You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
131 lines
4.2 KiB
131 lines
4.2 KiB
///////////////////////////////////////////////////////////////////////////////////////////////////
|
|
// OpenGL Mathematics Copyright (c) 2005 - 2013 G-Truc Creation (www.g-truc.net)
|
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
|
// Created : 2011-03-05
|
|
// Updated : 2011-03-05
|
|
// Licence : This source is under MIT License
|
|
// File : glm/gtx/matrix_interpolation.inl
|
|
///////////////////////////////////////////////////////////////////////////////////////////////////
|
|
|
|
namespace glm
|
|
{
|
|
template <typename T>
|
|
GLM_FUNC_QUALIFIER void axisAngle
|
|
(
|
|
detail::tmat4x4<T> const & mat,
|
|
detail::tvec3<T> & axis,
|
|
T & angle
|
|
)
|
|
{
|
|
T epsilon = (T)0.01;
|
|
T epsilon2 = (T)0.1;
|
|
|
|
if ((fabs(mat[1][0] - mat[0][1]) < epsilon) && (fabs(mat[2][0] - mat[0][2]) < epsilon) && (fabs(mat[2][1] - mat[1][2]) < epsilon)) {
|
|
if ((fabs(mat[1][0] + mat[0][1]) < epsilon2) && (fabs(mat[2][0] + mat[0][2]) < epsilon2) && (fabs(mat[2][1] + mat[1][2]) < epsilon2) && (fabs(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 = 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>
|
|
GLM_FUNC_QUALIFIER detail::tmat4x4<T> axisAngleMatrix
|
|
(
|
|
detail::tvec3<T> const & axis,
|
|
T const angle
|
|
)
|
|
{
|
|
T c = cos(angle);
|
|
T s = sin(angle);
|
|
T t = T(1) - c;
|
|
detail::tvec3<T> n = normalize(axis);
|
|
|
|
return detail::tmat4x4<T>(
|
|
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>
|
|
GLM_FUNC_QUALIFIER detail::tmat4x4<T> extractMatrixRotation(
|
|
detail::tmat4x4<T> const & mat)
|
|
{
|
|
return detail::tmat4x4<T>(
|
|
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>
|
|
GLM_FUNC_QUALIFIER detail::tmat4x4<T> interpolate
|
|
(
|
|
detail::tmat4x4<T> const & m1,
|
|
detail::tmat4x4<T> const & m2,
|
|
T const delta
|
|
)
|
|
{
|
|
detail::tmat4x4<T> m1rot = extractMatrixRotation(m1);
|
|
detail::tmat4x4<T> dltRotation = m2 * transpose(m1rot);
|
|
detail::tvec3<T> dltAxis;
|
|
T dltAngle;
|
|
axisAngle(dltRotation, dltAxis, dltAngle);
|
|
detail::tmat4x4<T> 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
|