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sockscape/include/client/glm/gtc/quaternion.inl
malloc 5e02c1a212 restructure
2018-08-14 10:28:14 -05:00

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/// @ref gtc_quaternion
#include "../trigonometric.hpp"
#include "../geometric.hpp"
#include "../exponential.hpp"
#include "epsilon.hpp"
#include <limits>
namespace glm
{
// -- Operations --
/*
// (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle))
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> mix(qua<T, Q> const& x, qua<T, Q> const& y, T const& a)
{
if(a <= T(0)) return x;
if(a >= T(1)) return y;
float fCos = dot(x, y);
qua<T, Q> y2(y); //BUG!!! qua<T, Q> 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 qua<T, Q>(
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, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> mix2
(
qua<T, Q> const& x,
qua<T, Q> 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, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> mix(qua<T, Q> const& x, qua<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 qua<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 qua<T, Q> lerp(qua<T, Q> const& x, qua<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 qua<T, Q> slerp(qua<T, Q> const& x, qua<T, Q> const& y, T a)
{
qua<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 qua<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 qua<T, Q> rotate(qua<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 * qua<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
//return gtc::quaternion::cross(q, qua<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(qua<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(qua<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(qua<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));
T const y = static_cast<T>(2) * (q.y * q.z + q.w * q.x);
T const x = q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z;
if(all(equal(vec<2, T, Q>(x, y), vec<2, T, Q>(0), epsilon<T>()))) //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(qua<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(qua<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(qua<T, Q> const& q)
{
return mat<4, 4, T, Q>(mat3_cast(q));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<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 qua<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 qua<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 qua<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 qua<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 qua<T, Q>(1, 0, 0, 0);
}
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<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(qua<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(qua<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 qua<T, Q> angleAxis(T const& angle, vec<3, T, Q> const& v)
{
qua<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> isnan(qua<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(qua<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));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThan(qua<T, Q> const& x, qua<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(qua<T, Q> const& x, qua<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(qua<T, Q> const& x, qua<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(qua<T, Q> const& x, qua<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;
}
}//namespace glm
#if GLM_CONFIG_SIMD == GLM_ENABLE
# include "quaternion_simd.inl"
#endif
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