2] = s2 * s3;
|
||
|
|
Result[1][3] = static_cast<T>(0);
|
||
|
|
Result[2][0] = c1 * s2;
|
||
|
|
Result[2][1] = s1 * s2;
|
||
|
|
Result[2][2] = c2;
|
||
|
|
Result[2][3] = static_cast<T>(0);
|
||
|
|
Result[3][0] = static_cast<T>(0);
|
||
|
|
Result[3][1] = static_cast<T>(0);
|
||
|
|
Result[3][2] = static_cast<T>(0);
|
||
|
|
Result[3][3] = static_cast<T>(1);
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleZXZ
|
||
|
|
(
|
||
|
|
T const & t1,
|
||
|
|
T const & t2,
|
||
|
|
T const & t3
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T c1 = glm::cos(t1);
|
||
|
|
T s1 = glm::sin(t1);
|
||
|
|
T c2 = glm::cos(t2);
|
||
|
|
T s2 = glm::sin(t2);
|
||
|
|
T c3 = glm::cos(t3);
|
||
|
|
T s3 = glm::sin(t3);
|
||
|
|
|
||
|
|
mat<4, 4, T, defaultp> Result;
|
||
|
|
Result[0][0] = c1 * c3 - c2 * s1 * s3;
|
||
|
|
Result[0][1] = c3 * s1 + c1 * c2 * s3;
|
||
|
|
Result[0][2] = s2 *s3;
|
||
|
|
Result[0][3] = static_cast<T>(0);
|
||
|
|
Result[1][0] =-c1 * s3 - c2 * c3 * s1;
|
||
|
|
Result[1][1] = c1 * c2 * c3 - s1 * s3;
|
||
|
|
Result[1][2] = c3 * s2;
|
||
|
|
Result[1][3] = static_cast<T>(0);
|
||
|
|
Result[2][0] = s1 * s2;
|
||
|
|
Result[2][1] =-c1 * s2;
|
||
|
|
Result[2][2] = c2;
|
||
|
|
Result[2][3] = static_cast<T>(0);
|
||
|
|
Result[3][0] = static_cast<T>(0);
|
||
|
|
Result[3][1] = static_cast<T>(0);
|
||
|
|
Result[3][2] = static_cast<T>(0);
|
||
|
|
Result[3][3] = static_cast<T>(1);
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleXZY
|
||
|
|
(
|
||
|
|
T const & t1,
|
||
|
|
T const & t2,
|
||
|
|
T const & t3
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T c1 = glm::cos(t1);
|
||
|
|
T s1 = glm::sin(t1);
|
||
|
|
T c2 = glm::cos(t2);
|
||
|
|
T s2 = glm::sin(t2);
|
||
|
|
T c3 = glm::cos(t3);
|
||
|
|
T s3 = glm::sin(t3);
|
||
|
|
|
||
|
|
mat<4, 4, T, defaultp> Result;
|
||
|
|
Result[0][0] = c2 * c3;
|
||
|
|
Result[0][1] = s1 * s3 + c1 * c3 * s2;
|
||
|
|
Result[0][2] = c3 * s1 * s2 - c1 * s3;
|
||
|
|
Result[0][3] = static_cast<T>(0);
|
||
|
|
Result[1][0] =-s2;
|
||
|
|
Result[1][1] = c1 * c2;
|
||
|
|
Result[1][2] = c2 * s1;
|
||
|
|
Result[1][3] = static_cast<T>(0);
|
||
|
|
Result[2][0] = c2 * s3;
|
||
|
|
Result[2][1] = c1 * s2 * s3 - c3 * s1;
|
||
|
|
Result[2][2] = c1 * c3 + s1 * s2 *s3;
|
||
|
|
Result[2][3] = static_cast<T>(0);
|
||
|
|
Result[3][0] = static_cast<T>(0);
|
||
|
|
Result[3][1] = static_cast<T>(0);
|
||
|
|
Result[3][2] = static_cast<T>(0);
|
||
|
|
Result[3][3] = static_cast<T>(1);
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleYZX
|
||
|
|
(
|
||
|
|
T const & t1,
|
||
|
|
T const & t2,
|
||
|
|
T const & t3
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T c1 = glm::cos(t1);
|
||
|
|
T s1 = glm::sin(t1);
|
||
|
|
T c2 = glm::cos(t2);
|
||
|
|
T s2 = glm::sin(t2);
|
||
|
|
T c3 = glm::cos(t3);
|
||
|
|
T s3 = glm::sin(t3);
|
||
|
|
|
||
|
|
mat<4, 4, T, defaultp> Result;
|
||
|
|
Result[0][0] = c1 * c2;
|
||
|
|
Result[0][1] = s2;
|
||
|
|
Result[0][2] =-c2 * s1;
|
||
|
|
Result[0][3] = static_cast<T>(0);
|
||
|
|
Result[1][0] = s1 * s3 - c1 * c3 * s2;
|
||
|
|
Result[1][1] = c2 * c3;
|
||
|
|
Result[1][2] = c1 * s3 + c3 * s1 * s2;
|
||
|
|
Result[1][3] = static_cast<T>(0);
|
||
|
|
Result[2][0] = c3 * s1 + c1 * s2 * s3;
|
||
|
|
Result[2][1] =-c2 * s3;
|
||
|
|
Result[2][2] = c1 * c3 - s1 * s2 * s3;
|
||
|
|
Result[2][3] = static_cast<T>(0);
|
||
|
|
Result[3][0] = static_cast<T>(0);
|
||
|
|
Result[3][1] = static_cast<T>(0);
|
||
|
|
Result[3][2] = static_cast<T>(0);
|
||
|
|
Result[3][3] = static_cast<T>(1);
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleZYX
|
||
|
|
(
|
||
|
|
T const & t1,
|
||
|
|
T const & t2,
|
||
|
|
T const & t3
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T c1 = glm::cos(t1);
|
||
|
|
T s1 = glm::sin(t1);
|
||
|
|
T c2 = glm::cos(t2);
|
||
|
|
T s2 = glm::sin(t2);
|
||
|
|
T c3 = glm::cos(t3);
|
||
|
|
T s3 = glm::sin(t3);
|
||
|
|
|
||
|
|
mat<4, 4, T, defaultp> Result;
|
||
|
|
Result[0][0] = c1 * c2;
|
||
|
|
Result[0][1] = c2 * s1;
|
||
|
|
Result[0][2] =-s2;
|
||
|
|
Result[0][3] = static_cast<T>(0);
|
||
|
|
Result[1][0] = c1 * s2 * s3 - c3 * s1;
|
||
|
|
Result[1][1] = c1 * c3 + s1 * s2 * s3;
|
||
|
|
Result[1][2] = c2 * s3;
|
||
|
|
Result[1][3] = static_cast<T>(0);
|
||
|
|
Result[2][0] = s1 * s3 + c1 * c3 * s2;
|
||
|
|
Result[2][1] = c3 * s1 * s2 - c1 * s3;
|
||
|
|
Result[2][2] = c2 * c3;
|
||
|
|
Result[2][3] = static_cast<T>(0);
|
||
|
|
Result[3][0] = static_cast<T>(0);
|
||
|
|
Result[3][1] = static_cast<T>(0);
|
||
|
|
Result[3][2] = static_cast<T>(0);
|
||
|
|
Result[3][3] = static_cast<T>(1);
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> eulerAngleZXY
|
||
|
|
(
|
||
|
|
T const & t1,
|
||
|
|
T const & t2,
|
||
|
|
T const & t3
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T c1 = glm::cos(t1);
|
||
|
|
T s1 = glm::sin(t1);
|
||
|
|
T c2 = glm::cos(t2);
|
||
|
|
T s2 = glm::sin(t2);
|
||
|
|
T c3 = glm::cos(t3);
|
||
|
|
T s3 = glm::sin(t3);
|
||
|
|
|
||
|
|
mat<4, 4, T, defaultp> Result;
|
||
|
|
Result[0][0] = c1 * c3 - s1 * s2 * s3;
|
||
|
|
Result[0][1] = c3 * s1 + c1 * s2 * s3;
|
||
|
|
Result[0][2] =-c2 * s3;
|
||
|
|
Result[0][3] = static_cast<T>(0);
|
||
|
|
Result[1][0] =-c2 * s1;
|
||
|
|
Result[1][1] = c1 * c2;
|
||
|
|
Result[1][2] = s2;
|
||
|
|
Result[1][3] = static_cast<T>(0);
|
||
|
|
Result[2][0] = c1 * s3 + c3 * s1 * s2;
|
||
|
|
Result[2][1] = s1 * s3 - c1 * c3 * s2;
|
||
|
|
Result[2][2] = c2 * c3;
|
||
|
|
Result[2][3] = static_cast<T>(0);
|
||
|
|
Result[3][0] = static_cast<T>(0);
|
||
|
|
Result[3][1] = static_cast<T>(0);
|
||
|
|
Result[3][2] = static_cast<T>(0);
|
||
|
|
Result[3][3] = static_cast<T>(1);
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename T>
|
||
|
|
GLM_FUNC_QUALIFIER mat<4, 4, T, defaultp> yawPitchRoll
|
||
|
|
(
|
||
|
|
T const& yaw,
|
||
|
|
T const& pitch,
|
||
|
|
T const& roll
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T tmp_ch = glm::cos(yaw);
|
||
|
|
T tmp_sh = glm::sin(yaw);
|
||
|
|
T tmp_cp = glm::cos(pitch);
|
||
|
|
T tmp_sp = glm::sin(pitch);
|
||
|
|
T tmp_cb = glm::cos(roll);
|
||
|
|
T tmp_sb = glm::sin(roll);
|
||
|
|
|
||
|
|
mat<4, 4, T, defaultp> Result;
|
||
|
|
Result[0][0] = tmp_ch * tmp_cb + tmp_sh * tmp_sp * tmp_sb;
|
||
|
|
Result[0][1] = tmp_sb * tmp_cp;
|
||
|
|
Result[0][2] = -tmp_sh * tmp_cb + tmp_ch * tmp_sp * tmp_sb;
|
||
|
|
Result[0][3] = static_cast<T>(0);
|
||
|
|
Result[1][0] = -tmp_ch * tmp_sb + tmp_sh * tmp_sp * tmp_cb;
|
||
|
|
Result[1][1] = tmp_cb * tmp_cp;
|
||
|
|
Result[1][2] = tmp_sb * tmp_sh + tmp_ch * tmp_sp * tmp_cb;
|
||
|
|
Result[1][3] = static_cast<T>(0);
|
||
|
|
Result[2][0] = tmp_sh * tmp_cp;
|
||
|
|
Result[2][1] = -tmp_sp;
|
||
|
|
Result[2][2] = tmp_ch * tmp_cp;
|
||
|
|
Result[2][3] = static_cast<T>(0);
|
||
|
|
Result[3][0] = static_cast<T>(0);
|
||
|
|
Result[3][1] = static_cast<T>(0);
|
||
|
|
Result[3][2] = static_cast<T>(0);
|
||
|
|
Result[3][3] = static_cast<T>(1);
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename T>
|
||
|
|
GLM_FUNC_QUALIFIER mat<2, 2, T, defaultp> orientate2
|
||
|
|
(
|
||
|
|
T const& angle
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T c = glm::cos(angle);
|
||
|
|
T s = glm::sin(angle);
|
||
|
|
|
||
|
|
mat<2, 2, T, defaultp> Result;
|
||
|
|
Result[0][0] = c;
|
||
|
|
Result[0][1] = s;
|
||
|
|
Result[1][0] = -s;
|
||
|
|
Result[1][1] = c;
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename T>
|
||
|
|
GLM_FUNC_QUALIFIER mat<3, 3, T, defaultp> orientate3
|
||
|
|
(
|
||
|
|
T const& angle
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T c = glm::cos(angle);
|
||
|
|
T s = glm::sin(angle);
|
||
|
|
|
||
|
|
mat<3, 3, T, defaultp> Result;
|
||
|
|
Result[0][0] = c;
|
||
|
|
Result[0][1] = s;
|
||
|
|
Result[0][2] = 0.0f;
|
||
|
|
Result[1][0] = -s;
|
||
|
|
Result[1][1] = c;
|
||
|
|
Result[1][2] = 0.0f;
|
||
|
|
Result[2][0] = 0.0f;
|
||
|
|
Result[2][1] = 0.0f;
|
||
|
|
Result[2][2] = 1.0f;
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename T, qualifier Q>
|
||
|
|
GLM_FUNC_QUALIFIER mat<3, 3, T, Q> orientate3
|
||
|
|
(
|
||
|
|
vec<3, T, Q> const& angles
|
||
|
|
)
|
||
|
|
{
|
||
|
|
return mat<3, 3, T, Q>(yawPitchRoll(angles.z, angles.x, angles.y));
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename T, qualifier Q>
|
||
|
|
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> orientate4
|
||
|
|
(
|
||
|
|
vec<3, T, Q> const& angles
|
||
|
|
)
|
||
|
|
{
|
||
|
|
return yawPitchRoll(angles.z, angles.x, angles.y);
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename T>
|
||
|
|
GLM_FUNC_DECL void extractEulerAngleXYZ(mat<4, 4, T, defaultp> const& M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(M[2][1], M[2][2]);
|
||
|
|
T C2 = glm::sqrt(M[0][0]*M[0][0] + M[1][0]*M[1][0]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(-M[2][0], C2);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(S1*M[0][2] - C1*M[0][1], C1*M[1][1] - S1*M[1][2 ]);
|
||
|
|
t1 = -T1;
|
||
|
|
t2 = -T2;
|
||
|
|
t3 = -T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleYXZ(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(M[2][0], M[2][2]);
|
||
|
|
T C2 = glm::sqrt(M[0][1]*M[0][1] + M[1][1]*M[1][1]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(-M[2][1], C2);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(S1*M[1][2] - C1*M[1][0], C1*M[0][0] - S1*M[0][2]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleXZX(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(M[0][2], M[0][1]);
|
||
|
|
T S2 = glm::sqrt(M[1][0]*M[1][0] + M[2][0]*M[2][0]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(S2, M[0][0]);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(C1*M[1][2] - S1*M[1][1], C1*M[2][2] - S1*M[2][1]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleXYX(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(M[0][1], -M[0][2]);
|
||
|
|
T S2 = glm::sqrt(M[1][0]*M[1][0] + M[2][0]*M[2][0]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(S2, M[0][0]);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(-C1*M[2][1] - S1*M[2][2], C1*M[1][1] + S1*M[1][2]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleYXY(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(M[1][0], M[1][2]);
|
||
|
|
T S2 = glm::sqrt(M[0][1]*M[0][1] + M[2][1]*M[2][1]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(S2, M[1][1]);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(C1*M[2][0] - S1*M[2][2], C1*M[0][0] - S1*M[0][2]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleYZY(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(M[1][2], -M[1][0]);
|
||
|
|
T S2 = glm::sqrt(M[0][1]*M[0][1] + M[2][1]*M[2][1]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(S2, M[1][1]);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(-S1*M[0][0] - C1*M[0][2], S1*M[2][0] + C1*M[2][2]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleZYZ(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(M[2][1], M[2][0]);
|
||
|
|
T S2 = glm::sqrt(M[0][2]*M[0][2] + M[1][2]*M[1][2]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(S2, M[2][2]);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(C1*M[0][1] - S1*M[0][0], C1*M[1][1] - S1*M[1][0]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleZXZ(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(M[2][0], -M[2][1]);
|
||
|
|
T S2 = glm::sqrt(M[0][2]*M[0][2] + M[1][2]*M[1][2]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(S2, M[2][2]);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(-C1*M[1][0] - S1*M[1][1], C1*M[0][0] + S1*M[0][1]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleXZY(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(M[1][2], M[1][1]);
|
||
|
|
T C2 = glm::sqrt(M[0][0]*M[0][0] + M[2][0]*M[2][0]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(-M[1][0], C2);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(S1*M[0][1] - C1*M[0][2], C1*M[2][2] - S1*M[2][1]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleYZX(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(-M[0][2], M[0][0]);
|
||
|
|
T C2 = glm::sqrt(M[1][1]*M[1][1] + M[2][1]*M[2][1]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(M[0][1], C2);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(S1*M[1][0] + C1*M[1][2], S1*M[2][0] + C1*M[2][2]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleZYX(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(M[0][1], M[0][0]);
|
||
|
|
T C2 = glm::sqrt(M[1][2]*M[1][2] + M[2][2]*M[2][2]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(-M[0][2], C2);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(S1*M[2][0] - C1*M[2][1], C1*M[1][1] - S1*M[1][0]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER void extractEulerAngleZXY(mat<4, 4, T, defaultp> const & M,
|
||
|
|
T & t1,
|
||
|
|
T & t2,
|
||
|
|
T & t3)
|
||
|
|
{
|
||
|
|
T T1 = glm::atan2<T, defaultp>(-M[1][0], M[1][1]);
|
||
|
|
T C2 = glm::sqrt(M[0][2]*M[0][2] + M[2][2]*M[2][2]);
|
||
|
|
T T2 = glm::atan2<T, defaultp>(M[1][2], C2);
|
||
|
|
T S1 = glm::sin(T1);
|
||
|
|
T C1 = glm::cos(T1);
|
||
|
|
T T3 = glm::atan2<T, defaultp>(C1*M[2][0] + S1*M[2][1], C1*M[0][0] + S1*M[0][1]);
|
||
|
|
t1 = T1;
|
||
|
|
t2 = T2;
|
||
|
|
t3 = T3;
|
||
|
|
}
|
||
|
|
}//namespace glm
|