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-///////////////////////////////////////////////////////////////////////////////////
-/// OpenGL Mathematics (glm.g-truc.net)
-///
-/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
-/// Permission is hereby granted, free of charge, to any person obtaining a copy
-/// of this software and associated documentation files (the "Software"), to deal
-/// in the Software without restriction, including without limitation the rights
-/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-/// copies of the Software, and to permit persons to whom the Software is
-/// furnished to do so, subject to the following conditions:
-///
-/// The above copyright notice and this permission notice shall be included in
-/// all copies or substantial portions of the Software.
-///
-/// Restrictions:
-/// By making use of the Software for military purposes, you choose to make
-/// a Bunny unhappy.
-///
-/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
-/// THE SOFTWARE.
-///
-/// @ref gtc_quaternion
-/// @file glm/gtc/quaternion.inl
-/// @date 2009-05-21 / 2011-06-15
-/// @author Christophe Riccio
-///////////////////////////////////////////////////////////////////////////////////
-
-#include "../trigonometric.hpp"
-#include "../geometric.hpp"
-#include "../exponential.hpp"
-#include <limits>
-
-namespace glm{
-namespace detail
-{
- template <typename T, precision P>
- struct compute_dot<tquat, T, P>
- {
- static GLM_FUNC_QUALIFIER T call(tquat<T, P> const & x, tquat<T, P> const & y)
- {
- tvec4<T, P> tmp(x.x * y.x, x.y * y.y, x.z * y.z, x.w * y.w);
- return (tmp.x + tmp.y) + (tmp.z + tmp.w);
- }
- };
-}//namespace detail
-
- //////////////////////////////////////
- // Component accesses
-
-# ifdef GLM_FORCE_SIZE_FUNC
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tquat<T, P>::size_type tquat<T, P>::size() const
- {
- return 4;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[](typename tquat<T, P>::size_type i)
- {
- assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
- return (&x)[i];
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[](typename tquat<T, P>::size_type i) const
- {
- assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
- return (&x)[i];
- }
-# else
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tquat<T, P>::length_type tquat<T, P>::length() const
- {
- return 4;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[](typename tquat<T, P>::length_type i)
- {
- assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
- return (&x)[i];
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[](typename tquat<T, P>::length_type i) const
- {
- assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
- return (&x)[i];
- }
-# endif//GLM_FORCE_SIZE_FUNC
-
- //////////////////////////////////////
- // Implicit basic constructors
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat()
-# ifndef GLM_FORCE_NO_CTOR_INIT
- : x(0), y(0), z(0), w(1)
-# endif
- {}
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<T, P> const & q)
- : x(q.x), y(q.y), z(q.z), w(q.w)
- {}
-
- template <typename T, precision P>
- template <precision Q>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<T, Q> const & q)
- : x(q.x), y(q.y), z(q.z), w(q.w)
- {}
-
- //////////////////////////////////////
- // Explicit basic constructors
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat(ctor)
- {}
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat(T const & s, tvec3<T, P> const & v)
- : x(v.x), y(v.y), z(v.z), w(s)
- {}
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat(T const & w, T const & x, T const & y, T const & z)
- : x(x), y(y), z(z), w(w)
- {}
-
- //////////////////////////////////////////////////////////////
- // Conversions
-
- template <typename T, precision P>
- template <typename U, precision Q>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<U, Q> const & q)
- : x(static_cast<T>(q.x))
- , y(static_cast<T>(q.y))
- , z(static_cast<T>(q.z))
- , w(static_cast<T>(q.w))
- {}
-
- //template <typename valType>
- //GLM_FUNC_QUALIFIER tquat<valType>::tquat
- //(
- // valType const & pitch,
- // valType const & yaw,
- // valType const & roll
- //)
- //{
- // tvec3<valType> eulerAngle(pitch * valType(0.5), yaw * valType(0.5), roll * valType(0.5));
- // tvec3<valType> c = glm::cos(eulerAngle * valType(0.5));
- // tvec3<valType> s = glm::sin(eulerAngle * valType(0.5));
- //
- // this->w = c.x * c.y * c.z + s.x * s.y * s.z;
- // this->x = s.x * c.y * c.z - c.x * s.y * s.z;
- // this->y = c.x * s.y * c.z + s.x * c.y * s.z;
- // this->z = c.x * c.y * s.z - s.x * s.y * c.z;
- //}
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tvec3<T, P> const & u, tvec3<T, P> const & v)
- {
- tvec3<T, P> const LocalW(cross(u, v));
- T Dot = detail::compute_dot<tvec3, T, P>::call(u, v);
- tquat<T, P> q(T(1) + Dot, LocalW.x, LocalW.y, LocalW.z);
-
- *this = normalize(q);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tvec3<T, P> const & eulerAngle)
- {
- tvec3<T, P> c = glm::cos(eulerAngle * T(0.5));
- tvec3<T, P> s = glm::sin(eulerAngle * T(0.5));
-
- this->w = c.x * c.y * c.z + s.x * s.y * s.z;
- this->x = s.x * c.y * c.z - c.x * s.y * s.z;
- this->y = c.x * s.y * c.z + s.x * c.y * s.z;
- this->z = c.x * c.y * s.z - s.x * s.y * c.z;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tmat3x3<T, P> const & m)
- {
- *this = quat_cast(m);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tmat4x4<T, P> const & m)
- {
- *this = quat_cast(m);
- }
-
-# if GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat3x3<T, P>()
- {
- return mat3_cast(*this);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat4x4<T, P>()
- {
- return mat4_cast(*this);
- }
-# endif//GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P> conjugate(tquat<T, P> const & q)
- {
- return tquat<T, P>(q.w, -q.x, -q.y, -q.z);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P> inverse(tquat<T, P> const & q)
- {
- return conjugate(q) / dot(q, q);
- }
-
- //////////////////////////////////////////////////////////////
- // tquat<valType> operators
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator=(tquat<T, P> const & q)
- {
- this->w = q.w;
- this->x = q.x;
- this->y = q.y;
- this->z = q.z;
- return *this;
- }
-
- template <typename T, precision P>
- template <typename U>
- GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator=(tquat<U, P> const & q)
- {
- this->w = static_cast<T>(q.w);
- this->x = static_cast<T>(q.x);
- this->y = static_cast<T>(q.y);
- this->z = static_cast<T>(q.z);
- return *this;
- }
-
- template <typename T, precision P>
- template <typename U>
- GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator+=(tquat<U, P> const & q)
- {
- this->w += static_cast<T>(q.w);
- this->x += static_cast<T>(q.x);
- this->y += static_cast<T>(q.y);
- this->z += static_cast<T>(q.z);
- return *this;
- }
-
- template <typename T, precision P>
- template <typename U>
- GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator*=(tquat<U, P> const & r)
- {
- tquat<T, P> const p(*this);
- tquat<T, P> const q(r);
-
- this->w = p.w * q.w - p.x * q.x - p.y * q.y - p.z * q.z;
- this->x = p.w * q.x + p.x * q.w + p.y * q.z - p.z * q.y;
- this->y = p.w * q.y + p.y * q.w + p.z * q.x - p.x * q.z;
- this->z = p.w * q.z + p.z * q.w + p.x * q.y - p.y * q.x;
- return *this;
- }
-
- template <typename T, precision P>
- template <typename U>
- GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator*=(U s)
- {
- this->w *= static_cast<U>(s);
- this->x *= static_cast<U>(s);
- this->y *= static_cast<U>(s);
- this->z *= static_cast<U>(s);
- return *this;
- }
-
- template <typename T, precision P>
- template <typename U>
- GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator/=(U s)
- {
- this->w /= static_cast<U>(s);
- this->x /= static_cast<U>(s);
- this->y /= static_cast<U>(s);
- this->z /= static_cast<U>(s);
- return *this;
- }
-
- //////////////////////////////////////////////////////////////
- // tquat<T, P> external operators
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P> operator-(tquat<T, P> const & q)
- {
- return tquat<T, P>(-q.w, -q.x, -q.y, -q.z);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P> operator+(tquat<T, P> const & q, tquat<T, P> const & p)
- {
- return tquat<T, P>(q) += p;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tquat<T, P> operator*(tquat<T, P> const & q, tquat<T, P> const & p)
- {
- return tquat<T, P>(q) *= p;
- }
-
- // Transformation
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tquat<T, P> const & q, tvec3<T, P> const & v)
- {
- tvec3<T, P> const QuatVector(q.x, q.y, q.z);
- tvec3<T, P> const uv(glm::cross(QuatVector, v));
- tvec3<T, P> const uuv(glm::cross(QuatVector, uv));
-
- return v + ((uv * q.w) + uuv) * static_cast<T>(2);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tvec3<T, P> const & v, tquat<T, P> const & q)
- {
- return glm::inverse(q) * v;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tquat<T, P> const & q, tvec4<T, P> const & v)
- {
- return tvec4<T, P>(q * tvec3<T, P>(v), v.w);
- }
-
- 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);
- }
-
- ////////////////////////////////////////////////////////
- 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(T(-2) * (q.x * q.z - q.w * q.y));
- }
-
- 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] = 1 - 2 * (qyy + qzz);
- Result[0][1] = 2 * (qxy + qwz);
- Result[0][2] = 2 * (qxz - qwy);
-
- Result[1][0] = 2 * (qxy - qwz);
- Result[1][1] = 1 - 2 * (qxx + qzz);
- Result[1][2] = 2 * (qyz + qwx);
-
- Result[2][0] = 2 * (qxz + qwy);
- Result[2][1] = 2 * (qyz - qwx);
- Result[2][2] = 1 - 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(detail::component_count_t i = 0; i < detail::component_count(x); ++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(detail::component_count_t i = 0; i < detail::component_count(x); ++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(detail::component_count_t i = 0; i < detail::component_count(x); ++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(detail::component_count_t i = 0; i < detail::component_count(x); ++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(detail::component_count_t i = 0; i < detail::component_count(x); ++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(detail::component_count_t i = 0; i < detail::component_count(x); ++i)
- Result[i] = x[i] != y[i];
- return Result;
- }
-}//namespace glm
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