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303 lines
7.6 KiB
C++
303 lines
7.6 KiB
C++
///////////////////////////////////////////////////////////////////////////////////////////////////
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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 : 2005-12-21
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// Updated : 2008-11-27
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// Licence : This source is under MIT License
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// File : glm/gtx/quaternion.inl
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///////////////////////////////////////////////////////////////////////////////////////////////////
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#include <limits>
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namespace glm{
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namespace gtx{
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namespace quaternion
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{
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template <typename valType>
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GLM_FUNC_QUALIFIER detail::tvec3<valType> cross
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(
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detail::tvec3<valType> const & v,
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detail::tquat<valType> 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 valType>
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GLM_FUNC_QUALIFIER detail::tvec3<valType> cross
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(
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detail::tquat<valType> const & q,
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detail::tvec3<valType> const & v
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)
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{
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return q * v;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tquat<T> squad
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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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detail::tquat<T> const & s1,
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detail::tquat<T> const & s2,
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T const & h)
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{
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return mix(mix(q1, q2, h), mix(s1, s2, h), T(2) * h (T(1) - h));
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tquat<T> intermediate
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(
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detail::tquat<T> const & prev,
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detail::tquat<T> const & curr,
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detail::tquat<T> const & next
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)
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{
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detail::tquat<T> invQuat = gtc::quaternion::inverse(curr);
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return ext((log(next + invQuat) + log(prev + invQuat)) / T(-4)) * curr;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tquat<T> exp
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(
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detail::tquat<T> const & q,
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T const & exponent
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)
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{
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detail::tvec3<T> u(q.x, q.y, q.z);
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float a = glm::length(u);
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detail::tvec3<T> v(u / a);
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return detail::tquat<T>(cos(a), sin(a) * v);
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tquat<T> log
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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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if((q.x == T(0)) && (q.y == T(0)) && (q.z == T(0)))
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{
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if(q.w > T(0))
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return detail::tquat<T>(log(q.w), T(0), T(0), T(0));
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else if(q.w < T(0))
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return detail::tquat<T>(log(-q.w), T(3.1415926535897932384626433832795), T(0),T(0));
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else
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return detail::tquat<T>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity());
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}
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else
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{
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T Vec3Len = sqrt(q.x * q.x + q.y * q.y + q.z * q.z);
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T QuatLen = sqrt(Vec3Len * Vec3Len + q.w * q.w);
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T t = atan(Vec3Len, T(q.w)) / Vec3Len;
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return detail::tquat<T>(t * q.x, t * q.y, t * q.z, log(QuatLen));
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}
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tquat<T> pow
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(
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detail::tquat<T> const & x,
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T const & y
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)
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{
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if(abs(x.w) > T(0.9999))
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return x;
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float Angle = acos(y);
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float NewAngle = Angle * y;
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float Div = sin(NewAngle) / sin(Angle);
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return detail::tquat<T>(
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cos(NewAngle),
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x.x * Div,
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x.y * Div,
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x.z * Div);
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}
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//template <typename T>
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//GLM_FUNC_QUALIFIER detail::tquat<T> sqrt
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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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// T q0 = T(1) - dot(q, q);
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// return T(2) * (T(1) + q0) * q;
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//}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tvec3<T> rotate
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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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return q * v;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tvec4<T> rotate
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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 q * v;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER T angle
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(
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detail::tquat<T> const & x
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)
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{
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return acos(x.w) * T(2);
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tvec3<T> axis
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(
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detail::tquat<T> const & x
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)
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{
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T tmp1 = T(1) - x.w * x.w;
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if(tmp1 <= T(0))
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return detail::tvec3<T>(0, 0, 1);
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T tmp2 = T(1) / sqrt(tmp1);
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return detail::tvec3<T>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
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}
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template <typename valType>
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GLM_FUNC_QUALIFIER detail::tquat<valType> angleAxis
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(
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valType const & angle,
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valType const & x,
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valType const & y,
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valType const & z
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)
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{
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return angleAxis(angle, detail::tvec3<valType>(x, y, z));
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}
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template <typename valType>
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GLM_FUNC_QUALIFIER detail::tquat<valType> angleAxis
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(
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valType const & angle,
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detail::tvec3<valType> const & v
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)
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{
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detail::tquat<valType> result;
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valType a = glm::radians(angle);
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valType s = glm::sin(a * valType(0.5));
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result.w = glm::cos(a * valType(0.5));
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result.x = v.x * s;
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result.y = v.y * s;
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result.z = v.z * s;
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return result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER T extractRealComponent
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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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T w = T(1.0) - q.x * q.x - q.y * q.y - q.z * q.z;
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if(w < T(0))
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return T(0);
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else
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return -sqrt(w);
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}
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template <typename valType>
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GLM_FUNC_QUALIFIER valType roll
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(
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detail::tquat<valType> const & q
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)
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{
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return atan2(valType(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z);
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}
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template <typename valType>
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GLM_FUNC_QUALIFIER valType pitch
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(
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detail::tquat<valType> const & q
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)
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{
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return atan2(valType(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z);
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}
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template <typename valType>
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GLM_FUNC_QUALIFIER valType yaw
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(
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detail::tquat<valType> const & q
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)
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{
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return asin(valType(-2) * (q.x * q.z - q.w * q.y));
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}
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template <typename valType>
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GLM_FUNC_QUALIFIER detail::tvec3<valType> eularAngles
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(
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detail::tquat<valType> const & x
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)
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{
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return detail::tvec3<valType>(pitch(x), yaw(x), roll(x));
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tquat<T> shortMix
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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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T 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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GLM_FUNC_QUALIFIER detail::tquat<T> fastMix
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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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T const & a
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)
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{
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return glm::normalize(x * (1 - a) + (y * a));
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}
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}//namespace quaternion
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}//namespace gtx
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}//namespace glm
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