/// @ref gtx_matrix_interpolation
/// @file glm/gtx/matrix_interpolation.hpp
namespace glm
{
template <typename T, precision P>
GLM_FUNC_QUALIFIER void axisAngle
(
tmat4x4<T, P> const & mat,
tvec3<T, P> & axis,
T & angle
)
{
T epsilon = (T)0.01;
T epsilon2 = (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] - (T)3.0) < epsilon2))
{
angle = (T)0.0;
axis.x = (T)1.0;
axis.y = (T)0.0;
axis.z = (T)0.0;
return;
}
angle = static_cast<T>(3.1415926535897932384626433832795);
T xx = (mat[0][0] + (T)1.0) / (T)2.0;
T yy = (mat[1][1] + (T)1.0) / (T)2.0;
T zz = (mat[2][2] + (T)1.0) / (T)2.0;
T xy = (mat[1][0] + mat[0][1]) / (T)4.0;
T xz = (mat[2][0] + mat[0][2]) / (T)4.0;
T yz = (mat[2][1] + mat[1][2]) / (T)4.0;
if((xx > yy) && (xx > zz))
{
if (xx < epsilon) {
axis.x = (T)0.0;
axis.y = (T)0.7071;
axis.z = (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 = (T)0.7071;
axis.y = (T)0.0;
axis.z = (T)0.7071;
} else {
axis.y = sqrt(yy);
axis.x = xy / axis.y;
axis.z = yz / axis.y;
}
}
else
{
if (zz < epsilon) {
axis.x = (T)0.7071;
axis.y = (T)0.7071;
axis.z = (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 = (T)1.0;
angle = acos((mat[0][0] + mat[1][1] + mat[2][2] - (T)1.0) / (T)2.0);
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, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> axisAngleMatrix
(
tvec3<T, P> const & axis,
T const angle
)
{
T c = cos(angle);
T s = sin(angle);
T t = static_cast<T>(1) - c;
tvec3<T, P> n = normalize(axis);
return tmat4x4<T, P>(
t * n.x * n.x + c, t * n.x * n.y + n.z * s, t * n.x * n.z - n.y * s, T(0),
t * n.x * n.y - n.z * s, t * n.y * n.y + c, t * n.y * n.z + n.x * s, T(0),
t * n.x * n.z + n.y * s, t * n.y * n.z - n.x * s, t * n.z * n.z + c, T(0),
T(0), T(0), T(0), T(1)
);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> extractMatrixRotation
(
tmat4x4<T, P> const & mat
)
{
return tmat4x4<T, P>(
mat[0][0], mat[0][1], mat[0][2], 0.0,
mat[1][0], mat[1][1], mat[1][2], 0.0,
mat[2][0], mat[2][1], mat[2][2], 0.0,
0.0, 0.0, 0.0, 1.0
);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> interpolate
(
tmat4x4<T, P> const & m1,
tmat4x4<T, P> const & m2,
T const delta
)
{
tmat4x4<T, P> m1rot = extractMatrixRotation(m1);
tmat4x4<T, P> dltRotation = m2 * transpose(m1rot);
tvec3<T, P> dltAxis;
T dltAngle;
axisAngle(dltRotation, dltAxis, dltAngle);
tmat4x4<T, P> 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
