796 lines
21 KiB
Plaintext
796 lines
21 KiB
Plaintext
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/// @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 <limits>
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namespace glm{
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namespace detail
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{
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template <typename T, precision P, bool Aligned>
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struct compute_dot<tquat, T, P, Aligned>
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{
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static GLM_FUNC_QUALIFIER T call(tquat<T, P> const& x, tquat<T, P> const& y)
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{
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tvec4<T, P> tmp(x.x * y.x, x.y * y.y, x.z * y.z, x.w * y.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, precision P, bool Aligned>
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struct compute_quat_add
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{
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static tquat<T, P> call(tquat<T, P> const& q, tquat<T, P> const& p)
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{
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return tquat<T, P>(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, precision P, bool Aligned>
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struct compute_quat_sub
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{
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static tquat<T, P> call(tquat<T, P> const& q, tquat<T, P> const& p)
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{
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return tquat<T, P>(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, precision P, bool Aligned>
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struct compute_quat_mul_scalar
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{
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static tquat<T, P> call(tquat<T, P> const& q, T s)
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{
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return tquat<T, P>(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, precision P, bool Aligned>
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struct compute_quat_div_scalar
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{
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static tquat<T, P> call(tquat<T, P> const& q, T s)
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{
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return tquat<T, P>(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, precision P, bool Aligned>
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struct compute_quat_mul_vec4
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{
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static tvec4<T, P> call(tquat<T, P> const & q, tvec4<T, P> const & v)
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{
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return tvec4<T, P>(q * tvec3<T, P>(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, precision P>
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GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[](typename tquat<T, P>::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, precision P>
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GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[](typename tquat<T, P>::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_HAS_DEFAULTED_FUNCTIONS || !defined(GLM_FORCE_NO_CTOR_INIT)
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::tquat()
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# ifndef GLM_FORCE_NO_CTOR_INIT
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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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# endif
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# if !GLM_HAS_DEFAULTED_FUNCTIONS
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::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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# endif//!GLM_HAS_DEFAULTED_FUNCTIONS
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template <typename T, precision P>
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template <precision Q>
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::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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// -- Explicit basic constructors --
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR_CTOR tquat<T, P>::tquat(ctor)
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{}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::tquat(T const & s, tvec3<T, P> 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, precision P>
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::tquat(T const & w, T const & x, T const & y, T const & 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, precision P>
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template <typename U, precision Q>
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::tquat(tquat<U, Q> 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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// 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, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tvec3<T, P> const & u, tvec3<T, P> const & v)
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{
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tvec3<T, P> const LocalW(cross(u, v));
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T Dot = detail::compute_dot<tvec3, T, P, detail::is_aligned<P>::value>::call(u, v);
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tquat<T, P> q(T(1) + Dot, LocalW.x, LocalW.y, LocalW.z);
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*this = normalize(q);
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tvec3<T, P> const & eulerAngle)
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{
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tvec3<T, P> c = glm::cos(eulerAngle * T(0.5));
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tvec3<T, P> 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, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tmat3x3<T, P> 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, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tmat4x4<T, P> 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, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat3x3<T, P>()
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{
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return mat3_cast(*this);
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat4x4<T, P>()
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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, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> conjugate(tquat<T, P> const & q)
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{
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return tquat<T, P>(q.w, -q.x, -q.y, -q.z);
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> inverse(tquat<T, P> 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_HAS_DEFAULTED_FUNCTIONS
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator=(tquat<T, P> 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//!GLM_HAS_DEFAULTED_FUNCTIONS
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template <typename T, precision P>
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template <typename U>
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GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator=(tquat<U, P> 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, precision P>
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template <typename U>
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GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator+=(tquat<U, P> const& q)
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{
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return (*this = detail::compute_quat_add<T, P, detail::is_aligned<P>::value>::call(*this, tquat<T, P>(q)));
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}
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template <typename T, precision P>
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template <typename U>
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GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator-=(tquat<U, P> const& q)
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{
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return (*this = detail::compute_quat_sub<T, P, detail::is_aligned<P>::value>::call(*this, tquat<T, P>(q)));
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}
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template <typename T, precision P>
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template <typename U>
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GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator*=(tquat<U, P> const & r)
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{
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tquat<T, P> const p(*this);
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tquat<T, P> 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, precision P>
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template <typename U>
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GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator*=(U s)
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{
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return (*this = detail::compute_quat_mul_scalar<T, P, detail::is_aligned<P>::value>::call(*this, static_cast<U>(s)));
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}
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template <typename T, precision P>
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template <typename U>
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GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator/=(U s)
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{
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return (*this = detail::compute_quat_div_scalar<T, P, detail::is_aligned<P>::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, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> operator+(tquat<T, P> const & q)
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{
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return q;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> operator-(tquat<T, P> const & q)
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{
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return tquat<T, P>(-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, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> operator+(tquat<T, P> const & q, tquat<T, P> const & p)
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{
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return tquat<T, P>(q) += p;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tquat<T, P> operator*(tquat<T, P> const & q, tquat<T, P> const & p)
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{
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return tquat<T, P>(q) *= p;
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}
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template <typename T, precision P>
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GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tquat<T, P> const & q, tvec3<T, P> const & v)
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{
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tvec3<T, P> const QuatVector(q.x, q.y, q.z);
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tvec3<T, P> const uv(glm::cross(QuatVector, v));
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tvec3<T, P> 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, precision P>
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GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tvec3<T, P> const & v, tquat<T, P> 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, precision P>
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GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tquat<T, P> const& q, tvec4<T, P> const& v)
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{
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return detail::compute_quat_mul_vec4<T, P, detail::is_aligned<P>::value>::call(q, v);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tvec4<T, P> const & v, tquat<T, P> const & q)
|
||
|
|
{
|
||
|
|
return glm::inverse(q) * v;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> operator*(tquat<T, P> const & q, T const & s)
|
||
|
|
{
|
||
|
|
return tquat<T, P>(
|
||
|
|
q.w * s, q.x * s, q.y * s, q.z * s);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> operator*(T const & s, tquat<T, P> const & q)
|
||
|
|
{
|
||
|
|
return q * s;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> operator/(tquat<T, P> const & q, T const & s)
|
||
|
|
{
|
||
|
|
return tquat<T, P>(
|
||
|
|
q.w / s, q.x / s, q.y / s, q.z / s);
|
||
|
|
}
|
||
|
|
|
||
|
|
// -- Boolean operators --
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER bool operator==(tquat<T, P> const & q1, tquat<T, P> const & q2)
|
||
|
|
{
|
||
|
|
return (q1.x == q2.x) && (q1.y == q2.y) && (q1.z == q2.z) && (q1.w == q2.w);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER bool operator!=(tquat<T, P> const & q1, tquat<T, P> const & q2)
|
||
|
|
{
|
||
|
|
return (q1.x != q2.x) || (q1.y != q2.y) || (q1.z != q2.z) || (q1.w != q2.w);
|
||
|
|
}
|
||
|
|
|
||
|
|
// -- Operations --
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER T length(tquat<T, P> const & q)
|
||
|
|
{
|
||
|
|
return glm::sqrt(dot(q, q));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> normalize(tquat<T, P> const & q)
|
||
|
|
{
|
||
|
|
T len = length(q);
|
||
|
|
if(len <= T(0)) // Problem
|
||
|
|
return tquat<T, P>(1, 0, 0, 0);
|
||
|
|
T oneOverLen = T(1) / len;
|
||
|
|
return tquat<T, P>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> cross(tquat<T, P> const & q1, tquat<T, P> const & q2)
|
||
|
|
{
|
||
|
|
return tquat<T, P>(
|
||
|
|
q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z,
|
||
|
|
q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y,
|
||
|
|
q1.w * q2.y + q1.y * q2.w + q1.z * q2.x - q1.x * q2.z,
|
||
|
|
q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x);
|
||
|
|
}
|
||
|
|
/*
|
||
|
|
// (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle))
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> mix(tquat<T, P> const & x, tquat<T, P> const & y, T const & a)
|
||
|
|
{
|
||
|
|
if(a <= T(0)) return x;
|
||
|
|
if(a >= T(1)) return y;
|
||
|
|
|
||
|
|
float fCos = dot(x, y);
|
||
|
|
tquat<T, P> y2(y); //BUG!!! tquat<T, P> y2;
|
||
|
|
if(fCos < T(0))
|
||
|
|
{
|
||
|
|
y2 = -y;
|
||
|
|
fCos = -fCos;
|
||
|
|
}
|
||
|
|
|
||
|
|
//if(fCos > 1.0f) // problem
|
||
|
|
float k0, k1;
|
||
|
|
if(fCos > T(0.9999))
|
||
|
|
{
|
||
|
|
k0 = T(1) - a;
|
||
|
|
k1 = T(0) + a; //BUG!!! 1.0f + a;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
T fSin = sqrt(T(1) - fCos * fCos);
|
||
|
|
T fAngle = atan(fSin, fCos);
|
||
|
|
T fOneOverSin = static_cast<T>(1) / fSin;
|
||
|
|
k0 = sin((T(1) - a) * fAngle) * fOneOverSin;
|
||
|
|
k1 = sin((T(0) + a) * fAngle) * fOneOverSin;
|
||
|
|
}
|
||
|
|
|
||
|
|
return tquat<T, P>(
|
||
|
|
k0 * x.w + k1 * y2.w,
|
||
|
|
k0 * x.x + k1 * y2.x,
|
||
|
|
k0 * x.y + k1 * y2.y,
|
||
|
|
k0 * x.z + k1 * y2.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> mix2
|
||
|
|
(
|
||
|
|
tquat<T, P> const & x,
|
||
|
|
tquat<T, P> const & y,
|
||
|
|
T const & a
|
||
|
|
)
|
||
|
|
{
|
||
|
|
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, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> mix(tquat<T, P> const & x, tquat<T, P> 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, P>(
|
||
|
|
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, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> lerp(tquat<T, P> const & x, tquat<T, P> 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, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> slerp(tquat<T, P> const & x, tquat<T, P> const & y, T a)
|
||
|
|
{
|
||
|
|
tquat<T, P> 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, P>(
|
||
|
|
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, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> rotate(tquat<T, P> const & q, T const & angle, tvec3<T, P> const & v)
|
||
|
|
{
|
||
|
|
tvec3<T, P> 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, P>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
|
||
|
|
//return gtc::quaternion::cross(q, tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec3<T, P> eulerAngles(tquat<T, P> const & x)
|
||
|
|
{
|
||
|
|
return tvec3<T, P>(pitch(x), yaw(x), roll(x));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER T roll(tquat<T, P> const & q)
|
||
|
|
{
|
||
|
|
return T(atan(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, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER T pitch(tquat<T, P> 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));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER T yaw(tquat<T, P> const & q)
|
||
|
|
{
|
||
|
|
return asin(clamp(T(-2) * (q.x * q.z - q.w * q.y), T(-1), T(1)));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tmat3x3<T, P> mat3_cast(tquat<T, P> const & q)
|
||
|
|
{
|
||
|
|
tmat3x3<T, P> 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, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tmat4x4<T, P> mat4_cast(tquat<T, P> const & q)
|
||
|
|
{
|
||
|
|
return tmat4x4<T, P>(mat3_cast(q));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> quat_cast(tmat3x3<T, P> 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 + T(1)) * T(0.5);
|
||
|
|
T mult = static_cast<T>(0.25) / biggestVal;
|
||
|
|
|
||
|
|
tquat<T, P> Result(uninitialize);
|
||
|
|
switch(biggestIndex)
|
||
|
|
{
|
||
|
|
case 0:
|
||
|
|
Result.w = biggestVal;
|
||
|
|
Result.x = (m[1][2] - m[2][1]) * mult;
|
||
|
|
Result.y = (m[2][0] - m[0][2]) * mult;
|
||
|
|
Result.z = (m[0][1] - m[1][0]) * mult;
|
||
|
|
break;
|
||
|
|
case 1:
|
||
|
|
Result.w = (m[1][2] - m[2][1]) * mult;
|
||
|
|
Result.x = biggestVal;
|
||
|
|
Result.y = (m[0][1] + m[1][0]) * mult;
|
||
|
|
Result.z = (m[2][0] + m[0][2]) * mult;
|
||
|
|
break;
|
||
|
|
case 2:
|
||
|
|
Result.w = (m[2][0] - m[0][2]) * mult;
|
||
|
|
Result.x = (m[0][1] + m[1][0]) * mult;
|
||
|
|
Result.y = biggestVal;
|
||
|
|
Result.z = (m[1][2] + m[2][1]) * mult;
|
||
|
|
break;
|
||
|
|
case 3:
|
||
|
|
Result.w = (m[0][1] - m[1][0]) * mult;
|
||
|
|
Result.x = (m[2][0] + m[0][2]) * mult;
|
||
|
|
Result.y = (m[1][2] + m[2][1]) * mult;
|
||
|
|
Result.z = biggestVal;
|
||
|
|
break;
|
||
|
|
|
||
|
|
default: // Silence a -Wswitch-default warning in GCC. Should never actually get here. Assert is just for sanity.
|
||
|
|
assert(false);
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> quat_cast(tmat4x4<T, P> const & m4)
|
||
|
|
{
|
||
|
|
return quat_cast(tmat3x3<T, P>(m4));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER T angle(tquat<T, P> const & x)
|
||
|
|
{
|
||
|
|
return acos(x.w) * T(2);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec3<T, P> axis(tquat<T, P> const & x)
|
||
|
|
{
|
||
|
|
T tmp1 = static_cast<T>(1) - x.w * x.w;
|
||
|
|
if(tmp1 <= static_cast<T>(0))
|
||
|
|
return tvec3<T, P>(0, 0, 1);
|
||
|
|
T tmp2 = static_cast<T>(1) / sqrt(tmp1);
|
||
|
|
return tvec3<T, P>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tquat<T, P> angleAxis(T const & angle, tvec3<T, P> const & v)
|
||
|
|
{
|
||
|
|
tquat<T, P> Result(uninitialize);
|
||
|
|
|
||
|
|
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, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec4<bool, P> lessThan(tquat<T, P> const & x, tquat<T, P> const & y)
|
||
|
|
{
|
||
|
|
tvec4<bool, P> Result(uninitialize);
|
||
|
|
for(length_t i = 0; i < x.length(); ++i)
|
||
|
|
Result[i] = x[i] < y[i];
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec4<bool, P> lessThanEqual(tquat<T, P> const & x, tquat<T, P> const & y)
|
||
|
|
{
|
||
|
|
tvec4<bool, P> Result(uninitialize);
|
||
|
|
for(length_t i = 0; i < x.length(); ++i)
|
||
|
|
Result[i] = x[i] <= y[i];
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec4<bool, P> greaterThan(tquat<T, P> const & x, tquat<T, P> const & y)
|
||
|
|
{
|
||
|
|
tvec4<bool, P> Result(uninitialize);
|
||
|
|
for(length_t i = 0; i < x.length(); ++i)
|
||
|
|
Result[i] = x[i] > y[i];
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec4<bool, P> greaterThanEqual(tquat<T, P> const & x, tquat<T, P> const & y)
|
||
|
|
{
|
||
|
|
tvec4<bool, P> Result(uninitialize);
|
||
|
|
for(length_t i = 0; i < x.length(); ++i)
|
||
|
|
Result[i] = x[i] >= y[i];
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec4<bool, P> equal(tquat<T, P> const & x, tquat<T, P> const & y)
|
||
|
|
{
|
||
|
|
tvec4<bool, P> Result(uninitialize);
|
||
|
|
for(length_t i = 0; i < x.length(); ++i)
|
||
|
|
Result[i] = x[i] == y[i];
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec4<bool, P> notEqual(tquat<T, P> const & x, tquat<T, P> const & y)
|
||
|
|
{
|
||
|
|
tvec4<bool, P> Result(uninitialize);
|
||
|
|
for(length_t i = 0; i < x.length(); ++i)
|
||
|
|
Result[i] = x[i] != y[i];
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec4<bool, P> isnan(tquat<T, P> const& q)
|
||
|
|
{
|
||
|
|
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isnan' only accept floating-point inputs");
|
||
|
|
|
||
|
|
return tvec4<bool, P>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, precision P>
|
||
|
|
GLM_FUNC_QUALIFIER tvec4<bool, P> isinf(tquat<T, P> const& q)
|
||
|
|
{
|
||
|
|
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs");
|
||
|
|
|
||
|
|
return tvec4<bool, P>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w));
|
||
|
|
}
|
||
|
|
}//namespace glm
|
||
|
|
|
||
|
|
#if GLM_ARCH != GLM_ARCH_PURE && GLM_HAS_ALIGNED_TYPE
|
||
|
|
# include "quaternion_simd.inl"
|
||
|
|
#endif
|
||
|
|
|