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805 lines
22 KiB
805 lines
22 KiB
/// @ref gtc_quaternion |
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/// @file glm/gtc/quaternion.inl |
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#include "../trigonometric.hpp" |
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#include "../geometric.hpp" |
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#include "../exponential.hpp" |
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#include "epsilon.hpp" |
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#include <limits> |
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namespace glm{ |
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namespace detail |
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{ |
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template<typename T, qualifier Q, bool Aligned> |
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struct compute_dot<tquat<T, Q>, T, Aligned> |
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{ |
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static GLM_FUNC_QUALIFIER T call(tquat<T, Q> const& a, tquat<T, Q> const& b) |
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{ |
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vec<4, T, Q> tmp(a.x * b.x, a.y * b.y, a.z * b.z, a.w * b.w); |
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return (tmp.x + tmp.y) + (tmp.z + tmp.w); |
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} |
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}; |
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template<typename T, qualifier Q, bool Aligned> |
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struct compute_quat_add |
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{ |
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static tquat<T, Q> call(tquat<T, Q> const& q, tquat<T, Q> const& p) |
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{ |
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return tquat<T, Q>(q.w + p.w, q.x + p.x, q.y + p.y, q.z + p.z); |
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} |
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}; |
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template<typename T, qualifier Q, bool Aligned> |
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struct compute_quat_sub |
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{ |
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static tquat<T, Q> call(tquat<T, Q> const& q, tquat<T, Q> const& p) |
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{ |
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return tquat<T, Q>(q.w - p.w, q.x - p.x, q.y - p.y, q.z - p.z); |
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} |
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}; |
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template<typename T, qualifier Q, bool Aligned> |
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struct compute_quat_mul_scalar |
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{ |
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static tquat<T, Q> call(tquat<T, Q> const& q, T s) |
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{ |
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return tquat<T, Q>(q.w * s, q.x * s, q.y * s, q.z * s); |
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} |
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}; |
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template<typename T, qualifier Q, bool Aligned> |
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struct compute_quat_div_scalar |
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{ |
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static tquat<T, Q> call(tquat<T, Q> const& q, T s) |
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{ |
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return tquat<T, Q>(q.w / s, q.x / s, q.y / s, q.z / s); |
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} |
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}; |
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template<typename T, qualifier Q, bool Aligned> |
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struct compute_quat_mul_vec4 |
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{ |
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static vec<4, T, Q> call(tquat<T, Q> const& q, vec<4, T, Q> const& v) |
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{ |
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return vec<4, T, Q>(q * vec<3, T, Q>(v), v.w); |
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} |
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}; |
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}//namespace detail |
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// -- Component accesses -- |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER T & tquat<T, Q>::operator[](typename tquat<T, Q>::length_type i) |
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{ |
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assert(i >= 0 && i < this->length()); |
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return (&x)[i]; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER T const& tquat<T, Q>::operator[](typename tquat<T, Q>::length_type i) const |
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{ |
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assert(i >= 0 && i < this->length()); |
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return (&x)[i]; |
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} |
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// -- Implicit basic constructors -- |
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# if GLM_USE_DEFAULTED_FUNCTIONS == GLM_DISABLE |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR_CXX11 tquat<T, Q>::tquat() |
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# if GLM_USE_DEFAULTED_FUNCTIONS != GLM_DISABLE |
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: x(0), y(0), z(0), w(1) |
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# endif |
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{} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR_CXX11 tquat<T, Q>::tquat(tquat<T, Q> const& q) |
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: x(q.x), y(q.y), z(q.z), w(q.w) |
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{} |
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# endif |
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template<typename T, qualifier Q> |
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template<qualifier P> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR_CXX11 tquat<T, Q>::tquat(tquat<T, P> const& q) |
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: x(q.x), y(q.y), z(q.z), w(q.w) |
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{} |
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// -- Explicit basic constructors -- |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR_CXX11 tquat<T, Q>::tquat(T s, vec<3, T, Q> const& v) |
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: x(v.x), y(v.y), z(v.z), w(s) |
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{} |
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template <typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR_CXX11 tquat<T, Q>::tquat(T _w, T _x, T _y, T _z) |
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: x(_x), y(_y), z(_z), w(_w) |
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{} |
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// -- Conversion constructors -- |
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template<typename T, qualifier Q> |
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template<typename U, qualifier P> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR_CXX11 tquat<T, Q>::tquat(tquat<U, P> const& q) |
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: x(static_cast<T>(q.x)) |
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, y(static_cast<T>(q.y)) |
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, z(static_cast<T>(q.z)) |
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, w(static_cast<T>(q.w)) |
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{} |
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//template<typename valType> |
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//GLM_FUNC_QUALIFIER 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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// vec<3, valType> eulerAngle(pitch * valType(0.5), yaw * valType(0.5), roll * valType(0.5)); |
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// vec<3, valType> c = glm::cos(eulerAngle * valType(0.5)); |
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// vec<3, 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, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(vec<3, T, Q> const& u, vec<3, T, Q> const& v) |
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{ |
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T norm_u_norm_v = sqrt(dot(u, u) * dot(v, v)); |
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T real_part = norm_u_norm_v + dot(u, v); |
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vec<3, T, Q> t; |
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if(real_part < static_cast<T>(1.e-6f) * norm_u_norm_v) |
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{ |
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// If u and v are exactly opposite, rotate 180 degrees |
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// around an arbitrary orthogonal axis. Axis normalisation |
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// can happen later, when we normalise the quaternion. |
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real_part = static_cast<T>(0); |
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t = abs(u.x) > abs(u.z) ? vec<3, T, Q>(-u.y, u.x, static_cast<T>(0)) : vec<3, T, Q>(static_cast<T>(0), -u.z, u.y); |
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} |
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else |
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{ |
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// Otherwise, build quaternion the standard way. |
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t = cross(u, v); |
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} |
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*this = normalize(tquat<T, Q>(real_part, t.x, t.y, t.z)); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(vec<3, T, Q> const& eulerAngle) |
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{ |
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vec<3, T, Q> c = glm::cos(eulerAngle * T(0.5)); |
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vec<3, T, Q> s = glm::sin(eulerAngle * T(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, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(mat<3, 3, T, Q> const& m) |
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{ |
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*this = quat_cast(m); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(mat<4, 4, T, Q> const& m) |
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{ |
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*this = quat_cast(m); |
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} |
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# if GLM_HAS_EXPLICIT_CONVERSION_OPERATORS |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q>::operator mat<3, 3, T, Q>() |
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{ |
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return mat3_cast(*this); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q>::operator mat<4, 4, T, Q>() |
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{ |
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return mat4_cast(*this); |
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} |
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# endif//GLM_HAS_EXPLICIT_CONVERSION_OPERATORS |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> conjugate(tquat<T, Q> const& q) |
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{ |
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return tquat<T, Q>(q.w, -q.x, -q.y, -q.z); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> inverse(tquat<T, Q> const& q) |
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{ |
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return conjugate(q) / dot(q, q); |
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} |
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// -- Unary arithmetic operators -- |
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# if GLM_USE_DEFAULTED_FUNCTIONS == GLM_DISABLE |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator=(tquat<T, Q> const& q) |
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{ |
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this->w = q.w; |
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this->x = q.x; |
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this->y = q.y; |
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this->z = q.z; |
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return *this; |
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} |
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# endif |
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template<typename T, qualifier Q> |
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template<typename U> |
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GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator=(tquat<U, Q> const& q) |
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{ |
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this->w = static_cast<T>(q.w); |
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this->x = static_cast<T>(q.x); |
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this->y = static_cast<T>(q.y); |
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this->z = static_cast<T>(q.z); |
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return *this; |
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} |
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template<typename T, qualifier Q> |
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template<typename U> |
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GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator+=(tquat<U, Q> const& q) |
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{ |
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return (*this = detail::compute_quat_add<T, Q, detail::is_aligned<Q>::value>::call(*this, tquat<T, Q>(q))); |
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} |
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template<typename T, qualifier Q> |
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template<typename U> |
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GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator-=(tquat<U, Q> const& q) |
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{ |
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return (*this = detail::compute_quat_sub<T, Q, detail::is_aligned<Q>::value>::call(*this, tquat<T, Q>(q))); |
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} |
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template<typename T, qualifier Q> |
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template<typename U> |
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GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator*=(tquat<U, Q> const& r) |
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{ |
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tquat<T, Q> const p(*this); |
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tquat<T, Q> const q(r); |
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this->w = p.w * q.w - p.x * q.x - p.y * q.y - p.z * q.z; |
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this->x = p.w * q.x + p.x * q.w + p.y * q.z - p.z * q.y; |
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this->y = p.w * q.y + p.y * q.w + p.z * q.x - p.x * q.z; |
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this->z = p.w * q.z + p.z * q.w + p.x * q.y - p.y * q.x; |
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return *this; |
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} |
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template<typename T, qualifier Q> |
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template<typename U> |
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GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator*=(U s) |
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{ |
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return (*this = detail::compute_quat_mul_scalar<T, Q, detail::is_aligned<Q>::value>::call(*this, static_cast<U>(s))); |
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} |
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template<typename T, qualifier Q> |
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template<typename U> |
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GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator/=(U s) |
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{ |
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return (*this = detail::compute_quat_div_scalar<T, Q, detail::is_aligned<Q>::value>::call(*this, static_cast<U>(s))); |
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} |
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// -- Unary bit operators -- |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> operator+(tquat<T, Q> const& q) |
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{ |
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return q; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> operator-(tquat<T, Q> const& q) |
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{ |
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return tquat<T, Q>(-q.w, -q.x, -q.y, -q.z); |
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} |
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// -- Binary operators -- |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> operator+(tquat<T, Q> const& q, tquat<T, Q> const& p) |
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{ |
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return tquat<T, Q>(q) += p; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> operator-(tquat<T, Q> const& q, tquat<T, Q> const& p) |
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{ |
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return tquat<T, Q>(q) -= p; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> operator*(tquat<T, Q> const& q, tquat<T, Q> const& p) |
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{ |
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return tquat<T, Q>(q) *= p; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<3, T, Q> operator*(tquat<T, Q> const& q, vec<3, T, Q> const& v) |
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{ |
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vec<3, T, Q> const QuatVector(q.x, q.y, q.z); |
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vec<3, T, Q> const uv(glm::cross(QuatVector, v)); |
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vec<3, T, Q> const uuv(glm::cross(QuatVector, uv)); |
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return v + ((uv * q.w) + uuv) * static_cast<T>(2); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<3, T, Q> operator*(vec<3, T, Q> const& v, tquat<T, Q> const& q) |
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{ |
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return glm::inverse(q) * v; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<4, T, Q> operator*(tquat<T, Q> const& q, vec<4, T, Q> const& v) |
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{ |
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return detail::compute_quat_mul_vec4<T, Q, detail::is_aligned<Q>::value>::call(q, v); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<4, T, Q> operator*(vec<4, T, Q> const& v, tquat<T, Q> const& q) |
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{ |
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return glm::inverse(q) * v; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> operator*(tquat<T, Q> const& q, T const& s) |
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{ |
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return tquat<T, Q>( |
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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, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> operator*(T const& s, tquat<T, Q> const& q) |
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{ |
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return q * s; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> operator/(tquat<T, Q> const& q, T const& s) |
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{ |
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return tquat<T, Q>( |
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q.w / s, q.x / s, q.y / s, q.z / s); |
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} |
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// -- Boolean operators -- |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER bool operator==(tquat<T, Q> const& q1, tquat<T, Q> const& q2) |
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{ |
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return all(epsilonEqual(q1, q2, epsilon<T>())); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER bool operator!=(tquat<T, Q> const& q1, tquat<T, Q> const& q2) |
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{ |
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return any(epsilonNotEqual(q1, q2, epsilon<T>())); |
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} |
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// -- Operations -- |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER T dot(tquat<T, Q> const& x, tquat<T, Q> const& y) |
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{ |
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GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'dot' accepts only floating-point inputs"); |
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return detail::compute_dot<tquat<T, Q>, T, detail::is_aligned<Q>::value>::call(x, y); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER T length(tquat<T, Q> const& q) |
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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, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> normalize(tquat<T, Q> const& q) |
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{ |
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T len = length(q); |
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if(len <= T(0)) // Problem |
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return tquat<T, Q>(static_cast<T>(1), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0)); |
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T oneOverLen = T(1) / len; |
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return tquat<T, Q>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> cross(tquat<T, Q> const& q1, tquat<T, Q> const& q2) |
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{ |
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return tquat<T, Q>( |
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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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/* |
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// (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle)) |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> mix(tquat<T, Q> const& x, tquat<T, Q> const& y, T const& a) |
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{ |
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if(a <= T(0)) return x; |
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if(a >= T(1)) return y; |
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float fCos = dot(x, y); |
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tquat<T, Q> y2(y); //BUG!!! tquat<T, Q> y2; |
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if(fCos < T(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 > T(0.9999)) |
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{ |
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k0 = T(1) - a; |
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k1 = T(0) + a; //BUG!!! 1.0f + a; |
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} |
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else |
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{ |
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T fSin = sqrt(T(1) - fCos * fCos); |
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T fAngle = atan(fSin, fCos); |
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T fOneOverSin = static_cast<T>(1) / fSin; |
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k0 = sin((T(1) - a) * fAngle) * fOneOverSin; |
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k1 = sin((T(0) + a) * fAngle) * fOneOverSin; |
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} |
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return tquat<T, Q>( |
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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, qualifier Q> |
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GLM_FUNC_QUALIFIER tquat<T, Q> mix2 |
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( |
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tquat<T, Q> const& x, |
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tquat<T, Q> const& y, |
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T const& a |
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) |
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{ |
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bool flip = false; |
|
if(a <= static_cast<T>(0)) return x; |
|
if(a >= static_cast<T>(1)) return y; |
|
|
|
T cos_t = dot(x, y); |
|
if(cos_t < T(0)) |
|
{ |
|
cos_t = -cos_t; |
|
flip = true; |
|
} |
|
|
|
T alpha(0), beta(0); |
|
|
|
if(T(1) - cos_t < 1e-7) |
|
beta = static_cast<T>(1) - alpha; |
|
else |
|
{ |
|
T theta = acos(cos_t); |
|
T sin_t = sin(theta); |
|
beta = sin(theta * (T(1) - alpha)) / sin_t; |
|
alpha = sin(alpha * theta) / sin_t; |
|
} |
|
|
|
if(flip) |
|
alpha = -alpha; |
|
|
|
return normalize(beta * x + alpha * y); |
|
} |
|
*/ |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER tquat<T, Q> mix(tquat<T, Q> const& x, tquat<T, Q> const& y, T a) |
|
{ |
|
T cosTheta = dot(x, y); |
|
|
|
// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator |
|
if(cosTheta > T(1) - epsilon<T>()) |
|
{ |
|
// Linear interpolation |
|
return tquat<T, Q>( |
|
mix(x.w, y.w, a), |
|
mix(x.x, y.x, a), |
|
mix(x.y, y.y, a), |
|
mix(x.z, y.z, a)); |
|
} |
|
else |
|
{ |
|
// Essential Mathematics, page 467 |
|
T angle = acos(cosTheta); |
|
return (sin((T(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle); |
|
} |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER tquat<T, Q> lerp(tquat<T, Q> const& x, tquat<T, Q> const& y, T a) |
|
{ |
|
// Lerp is only defined in [0, 1] |
|
assert(a >= static_cast<T>(0)); |
|
assert(a <= static_cast<T>(1)); |
|
|
|
return x * (T(1) - a) + (y * a); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER tquat<T, Q> slerp(tquat<T, Q> const& x, tquat<T, Q> const& y, T a) |
|
{ |
|
tquat<T, Q> z = y; |
|
|
|
T cosTheta = dot(x, y); |
|
|
|
// If cosTheta < 0, the interpolation will take the long way around the sphere. |
|
// To fix this, one quat must be negated. |
|
if (cosTheta < T(0)) |
|
{ |
|
z = -y; |
|
cosTheta = -cosTheta; |
|
} |
|
|
|
// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator |
|
if(cosTheta > T(1) - epsilon<T>()) |
|
{ |
|
// Linear interpolation |
|
return tquat<T, Q>( |
|
mix(x.w, z.w, a), |
|
mix(x.x, z.x, a), |
|
mix(x.y, z.y, a), |
|
mix(x.z, z.z, a)); |
|
} |
|
else |
|
{ |
|
// Essential Mathematics, page 467 |
|
T angle = acos(cosTheta); |
|
return (sin((T(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle); |
|
} |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER tquat<T, Q> rotate(tquat<T, Q> const& q, T const& angle, vec<3, T, Q> const& v) |
|
{ |
|
vec<3, T, Q> Tmp = v; |
|
|
|
// Axis of rotation must be normalised |
|
T len = glm::length(Tmp); |
|
if(abs(len - T(1)) > T(0.001)) |
|
{ |
|
T oneOverLen = static_cast<T>(1) / len; |
|
Tmp.x *= oneOverLen; |
|
Tmp.y *= oneOverLen; |
|
Tmp.z *= oneOverLen; |
|
} |
|
|
|
T const AngleRad(angle); |
|
T const Sin = sin(AngleRad * T(0.5)); |
|
|
|
return q * tquat<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin); |
|
//return gtc::quaternion::cross(q, tquat<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin)); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER vec<3, T, Q> eulerAngles(tquat<T, Q> const& x) |
|
{ |
|
return vec<3, T, Q>(pitch(x), yaw(x), roll(x)); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER T roll(tquat<T, Q> const& q) |
|
{ |
|
return static_cast<T>(atan(static_cast<T>(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)); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER T pitch(tquat<T, Q> const& q) |
|
{ |
|
//return T(atan(T(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)); |
|
const T y = static_cast<T>(2) * (q.y * q.z + q.w * q.x); |
|
const T x = q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z; |
|
|
|
if(detail::compute_equal<T, std::numeric_limits<T>::is_iec559>::call(y, static_cast<T>(0)) && detail::compute_equal<T, std::numeric_limits<T>::is_iec559>::call(x, static_cast<T>(0))) //avoid atan2(0,0) - handle singularity - Matiis |
|
return static_cast<T>(static_cast<T>(2) * atan(q.x,q.w)); |
|
|
|
return static_cast<T>(atan(y,x)); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER T yaw(tquat<T, Q> const& q) |
|
{ |
|
return asin(clamp(static_cast<T>(-2) * (q.x * q.z - q.w * q.y), static_cast<T>(-1), static_cast<T>(1))); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER mat<3, 3, T, Q> mat3_cast(tquat<T, Q> const& q) |
|
{ |
|
mat<3, 3, T, Q> Result(T(1)); |
|
T qxx(q.x * q.x); |
|
T qyy(q.y * q.y); |
|
T qzz(q.z * q.z); |
|
T qxz(q.x * q.z); |
|
T qxy(q.x * q.y); |
|
T qyz(q.y * q.z); |
|
T qwx(q.w * q.x); |
|
T qwy(q.w * q.y); |
|
T qwz(q.w * q.z); |
|
|
|
Result[0][0] = T(1) - T(2) * (qyy + qzz); |
|
Result[0][1] = T(2) * (qxy + qwz); |
|
Result[0][2] = T(2) * (qxz - qwy); |
|
|
|
Result[1][0] = T(2) * (qxy - qwz); |
|
Result[1][1] = T(1) - T(2) * (qxx + qzz); |
|
Result[1][2] = T(2) * (qyz + qwx); |
|
|
|
Result[2][0] = T(2) * (qxz + qwy); |
|
Result[2][1] = T(2) * (qyz - qwx); |
|
Result[2][2] = T(1) - T(2) * (qxx + qyy); |
|
return Result; |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> mat4_cast(tquat<T, Q> const& q) |
|
{ |
|
return mat<4, 4, T, Q>(mat3_cast(q)); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER tquat<T, Q> quat_cast(mat<3, 3, T, Q> const& m) |
|
{ |
|
T fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2]; |
|
T fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2]; |
|
T fourZSquaredMinus1 = m[2][2] - m[0][0] - m[1][1]; |
|
T fourWSquaredMinus1 = m[0][0] + m[1][1] + m[2][2]; |
|
|
|
int biggestIndex = 0; |
|
T fourBiggestSquaredMinus1 = fourWSquaredMinus1; |
|
if(fourXSquaredMinus1 > fourBiggestSquaredMinus1) |
|
{ |
|
fourBiggestSquaredMinus1 = fourXSquaredMinus1; |
|
biggestIndex = 1; |
|
} |
|
if(fourYSquaredMinus1 > fourBiggestSquaredMinus1) |
|
{ |
|
fourBiggestSquaredMinus1 = fourYSquaredMinus1; |
|
biggestIndex = 2; |
|
} |
|
if(fourZSquaredMinus1 > fourBiggestSquaredMinus1) |
|
{ |
|
fourBiggestSquaredMinus1 = fourZSquaredMinus1; |
|
biggestIndex = 3; |
|
} |
|
|
|
T biggestVal = sqrt(fourBiggestSquaredMinus1 + static_cast<T>(1)) * static_cast<T>(0.5); |
|
T mult = static_cast<T>(0.25) / biggestVal; |
|
|
|
switch(biggestIndex) |
|
{ |
|
case 0: |
|
return tquat<T, Q>(biggestVal, (m[1][2] - m[2][1]) * mult, (m[2][0] - m[0][2]) * mult, (m[0][1] - m[1][0]) * mult); |
|
case 1: |
|
return tquat<T, Q>((m[1][2] - m[2][1]) * mult, biggestVal, (m[0][1] + m[1][0]) * mult, (m[2][0] + m[0][2]) * mult); |
|
case 2: |
|
return tquat<T, Q>((m[2][0] - m[0][2]) * mult, (m[0][1] + m[1][0]) * mult, biggestVal, (m[1][2] + m[2][1]) * mult); |
|
case 3: |
|
return tquat<T, Q>((m[0][1] - m[1][0]) * mult, (m[2][0] + m[0][2]) * mult, (m[1][2] + m[2][1]) * mult, biggestVal); |
|
default: // Silence a -Wswitch-default warning in GCC. Should never actually get here. Assert is just for sanity. |
|
assert(false); |
|
return tquat<T, Q>(1, 0, 0, 0); |
|
} |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER tquat<T, Q> quat_cast(mat<4, 4, T, Q> const& m4) |
|
{ |
|
return quat_cast(mat<3, 3, T, Q>(m4)); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER T angle(tquat<T, Q> const& x) |
|
{ |
|
return acos(x.w) * static_cast<T>(2); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER vec<3, T, Q> axis(tquat<T, Q> const& x) |
|
{ |
|
T tmp1 = static_cast<T>(1) - x.w * x.w; |
|
if(tmp1 <= static_cast<T>(0)) |
|
return vec<3, T, Q>(0, 0, 1); |
|
T tmp2 = static_cast<T>(1) / sqrt(tmp1); |
|
return vec<3, T, Q>(x.x * tmp2, x.y * tmp2, x.z * tmp2); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER tquat<T, Q> angleAxis(T const& angle, vec<3, T, Q> const& v) |
|
{ |
|
tquat<T, Q> Result; |
|
|
|
T const a(angle); |
|
T const s = glm::sin(a * static_cast<T>(0.5)); |
|
|
|
Result.w = glm::cos(a * static_cast<T>(0.5)); |
|
Result.x = v.x * s; |
|
Result.y = v.y * s; |
|
Result.z = v.z * s; |
|
return Result; |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThan(tquat<T, Q> const& x, tquat<T, Q> const& y) |
|
{ |
|
vec<4, bool, Q> Result; |
|
for(length_t i = 0; i < x.length(); ++i) |
|
Result[i] = x[i] < y[i]; |
|
return Result; |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThanEqual(tquat<T, Q> const& x, tquat<T, Q> const& y) |
|
{ |
|
vec<4, bool, Q> Result; |
|
for(length_t i = 0; i < x.length(); ++i) |
|
Result[i] = x[i] <= y[i]; |
|
return Result; |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThan(tquat<T, Q> const& x, tquat<T, Q> const& y) |
|
{ |
|
vec<4, bool, Q> Result; |
|
for(length_t i = 0; i < x.length(); ++i) |
|
Result[i] = x[i] > y[i]; |
|
return Result; |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThanEqual(tquat<T, Q> const& x, tquat<T, Q> const& y) |
|
{ |
|
vec<4, bool, Q> Result; |
|
for(length_t i = 0; i < x.length(); ++i) |
|
Result[i] = x[i] >= y[i]; |
|
return Result; |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> equal(tquat<T, Q> const& x, tquat<T, Q> const& y) |
|
{ |
|
vec<4, bool, Q> Result; |
|
for(length_t i = 0; i < x.length(); ++i) |
|
Result[i] = detail::compute_equal<T, std::numeric_limits<T>::is_iec559>::call(x[i], y[i]); |
|
return Result; |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> notEqual(tquat<T, Q> const& x, tquat<T, Q> const& y) |
|
{ |
|
vec<4, bool, Q> Result; |
|
for(length_t i = 0; i < x.length(); ++i) |
|
Result[i] = !detail::compute_equal<T, std::numeric_limits<T>::is_iec559>::call(x[i], y[i]); |
|
return Result; |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> isnan(tquat<T, Q> const& q) |
|
{ |
|
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isnan' only accept floating-point inputs"); |
|
|
|
return vec<4, bool, Q>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w)); |
|
} |
|
|
|
template<typename T, qualifier Q> |
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> isinf(tquat<T, Q> const& q) |
|
{ |
|
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs"); |
|
|
|
return vec<4, bool, Q>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w)); |
|
} |
|
}//namespace glm |
|
|
|
#if GLM_USE_SIMD == GLM_ENABLE |
|
# include "quaternion_simd.inl" |
|
#endif |
|
|
|
|