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/// @ref gtx_matrix_interpolation
/// @file glm/gtx/matrix_interpolation.hpp
#include "../gtc/constants.hpp"
namespace glm
{
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER void axisAngle(mat<4, 4, T, Q> const& mat, vec<3, T, Q> & axis, T & angle)
{
T epsilon = static_cast<T>(0.01);
T epsilon2 = static_cast<T>(0.1);
if((abs(mat[1][0] - mat[0][1]) < epsilon) && (abs(mat[2][0] - mat[0][2]) < epsilon) && (abs(mat[2][1] - mat[1][2]) < epsilon))
{
if ((abs(mat[1][0] + mat[0][1]) < epsilon2) && (abs(mat[2][0] + mat[0][2]) < epsilon2) && (abs(mat[2][1] + mat[1][2]) < epsilon2) && (abs(mat[0][0] + mat[1][1] + mat[2][2] - static_cast<T>(3.0)) < epsilon2))
{
angle = static_cast<T>(0.0);
axis.x = static_cast<T>(1.0);
axis.y = static_cast<T>(0.0);
axis.z = static_cast<T>(0.0);
return;
}
angle = static_cast<T>(3.1415926535897932384626433832795);
T xx = (mat[0][0] + static_cast<T>(1.0)) * static_cast<T>(0.5);
T yy = (mat[1][1] + static_cast<T>(1.0)) * static_cast<T>(0.5);
T zz = (mat[2][2] + static_cast<T>(1.0)) * static_cast<T>(0.5);
T xy = (mat[1][0] + mat[0][1]) * static_cast<T>(0.25);
T xz = (mat[2][0] + mat[0][2]) * static_cast<T>(0.25);
T yz = (mat[2][1] + mat[1][2]) * static_cast<T>(0.25);
if((xx > yy) && (xx > zz))
{
if(xx < epsilon)
{
axis.x = static_cast<T>(0.0);
axis.y = static_cast<T>(0.7071);
axis.z = static_cast<T>(0.7071);
}
else
{
axis.x = sqrt(xx);
axis.y = xy / axis.x;
axis.z = xz / axis.x;
}
}
else if (yy > zz)
{
if(yy < epsilon)
{
axis.x = static_cast<T>(0.7071);
axis.y = static_cast<T>(0.0);
axis.z = static_cast<T>(0.7071);
}
else
{
axis.y = sqrt(yy);
axis.x = xy / axis.y;
axis.z = yz / axis.y;
}
}
else
{
if (zz < epsilon)
{
axis.x = static_cast<T>(0.7071);
axis.y = static_cast<T>(0.7071);
axis.z = static_cast<T>(0.0);
}
else
{
axis.z = sqrt(zz);
axis.x = xz / axis.z;
axis.y = yz / axis.z;
}
}
return;
}
T s = sqrt((mat[2][1] - mat[1][2]) * (mat[2][1] - mat[1][2]) + (mat[2][0] - mat[0][2]) * (mat[2][0] - mat[0][2]) + (mat[1][0] - mat[0][1]) * (mat[1][0] - mat[0][1]));
if (glm::abs(s) < T(0.001))
s = static_cast<T>(1);
T const angleCos = (mat[0][0] + mat[1][1] + mat[2][2] - static_cast<T>(1)) * static_cast<T>(0.5);
if(angleCos - static_cast<T>(1) < epsilon)
angle = pi<T>() * static_cast<T>(0.25);
else
angle = acos(angleCos);
axis.x = (mat[1][2] - mat[2][1]) / s;
axis.y = (mat[2][0] - mat[0][2]) / s;
axis.z = (mat[0][1] - mat[1][0]) / s;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> axisAngleMatrix(vec<3, T, Q> const& axis, T const angle)
{
T c = cos(angle);
T s = sin(angle);
T t = static_cast<T>(1) - c;
vec<3, T, Q> n = normalize(axis);
return mat<4, 4, T, Q>(
t * n.x * n.x + c, t * n.x * n.y + n.z * s, t * n.x * n.z - n.y * s, static_cast<T>(0.0),
t * n.x * n.y - n.z * s, t * n.y * n.y + c, t * n.y * n.z + n.x * s, static_cast<T>(0.0),
t * n.x * n.z + n.y * s, t * n.y * n.z - n.x * s, t * n.z * n.z + c, static_cast<T>(0.0),
static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(1.0));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> extractMatrixRotation(mat<4, 4, T, Q> const& m)
{
return mat<4, 4, T, Q>(
m[0][0], m[0][1], m[0][2], static_cast<T>(0.0),
m[1][0], m[1][1], m[1][2], static_cast<T>(0.0),
m[2][0], m[2][1], m[2][2], static_cast<T>(0.0),
static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(1.0));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> interpolate(mat<4, 4, T, Q> const& m1, mat<4, 4, T, Q> const& m2, T const delta)
{
mat<4, 4, T, Q> m1rot = extractMatrixRotation(m1);
mat<4, 4, T, Q> dltRotation = m2 * transpose(m1rot);
vec<3, T, Q> dltAxis;
T dltAngle;
axisAngle(dltRotation, dltAxis, dltAngle);
mat<4, 4, T, Q> out = axisAngleMatrix(dltAxis, dltAngle * delta) * m1rot;
out[3][0] = m1[3][0] + delta * (m2[3][0] - m1[3][0]);
out[3][1] = m1[3][1] + delta * (m2[3][1] - m1[3][1]);
out[3][2] = m1[3][2] + delta * (m2[3][2] - m1[3][2]);
return out;
}
}//namespace glm
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