// get_euler returns a vector containing the Euler angles in the format
// (a1,a2,a3), where a3 is the angle of the first rotation, and a1 is the last
// (following the convention they are commonly defined in the literature).
//
// The current implementation uses XYZ convention (Z is the first rotation),
// so euler.z is the angle of the (first) rotation around Z axis and so on,
//
// And thus, assuming the matrix is a rotation matrix, this function returns
// the angles in the decomposition R = X(a1).Y(a2).Z(a3) where Z(a) rotates
// around the z-axis by a and so on.
Vector3 Basis::get_euler() const {
// Euler angles in XYZ convention.
// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
//
// rot = cy*cz -cy*sz sy
// cz*sx*sy+cx*sz cx*cz-sx*sy*sz -cy*sx
// -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy
Vector3 euler;
ERR_FAIL_COND_V(is_rotation() == false, euler);
euler.y = Math::asin(elements[0][2]);
if ( euler.y < Math_PI*0.5) {
if ( euler.y > -Math_PI*0.5) {
euler.x = Math::atan2(-elements[1][2],elements[2][2]);
euler.z = Math::atan2(-elements[0][1],elements[0][0]);
} else {
real_t r = Math::atan2(elements[1][0],elements[1][1]);
euler.z = 0.0;
euler.x = euler.z - r;
}
} else {
real_t r = Math::atan2(elements[0][1],elements[1][1]);
euler.z = 0;
euler.x = r - euler.z;
}
return euler;
}
int main(int argc, const char *argv[]){
//char s1[]="hello", s2[]="llohe";
if (is_rotation(argv[1], argv[2]))
puts("is a rotation");
else
puts("not a rotation");
return 0;
}
int main(int argc, char** argv)
{
assert(is_rotation("abc", "abc"));
assert(is_rotation("abc", string("abc")));
assert(!is_rotation(u8"aaa", u8"aa"));
assert(is_rotation(u"abc", u"bca"));
assert(is_rotation(L"abc", wstring(L"cab")));
assert(is_rotation(U"waterbottle", U"erbottlewat"));
assert(!is_rotation(R"(waterbottle)", R"(rbottlewat)"));
assert(!is_rotation(uR"(waterbottle)", uR"(Erbottlewat)"));
cout << "All tests passed!\n";
}
// get_euler_xyz returns a vector containing the Euler angles in the format
// (a1,a2,a3), where a3 is the angle of the first rotation, and a1 is the last
// (following the convention they are commonly defined in the literature).
//
// The current implementation uses XYZ convention (Z is the first rotation),
// so euler.z is the angle of the (first) rotation around Z axis and so on,
//
// And thus, assuming the matrix is a rotation matrix, this function returns
// the angles in the decomposition R = X(a1).Y(a2).Z(a3) where Z(a) rotates
// around the z-axis by a and so on.
Vector3 Basis::get_euler_xyz() const {
// Euler angles in XYZ convention.
// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
//
// rot = cy*cz -cy*sz sy
// cz*sx*sy+cx*sz cx*cz-sx*sy*sz -cy*sx
// -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy
Vector3 euler;
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(!is_rotation(), euler);
#endif
real_t sy = elements[0][2];
if (sy < 1.0) {
if (sy > -1.0) {
// is this a pure Y rotation?
if (elements[1][0] == 0.0 && elements[0][1] == 0.0 && elements[1][2] == 0 && elements[2][1] == 0 && elements[1][1] == 1) {
// return the simplest form (human friendlier in editor and scripts)
euler.x = 0;
euler.y = atan2(elements[0][2], elements[0][0]);
euler.z = 0;
} else {
euler.x = Math::atan2(-elements[1][2], elements[2][2]);
euler.y = Math::asin(sy);
euler.z = Math::atan2(-elements[0][1], elements[0][0]);
}
} else {
euler.x = -Math::atan2(elements[0][1], elements[1][1]);
euler.y = -Math_PI / 2.0;
euler.z = 0.0;
}
} else {
euler.x = Math::atan2(elements[0][1], elements[1][1]);
euler.y = Math_PI / 2.0;
euler.z = 0.0;
}
return euler;
}
Quat Basis::get_quat() const {
#ifdef MATH_CHECKS
if (!is_rotation()) {
ERR_EXPLAIN("Basis must be normalized in order to be casted to a Quaternion. Use get_rotation_quat() or call orthonormalized() instead.");
ERR_FAIL_V(Quat());
}
#endif
/* Allow getting a quaternion from an unnormalized transform */
Basis m = *this;
real_t trace = m.elements[0][0] + m.elements[1][1] + m.elements[2][2];
real_t temp[4];
if (trace > 0.0) {
real_t s = Math::sqrt(trace + 1.0);
temp[3] = (s * 0.5);
s = 0.5 / s;
temp[0] = ((m.elements[2][1] - m.elements[1][2]) * s);
temp[1] = ((m.elements[0][2] - m.elements[2][0]) * s);
temp[2] = ((m.elements[1][0] - m.elements[0][1]) * s);
} else {
int i = m.elements[0][0] < m.elements[1][1] ?
(m.elements[1][1] < m.elements[2][2] ? 2 : 1) :
(m.elements[0][0] < m.elements[2][2] ? 2 : 0);
int j = (i + 1) % 3;
int k = (i + 2) % 3;
real_t s = Math::sqrt(m.elements[i][i] - m.elements[j][j] - m.elements[k][k] + 1.0);
temp[i] = s * 0.5;
s = 0.5 / s;
temp[3] = (m.elements[k][j] - m.elements[j][k]) * s;
temp[j] = (m.elements[j][i] + m.elements[i][j]) * s;
temp[k] = (m.elements[k][i] + m.elements[i][k]) * s;
}
return Quat(temp[0], temp[1], temp[2], temp[3]);
}
static void vpp_get_min_max_variant(struct decon_win_config *config,
u32 *max_src, u32 *min_src_w, u32 *min_src_h,
u32 *max_dst, u32 *min_dst_w, u32 *min_dst_h)
{
if (is_rotation(config)) {
if (is_yuv(config)) {
*max_src = 2560;
*max_dst = 4096;
*min_src_w = 32;
*min_src_h = 64;
*min_dst_w = 16;
*min_dst_h = 8;
} else {
*max_src = 2560;
*max_dst = 4096;
*min_src_w = 16;
*min_src_h = 32;
*min_dst_w = 16;
*min_dst_h = 8;
}
} else {
if (is_yuv(config)) {
*max_src = 4096;
*max_dst = 4096;
*min_src_w = 64;
*min_src_h = 32;
*min_dst_w = 16;
*min_dst_h = 8;
} else {
*max_src = 4096;
*max_dst = 4096;
*min_src_w = 32;
*min_src_h = 16;
*min_dst_w = 16;
*min_dst_h = 8;
}
}
}
static void vpp_get_align_variant(struct decon_win_config *config,
u32 *offs, u32 *src_f, u32 *src_cr, u32 *dst_cr)
{
if (is_rotation(config)) {
if (is_yuv(config)) {
*offs = *src_f = 4;
*src_cr = 2;
*dst_cr = 1;
} else {
*offs = *src_f = 2;
*src_cr = *dst_cr = 1;
}
} else {
if (is_yuv(config)) {
*offs = *src_f = 2;
*src_cr = 2;
*dst_cr = 1;
} else {
*offs = *src_f = 1;
*src_cr = *dst_cr = 1;
}
}
}
Basis::operator Quat() const {
ERR_FAIL_COND_V(is_rotation() == false, Quat());
real_t trace = elements[0][0] + elements[1][1] + elements[2][2];
real_t temp[4];
if (trace > 0.0)
{
real_t s = Math::sqrt(trace + 1.0);
temp[3]=(s * 0.5);
s = 0.5 / s;
temp[0]=((elements[2][1] - elements[1][2]) * s);
temp[1]=((elements[0][2] - elements[2][0]) * s);
temp[2]=((elements[1][0] - elements[0][1]) * s);
}
else
{
int i = elements[0][0] < elements[1][1] ?
(elements[1][1] < elements[2][2] ? 2 : 1) :
(elements[0][0] < elements[2][2] ? 2 : 0);
int j = (i + 1) % 3;
int k = (i + 2) % 3;
real_t s = Math::sqrt(elements[i][i] - elements[j][j] - elements[k][k] + 1.0);
temp[i] = s * 0.5;
s = 0.5 / s;
temp[3] = (elements[k][j] - elements[j][k]) * s;
temp[j] = (elements[j][i] + elements[i][j]) * s;
temp[k] = (elements[k][i] + elements[i][k]) * s;
}
return Quat(temp[0],temp[1],temp[2],temp[3]);
}
void Basis::get_axis_and_angle(Vector3 &r_axis,real_t& r_angle) const {
ERR_FAIL_COND(is_rotation() == false);
double angle,x,y,z; // variables for result
double epsilon = 0.01; // margin to allow for rounding errors
double epsilon2 = 0.1; // margin to distinguish between 0 and 180 degrees
if ( (Math::abs(elements[1][0]-elements[0][1])< epsilon)
&& (Math::abs(elements[2][0]-elements[0][2])< epsilon)
&& (Math::abs(elements[2][1]-elements[1][2])< epsilon)) {
// singularity found
// first check for identity matrix which must have +1 for all terms
// in leading diagonaland zero in other terms
if ((Math::abs(elements[1][0]+elements[0][1]) < epsilon2)
&& (Math::abs(elements[2][0]+elements[0][2]) < epsilon2)
&& (Math::abs(elements[2][1]+elements[1][2]) < epsilon2)
&& (Math::abs(elements[0][0]+elements[1][1]+elements[2][2]-3) < epsilon2)) {
// this singularity is identity matrix so angle = 0
r_axis=Vector3(0,1,0);
r_angle=0;
return;
}
// otherwise this singularity is angle = 180
angle = Math_PI;
double xx = (elements[0][0]+1)/2;
double yy = (elements[1][1]+1)/2;
double zz = (elements[2][2]+1)/2;
double xy = (elements[1][0]+elements[0][1])/4;
double xz = (elements[2][0]+elements[0][2])/4;
double yz = (elements[2][1]+elements[1][2])/4;
if ((xx > yy) && (xx > zz)) { // elements[0][0] is the largest diagonal term
if (xx< epsilon) {
x = 0;
y = 0.7071;
z = 0.7071;
} else {
x = Math::sqrt(xx);
y = xy/x;
z = xz/x;
}
} else if (yy > zz) { // elements[1][1] is the largest diagonal term
if (yy< epsilon) {
x = 0.7071;
y = 0;
z = 0.7071;
} else {
y = Math::sqrt(yy);
x = xy/y;
z = yz/y;
}
} else { // elements[2][2] is the largest diagonal term so base result on this
if (zz< epsilon) {
x = 0.7071;
y = 0.7071;
z = 0;
} else {
z = Math::sqrt(zz);
x = xz/z;
y = yz/z;
}
}
r_axis=Vector3(x,y,z);
r_angle=angle;
return;
}
// as we have reached here there are no singularities so we can handle normally
double s = Math::sqrt((elements[1][2] - elements[2][1])*(elements[1][2] - elements[2][1])
+(elements[2][0] - elements[0][2])*(elements[2][0] - elements[0][2])
+(elements[0][1] - elements[1][0])*(elements[0][1] - elements[1][0])); // s=|axis||sin(angle)|, used to normalise
angle = Math::acos(( elements[0][0] + elements[1][1] + elements[2][2] - 1)/2);
if (angle < 0) s = -s;
x = (elements[2][1] - elements[1][2])/s;
y = (elements[0][2] - elements[2][0])/s;
z = (elements[1][0] - elements[0][1])/s;
r_axis=Vector3(x,y,z);
r_angle=angle;
}
