diff options
Diffstat (limited to 'include/gal/opengl/glm/gtc/quaternion.inl')
| -rw-r--r-- | include/gal/opengl/glm/gtc/quaternion.inl | 792 |
1 files changed, 792 insertions, 0 deletions
diff --git a/include/gal/opengl/glm/gtc/quaternion.inl b/include/gal/opengl/glm/gtc/quaternion.inl new file mode 100644 index 0000000..8b83865 --- /dev/null +++ b/include/gal/opengl/glm/gtc/quaternion.inl @@ -0,0 +1,792 @@ +/////////////////////////////////////////////////////////////////////////////////// +/// OpenGL Mathematics (glm.g-truc.net) +/// +/// Copyright (c) 2005 - 2013 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. +/// +/// 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 <limits> + +namespace glm{ +namespace detail +{ + template <typename T> + GLM_FUNC_QUALIFIER typename tquat<T>::size_type tquat<T>::length() const + { + return 4; + } + + template <typename T> + GLM_FUNC_QUALIFIER tquat<T>::tquat() : + x(0), + y(0), + z(0), + w(1) + {} + + template <typename T> + GLM_FUNC_QUALIFIER tquat<T>::tquat + ( + value_type const & s, + tvec3<T> const & v + ) : + x(v.x), + y(v.y), + z(v.z), + w(s) + {} + + template <typename T> + GLM_FUNC_QUALIFIER tquat<T>::tquat + ( + value_type const & w, + value_type const & x, + value_type const & y, + value_type const & z + ) : + x(x), + y(y), + z(z), + w(w) + {} + + ////////////////////////////////////////////////////////////// + // tquat conversions + + //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> + GLM_FUNC_QUALIFIER tquat<T>::tquat + ( + tvec3<T> const & eulerAngle + ) + { + tvec3<T> c = glm::cos(eulerAngle * value_type(0.5)); + tvec3<T> s = glm::sin(eulerAngle * value_type(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> + GLM_FUNC_QUALIFIER tquat<T>::tquat + ( + tmat3x3<T> const & m + ) + { + *this = quat_cast(m); + } + + template <typename T> + GLM_FUNC_QUALIFIER tquat<T>::tquat + ( + tmat4x4<T> const & m + ) + { + *this = quat_cast(m); + } + + ////////////////////////////////////////////////////////////// + // tquat<T> accesses + + template <typename T> + GLM_FUNC_QUALIFIER typename tquat<T>::value_type & tquat<T>::operator [] (int i) + { + return (&x)[i]; + } + + template <typename T> + GLM_FUNC_QUALIFIER typename tquat<T>::value_type const & tquat<T>::operator [] (int i) const + { + return (&x)[i]; + } + + ////////////////////////////////////////////////////////////// + // tquat<valType> operators + + template <typename T> + GLM_FUNC_QUALIFIER tquat<T> & tquat<T>::operator *= + ( + value_type const & s + ) + { + this->w *= s; + this->x *= s; + this->y *= s; + this->z *= s; + return *this; + } + + template <typename T> + GLM_FUNC_QUALIFIER tquat<T> & tquat<T>::operator /= + ( + value_type const & s + ) + { + this->w /= s; + this->x /= s; + this->y /= s; + this->z /= s; + return *this; + } + + ////////////////////////////////////////////////////////////// + // tquat<valType> external operators + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> operator- + ( + detail::tquat<T> const & q + ) + { + return detail::tquat<T>(-q.w, -q.x, -q.y, -q.z); + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> operator+ + ( + detail::tquat<T> const & q, + detail::tquat<T> const & p + ) + { + return detail::tquat<T>( + q.w + p.w, + q.x + p.x, + q.y + p.y, + q.z + p.z); + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> operator* + ( + detail::tquat<T> const & q, + detail::tquat<T> const & p + ) + { + return detail::tquat<T>( + q.w * p.w - q.x * p.x - q.y * p.y - q.z * p.z, + q.w * p.x + q.x * p.w + q.y * p.z - q.z * p.y, + q.w * p.y + q.y * p.w + q.z * p.x - q.x * p.z, + q.w * p.z + q.z * p.w + q.x * p.y - q.y * p.x); + } + + // Transformation + template <typename T> + GLM_FUNC_QUALIFIER detail::tvec3<T> operator* + ( + detail::tquat<T> const & q, + detail::tvec3<T> const & v + ) + { + typename detail::tquat<T>::value_type Two(2); + + detail::tvec3<T> uv, uuv; + detail::tvec3<T> QuatVector(q.x, q.y, q.z); + uv = glm::cross(QuatVector, v); + uuv = glm::cross(QuatVector, uv); + uv *= (Two * q.w); + uuv *= Two; + + return v + uv + uuv; + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tvec3<T> operator* + ( + detail::tvec3<T> const & v, + detail::tquat<T> const & q + ) + { + return inverse(q) * v; + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tvec4<T> operator* + ( + detail::tquat<T> const & q, + detail::tvec4<T> const & v + ) + { + return detail::tvec4<T>(q * detail::tvec3<T>(v), v.w); + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tvec4<T> operator* + ( + detail::tvec4<T> const & v, + detail::tquat<T> const & q + ) + { + return inverse(q) * v; + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> operator* + ( + detail::tquat<T> const & q, + typename detail::tquat<T>::value_type const & s + ) + { + return detail::tquat<T>( + q.w * s, q.x * s, q.y * s, q.z * s); + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> operator* + ( + typename detail::tquat<T>::value_type const & s, + detail::tquat<T> const & q + ) + { + return q * s; + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> operator/ + ( + detail::tquat<T> const & q, + typename detail::tquat<T>::value_type const & s + ) + { + return detail::tquat<T>( + q.w / s, q.x / s, q.y / s, q.z / s); + } + + ////////////////////////////////////// + // Boolean operators + + template <typename T> + GLM_FUNC_QUALIFIER bool operator== + ( + detail::tquat<T> const & q1, + detail::tquat<T> const & q2 + ) + { + return (q1.x == q2.x) && (q1.y == q2.y) && (q1.z == q2.z) && (q1.w == q2.w); + } + + template <typename T> + GLM_FUNC_QUALIFIER bool operator!= + ( + detail::tquat<T> const & q1, + detail::tquat<T> const & q2 + ) + { + return (q1.x != q2.x) || (q1.y != q2.y) || (q1.z != q2.z) || (q1.w != q2.w); + } + +}//namespace detail + + //////////////////////////////////////////////////////// + template <typename T> + GLM_FUNC_QUALIFIER T length + ( + detail::tquat<T> const & q + ) + { + return glm::sqrt(dot(q, q)); + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> normalize + ( + detail::tquat<T> const & q + ) + { + typename detail::tquat<T>::value_type len = length(q); + if(len <= typename detail::tquat<T>::value_type(0)) // Problem + return detail::tquat<T>(1, 0, 0, 0); + typename detail::tquat<T>::value_type oneOverLen = typename detail::tquat<T>::value_type(1) / len; + return detail::tquat<T>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen); + } + + template <typename T> + GLM_FUNC_QUALIFIER T dot + ( + detail::tquat<T> const & q1, + detail::tquat<T> const & q2 + ) + { + return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w; + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> cross + ( + detail::tquat<T> const & q1, + detail::tquat<T> const & q2 + ) + { + return detail::tquat<T>( + 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> + GLM_FUNC_QUALIFIER detail::tquat<T> mix + ( + detail::tquat<T> const & x, + detail::tquat<T> const & y, + typename detail::tquat<T>::value_type const & a + ) + { + if(a <= typename detail::tquat<T>::value_type(0)) return x; + if(a >= typename detail::tquat<T>::value_type(1)) return y; + + float fCos = dot(x, y); + detail::tquat<T> y2(y); //BUG!!! tquat<T> y2; + if(fCos < typename detail::tquat<T>::value_type(0)) + { + y2 = -y; + fCos = -fCos; + } + + //if(fCos > 1.0f) // problem + float k0, k1; + if(fCos > typename detail::tquat<T>::value_type(0.9999)) + { + k0 = typename detail::tquat<T>::value_type(1) - a; + k1 = typename detail::tquat<T>::value_type(0) + a; //BUG!!! 1.0f + a; + } + else + { + typename detail::tquat<T>::value_type fSin = sqrt(T(1) - fCos * fCos); + typename detail::tquat<T>::value_type fAngle = atan(fSin, fCos); + typename detail::tquat<T>::value_type fOneOverSin = T(1) / fSin; + k0 = sin((typename detail::tquat<T>::value_type(1) - a) * fAngle) * fOneOverSin; + k1 = sin((typename detail::tquat<T>::value_type(0) + a) * fAngle) * fOneOverSin; + } + + return detail::tquat<T>( + 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> + GLM_FUNC_QUALIFIER detail::tquat<T> mix2 + ( + detail::tquat<T> const & x, + detail::tquat<T> const & y, + T const & a + ) + { + bool flip = false; + if(a <= T(0)) return x; + if(a >= 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 = 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> + GLM_FUNC_QUALIFIER detail::tquat<T> mix + ( + detail::tquat<T> const & x, + detail::tquat<T> const & y, + T const & 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 detail::tquat<T>( + 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> + GLM_FUNC_QUALIFIER detail::tquat<T> lerp + ( + detail::tquat<T> const & x, + detail::tquat<T> const & y, + T const & a + ) + { + // Lerp is only defined in [0, 1] + assert(a >= T(0)); + assert(a <= T(1)); + + return x * (T(1) - a) + (y * a); + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> slerp + ( + detail::tquat<T> const & x, + detail::tquat<T> const & y, + T const & a + ) + { + detail::tquat<T> 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 detail::tquat<T>( + 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> + GLM_FUNC_QUALIFIER detail::tquat<T> conjugate + ( + detail::tquat<T> const & q + ) + { + return detail::tquat<T>(q.w, -q.x, -q.y, -q.z); + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> inverse + ( + detail::tquat<T> const & q + ) + { + return conjugate(q) / dot(q, q); + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> rotate + ( + detail::tquat<T> const & q, + typename detail::tquat<T>::value_type const & angle, + detail::tvec3<T> const & v + ) + { + detail::tvec3<T> Tmp = v; + + // Axis of rotation must be normalised + typename detail::tquat<T>::value_type len = glm::length(Tmp); + if(abs(len - T(1)) > T(0.001)) + { + T oneOverLen = T(1) / len; + Tmp.x *= oneOverLen; + Tmp.y *= oneOverLen; + Tmp.z *= oneOverLen; + } + +#ifdef GLM_FORCE_RADIANS + typename detail::tquat<T>::value_type const AngleRad(angle); +#else + typename detail::tquat<T>::value_type const AngleRad = radians(angle); +#endif + typename detail::tquat<T>::value_type const Sin = sin(AngleRad * T(0.5)); + + return q * detail::tquat<T>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin); + //return gtc::quaternion::cross(q, detail::tquat<T>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin)); + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tvec3<T> eulerAngles + ( + detail::tquat<T> const & x + ) + { + return detail::tvec3<T>(pitch(x), yaw(x), roll(x)); + } + + template <typename valType> + GLM_FUNC_QUALIFIER valType roll + ( + detail::tquat<valType> const & q + ) + { +#ifdef GLM_FORCE_RADIANS + return valType(atan2(valType(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z)); +#else + return glm::degrees(atan(valType(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z)); +#endif + } + + template <typename valType> + GLM_FUNC_QUALIFIER valType pitch + ( + detail::tquat<valType> const & q + ) + { +#ifdef GLM_FORCE_RADIANS + return valType(atan2(valType(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z)); +#else + return glm::degrees(atan(valType(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z)); +#endif + } + + template <typename valType> + GLM_FUNC_QUALIFIER valType yaw + ( + detail::tquat<valType> const & q + ) + { +#ifdef GLM_FORCE_RADIANS + return asin(valType(-2) * (q.x * q.z - q.w * q.y)); +#else + return glm::degrees(asin(valType(-2) * (q.x * q.z - q.w * q.y))); +#endif + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tmat3x3<T> mat3_cast + ( + detail::tquat<T> const & q + ) + { + detail::tmat3x3<T> Result(T(1)); + Result[0][0] = 1 - 2 * q.y * q.y - 2 * q.z * q.z; + Result[0][1] = 2 * q.x * q.y + 2 * q.w * q.z; + Result[0][2] = 2 * q.x * q.z - 2 * q.w * q.y; + + Result[1][0] = 2 * q.x * q.y - 2 * q.w * q.z; + Result[1][1] = 1 - 2 * q.x * q.x - 2 * q.z * q.z; + Result[1][2] = 2 * q.y * q.z + 2 * q.w * q.x; + + Result[2][0] = 2 * q.x * q.z + 2 * q.w * q.y; + Result[2][1] = 2 * q.y * q.z - 2 * q.w * q.x; + Result[2][2] = 1 - 2 * q.x * q.x - 2 * q.y * q.y; + return Result; + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tmat4x4<T> mat4_cast + ( + detail::tquat<T> const & q + ) + { + return detail::tmat4x4<T>(mat3_cast(q)); + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tquat<T> quat_cast + ( + detail::tmat3x3<T> const & m + ) + { + typename detail::tquat<T>::value_type fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2]; + typename detail::tquat<T>::value_type fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2]; + typename detail::tquat<T>::value_type fourZSquaredMinus1 = m[2][2] - m[0][0] - m[1][1]; + typename detail::tquat<T>::value_type fourWSquaredMinus1 = m[0][0] + m[1][1] + m[2][2]; + + int biggestIndex = 0; + typename detail::tquat<T>::value_type fourBiggestSquaredMinus1 = fourWSquaredMinus1; + if(fourXSquaredMinus1 > fourBiggestSquaredMinus1) + { + fourBiggestSquaredMinus1 = fourXSquaredMinus1; + biggestIndex = 1; + } + if(fourYSquaredMinus1 > fourBiggestSquaredMinus1) + { + fourBiggestSquaredMinus1 = fourYSquaredMinus1; + biggestIndex = 2; + } + if(fourZSquaredMinus1 > fourBiggestSquaredMinus1) + { + fourBiggestSquaredMinus1 = fourZSquaredMinus1; + biggestIndex = 3; + } + + typename detail::tquat<T>::value_type biggestVal = sqrt(fourBiggestSquaredMinus1 + T(1)) * T(0.5); + typename detail::tquat<T>::value_type mult = T(0.25) / biggestVal; + + detail::tquat<T> Result; + 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> + GLM_FUNC_QUALIFIER detail::tquat<T> quat_cast + ( + detail::tmat4x4<T> const & m4 + ) + { + return quat_cast(detail::tmat3x3<T>(m4)); + } + + template <typename T> + GLM_FUNC_QUALIFIER T angle + ( + detail::tquat<T> const & x + ) + { +#ifdef GLM_FORCE_RADIANS + return acos(x.w) * T(2); +#else + return glm::degrees(acos(x.w) * T(2)); +#endif + } + + template <typename T> + GLM_FUNC_QUALIFIER detail::tvec3<T> axis + ( + detail::tquat<T> const & x + ) + { + T tmp1 = T(1) - x.w * x.w; + if(tmp1 <= T(0)) + return detail::tvec3<T>(0, 0, 1); + T tmp2 = T(1) / sqrt(tmp1); + return detail::tvec3<T>(x.x * tmp2, x.y * tmp2, x.z * tmp2); + } + + template <typename valType> + GLM_FUNC_QUALIFIER detail::tquat<valType> angleAxis + ( + valType const & angle, + valType const & x, + valType const & y, + valType const & z + ) + { + return angleAxis(angle, detail::tvec3<valType>(x, y, z)); + } + + template <typename valType> + GLM_FUNC_QUALIFIER detail::tquat<valType> angleAxis + ( + valType const & angle, + detail::tvec3<valType> const & v + ) + { + detail::tquat<valType> result; + +#ifdef GLM_FORCE_RADIANS + valType a(angle); +#else + valType a(glm::radians(angle)); +#endif + valType s = glm::sin(a * valType(0.5)); + + result.w = glm::cos(a * valType(0.5)); + result.x = v.x * s; + result.y = v.y * s; + result.z = v.z * s; + return result; + } + +}//namespace glm |