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506 lines
13 KiB
506 lines
13 KiB
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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// OpenGL Mathematics Copyright (c) 2005 - 2011 G-Truc Creation (www.g-truc.net) |
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/////////////////////////////////////////////////////////////////////////////////////////////////// |
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// Created : 2009-05-21 |
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// Updated : 2010-02-04 |
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// Licence : This source is under MIT License |
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// File : glm/gtc/quaternion.inl |
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/////////////////////////////////////////////////////////////////////////////////////////////////// |
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#include <limits> |
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namespace glm{ |
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namespace detail{ |
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template <typename T> |
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inline tquat<T>::tquat() : |
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x(0), |
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y(0), |
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z(0), |
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w(1) |
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{} |
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template <typename T> |
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inline tquat<T>::tquat |
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( |
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value_type const & s, |
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tvec3<T> const & v |
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) : |
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x(v.x), |
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y(v.y), |
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z(v.z), |
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w(s) |
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{} |
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template <typename T> |
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inline tquat<T>::tquat |
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( |
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value_type const & w, |
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value_type const & x, |
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value_type const & y, |
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value_type const & z |
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) : |
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x(x), |
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y(y), |
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z(z), |
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w(w) |
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{} |
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////////////////////////////////////////////////////////////// |
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// tquat conversions |
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//template <typename valType> |
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//inline tquat<valType>::tquat |
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//( |
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// valType const & pitch, |
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// valType const & yaw, |
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// valType const & roll |
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//) |
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//{ |
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// tvec3<valType> eulerAngle(pitch * valType(0.5), yaw * valType(0.5), roll * valType(0.5)); |
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// tvec3<valType> c = glm::cos(eulerAngle * valType(0.5)); |
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// tvec3<valType> s = glm::sin(eulerAngle * valType(0.5)); |
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// |
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// this->w = c.x * c.y * c.z + s.x * s.y * s.z; |
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// this->x = s.x * c.y * c.z - c.x * s.y * s.z; |
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// this->y = c.x * s.y * c.z + s.x * c.y * s.z; |
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// this->z = c.x * c.y * s.z - s.x * s.y * c.z; |
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//} |
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template <typename T> |
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inline tquat<T>::tquat |
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( |
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tvec3<T> const & eulerAngle |
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) |
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{ |
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tvec3<T> c = glm::cos(eulerAngle * value_type(0.5)); |
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tvec3<T> s = glm::sin(eulerAngle * value_type(0.5)); |
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this->w = c.x * c.y * c.z + s.x * s.y * s.z; |
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this->x = s.x * c.y * c.z - c.x * s.y * s.z; |
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this->y = c.x * s.y * c.z + s.x * c.y * s.z; |
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this->z = c.x * c.y * s.z - s.x * s.y * c.z; |
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} |
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template <typename T> |
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inline tquat<T>::tquat |
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( |
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tmat3x3<T> const & m |
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) |
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{ |
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*this = toQuat(m); |
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} |
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template <typename T> |
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inline tquat<T>::tquat |
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( |
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tmat4x4<T> const & m |
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) |
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{ |
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*this = toQuat(m); |
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} |
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////////////////////////////////////////////////////////////// |
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// tquat<T> accesses |
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template <typename T> |
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inline typename tquat<T>::value_type & tquat<T>::operator [] (int i) |
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{ |
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return (&x)[i]; |
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} |
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template <typename T> |
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inline typename tquat<T>::value_type const & tquat<T>::operator [] (int i) const |
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{ |
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return (&x)[i]; |
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} |
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////////////////////////////////////////////////////////////// |
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// tquat<valType> operators |
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template <typename T> |
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inline tquat<T> & tquat<T>::operator *= |
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( |
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value_type const & s |
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) |
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{ |
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this->w *= s; |
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this->x *= s; |
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this->y *= s; |
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this->z *= s; |
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return *this; |
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} |
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template <typename T> |
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inline tquat<T> & tquat<T>::operator /= |
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( |
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value_type const & s |
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) |
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{ |
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this->w /= s; |
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this->x /= s; |
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this->y /= s; |
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this->z /= s; |
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return *this; |
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} |
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////////////////////////////////////////////////////////////// |
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// tquat<valType> external operators |
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template <typename T> |
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inline detail::tquat<T> operator- |
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( |
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detail::tquat<T> const & q |
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) |
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{ |
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return detail::tquat<T>(-q.w, -q.x, -q.y, -q.z); |
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} |
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// Transformation |
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template <typename T> |
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inline detail::tvec3<T> operator* |
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( |
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detail::tquat<T> const & q, |
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detail::tvec3<T> const & v |
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) |
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{ |
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typename detail::tquat<T>::value_type Two(2); |
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detail::tvec3<T> uv, uuv; |
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detail::tvec3<T> QuatVector(q.x, q.y, q.z); |
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uv = glm::cross(QuatVector, v); |
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uuv = glm::cross(QuatVector, uv); |
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uv *= (Two * q.w); |
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uuv *= Two; |
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return v + uv + uuv; |
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} |
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template <typename T> |
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inline detail::tvec3<T> operator* |
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( |
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detail::tvec3<T> const & v, |
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detail::tquat<T> const & q |
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) |
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{ |
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return gtc::quaternion::inverse(q) * v; |
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} |
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template <typename T> |
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inline detail::tvec4<T> operator* |
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( |
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detail::tquat<T> const & q, |
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detail::tvec4<T> const & v |
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) |
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{ |
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return detail::tvec4<T>(q * detail::tvec3<T>(v), v.w); |
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} |
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template <typename T> |
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inline detail::tvec4<T> operator* |
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( |
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detail::tvec4<T> const & v, |
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detail::tquat<T> const & q |
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) |
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{ |
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return gtc::quaternion::inverse(q) * v; |
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} |
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template <typename T> |
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inline detail::tquat<T> operator* |
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( |
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detail::tquat<T> const & q, |
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typename detail::tquat<T>::value_type const & s |
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) |
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{ |
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return detail::tquat<T>( |
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q.w * s, q.x * s, q.y * s, q.z * s); |
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} |
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template <typename T> |
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inline detail::tquat<T> operator* |
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( |
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typename detail::tquat<T>::value_type const & s, |
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detail::tquat<T> const & q |
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) |
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{ |
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return q * s; |
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} |
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template <typename T> |
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inline detail::tquat<T> operator/ |
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( |
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detail::tquat<T> const & q, |
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typename detail::tquat<T>::value_type const & s |
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) |
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{ |
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return detail::tquat<T>( |
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q.w / s, q.x / s, q.y / s, q.z / s); |
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} |
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////////////////////////////////////// |
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// Boolean operators |
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template <typename T> |
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inline bool operator== |
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( |
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detail::tquat<T> const & q1, |
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detail::tquat<T> const & q2 |
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) |
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{ |
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return (q1.x == q2.x) && (q1.y == q2.y) && (q1.z == q2.z) && (q1.w == q2.w); |
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} |
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template <typename T> |
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inline bool operator!= |
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( |
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detail::tquat<T> const & q1, |
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detail::tquat<T> const & q2 |
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) |
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{ |
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return (q1.x != q2.x) || (q1.y != q2.y) || (q1.z != q2.z) || (q1.w != q2.w); |
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} |
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}//namespace detail |
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namespace gtc{ |
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namespace quaternion{ |
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//////////////////////////////////////////////////////// |
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template <typename T> |
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inline typename detail::tquat<T>::value_type length |
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( |
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detail::tquat<T> const & q |
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) |
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{ |
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return glm::sqrt(dot(q, q)); |
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} |
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template <typename T> |
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inline detail::tquat<T> normalize |
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( |
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detail::tquat<T> const & q |
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) |
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{ |
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typename detail::tquat<T>::value_type len = length(q); |
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if(len <= typename detail::tquat<T>::value_type(0)) // Problem |
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return detail::tquat<T>(1, 0, 0, 0); |
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typename detail::tquat<T>::value_type oneOverLen = typename detail::tquat<T>::value_type(1) / len; |
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return detail::tquat<T>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen); |
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} |
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template <typename T> |
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inline typename detail::tquat<T>::value_type dot |
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( |
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detail::tquat<T> const & q1, |
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detail::tquat<T> const & q2 |
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) |
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{ |
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return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w; |
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} |
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template <typename T> |
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inline detail::tquat<T> cross |
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( |
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detail::tquat<T> const & q1, |
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detail::tquat<T> const & q2 |
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) |
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{ |
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return detail::tquat<T>( |
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q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z, |
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q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y, |
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q1.w * q2.y + q1.y * q2.w + q1.z * q2.x - q1.x * q2.z, |
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q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x); |
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} |
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template <typename T> |
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inline detail::tquat<T> mix |
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( |
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detail::tquat<T> const & x, |
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detail::tquat<T> const & y, |
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typename detail::tquat<T>::value_type const & a |
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) |
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{ |
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if(a <= typename detail::tquat<T>::value_type(0)) return x; |
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if(a >= typename detail::tquat<T>::value_type(1)) return y; |
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float fCos = dot(x, y); |
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detail::tquat<T> y2(y); //BUG!!! tquat<T> y2; |
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if(fCos < typename detail::tquat<T>::value_type(0)) |
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{ |
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y2 = -y; |
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fCos = -fCos; |
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} |
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//if(fCos > 1.0f) // problem |
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float k0, k1; |
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if(fCos > typename detail::tquat<T>::value_type(0.9999)) |
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{ |
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k0 = typename detail::tquat<T>::value_type(1) - a; |
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k1 = typename detail::tquat<T>::value_type(0) + a; //BUG!!! 1.0f + a; |
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} |
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else |
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{ |
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typename detail::tquat<T>::value_type fSin = sqrt(T(1) - fCos * fCos); |
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typename detail::tquat<T>::value_type fAngle = atan(fSin, fCos); |
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typename detail::tquat<T>::value_type fOneOverSin = T(1) / fSin; |
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k0 = sin((typename detail::tquat<T>::value_type(1) - a) * fAngle) * fOneOverSin; |
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k1 = sin((typename detail::tquat<T>::value_type(0) + a) * fAngle) * fOneOverSin; |
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} |
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return detail::tquat<T>( |
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k0 * x.w + k1 * y2.w, |
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k0 * x.x + k1 * y2.x, |
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k0 * x.y + k1 * y2.y, |
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k0 * x.z + k1 * y2.z); |
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} |
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template <typename T> |
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inline detail::tquat<T> conjugate |
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( |
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detail::tquat<T> const & q |
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) |
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{ |
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return detail::tquat<T>(q.w, -q.x, -q.y, -q.z); |
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} |
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template <typename T> |
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inline detail::tquat<T> inverse |
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( |
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detail::tquat<T> const & q |
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) |
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{ |
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return gtc::quaternion::conjugate(q) / gtc::quaternion::length(q); |
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} |
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template <typename T> |
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inline detail::tquat<T> rotate |
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( |
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detail::tquat<T> const & q, |
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typename detail::tquat<T>::value_type const & angle, |
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detail::tvec3<T> const & v |
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) |
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{ |
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detail::tvec3<T> Tmp = v; |
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// Axis of rotation must be normalised |
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typename detail::tquat<T>::value_type len = glm::core::function::geometric::length(Tmp); |
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if(abs(len - typename detail::tquat<T>::value_type(1)) > typename detail::tquat<T>::value_type(0.001)) |
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{ |
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T oneOverLen = T(1) / len; |
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Tmp.x *= oneOverLen; |
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Tmp.y *= oneOverLen; |
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Tmp.z *= oneOverLen; |
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} |
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typename detail::tquat<T>::value_type AngleRad = radians(angle); |
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typename detail::tquat<T>::value_type fSin = sin(AngleRad * T(0.5)); |
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return gtc::quaternion::cross(q, detail::tquat<T>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin)); |
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} |
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template <typename T> |
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inline detail::tmat3x3<T> mat3_cast |
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( |
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detail::tquat<T> const & q |
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) |
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{ |
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detail::tmat3x3<T> Result(typename detail::tquat<T>::value_type(1)); |
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Result[0][0] = 1 - 2 * q.y * q.y - 2 * q.z * q.z; |
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Result[0][1] = 2 * q.x * q.y + 2 * q.w * q.z; |
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Result[0][2] = 2 * q.x * q.z - 2 * q.w * q.y; |
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Result[1][0] = 2 * q.x * q.y - 2 * q.w * q.z; |
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Result[1][1] = 1 - 2 * q.x * q.x - 2 * q.z * q.z; |
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Result[1][2] = 2 * q.y * q.z + 2 * q.w * q.x; |
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Result[2][0] = 2 * q.x * q.z + 2 * q.w * q.y; |
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Result[2][1] = 2 * q.y * q.z - 2 * q.w * q.x; |
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Result[2][2] = 1 - 2 * q.x * q.x - 2 * q.y * q.y; |
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return Result; |
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} |
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template <typename T> |
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inline detail::tmat4x4<T> mat4_cast |
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( |
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detail::tquat<T> const & q |
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) |
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{ |
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return detail::tmat4x4<T>(mat3_cast(q)); |
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} |
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template <typename T> |
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inline detail::tquat<T> quat_cast |
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( |
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detail::tmat3x3<T> const & m |
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) |
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{ |
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typename detail::tquat<T>::value_type fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2]; |
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typename detail::tquat<T>::value_type fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2]; |
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typename detail::tquat<T>::value_type fourZSquaredMinus1 = m[2][2] - m[0][0] - m[1][1]; |
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typename detail::tquat<T>::value_type fourWSquaredMinus1 = m[0][0] + m[1][1] + m[2][2]; |
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int biggestIndex = 0; |
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typename detail::tquat<T>::value_type fourBiggestSquaredMinus1 = fourWSquaredMinus1; |
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if(fourXSquaredMinus1 > fourBiggestSquaredMinus1) |
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{ |
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fourBiggestSquaredMinus1 = fourXSquaredMinus1; |
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biggestIndex = 1; |
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} |
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if(fourYSquaredMinus1 > fourBiggestSquaredMinus1) |
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{ |
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fourBiggestSquaredMinus1 = fourYSquaredMinus1; |
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biggestIndex = 2; |
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} |
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if(fourZSquaredMinus1 > fourBiggestSquaredMinus1) |
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{ |
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fourBiggestSquaredMinus1 = fourZSquaredMinus1; |
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biggestIndex = 3; |
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} |
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typename detail::tquat<T>::value_type biggestVal = sqrt(fourBiggestSquaredMinus1 + typename detail::tquat<T>::value_type(1)) * typename detail::tquat<T>::value_type(0.5); |
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typename detail::tquat<T>::value_type mult = typename detail::tquat<T>::value_type(0.25) / biggestVal; |
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detail::tquat<T> Result; |
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switch(biggestIndex) |
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{ |
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case 0: |
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Result.w = biggestVal; |
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Result.x = (m[1][2] - m[2][1]) * mult; |
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Result.y = (m[2][0] - m[0][2]) * mult; |
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Result.z = (m[0][1] - m[1][0]) * mult; |
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break; |
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case 1: |
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Result.w = (m[1][2] - m[2][1]) * mult; |
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Result.x = biggestVal; |
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Result.y = (m[0][1] + m[1][0]) * mult; |
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Result.z = (m[2][0] + m[0][2]) * mult; |
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break; |
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case 2: |
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Result.w = (m[2][0] - m[0][2]) * mult; |
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Result.x = (m[0][1] + m[1][0]) * mult; |
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Result.y = biggestVal; |
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Result.z = (m[1][2] + m[2][1]) * mult; |
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break; |
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case 3: |
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Result.w = (m[0][1] - m[1][0]) * mult; |
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Result.x = (m[2][0] + m[0][2]) * mult; |
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Result.y = (m[1][2] + m[2][1]) * mult; |
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Result.z = biggestVal; |
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break; |
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} |
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return Result; |
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} |
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template <typename T> |
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inline detail::tquat<T> quat_cast |
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( |
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detail::tmat4x4<T> const & m4 |
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) |
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{ |
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return quat_cast(detail::tmat3x3<T>(m4)); |
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} |
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}//namespace quaternion |
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}//namespace gtc |
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}//namespace glm
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