quaternion.h
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#ifndef RTS_QUATERNION_H
#define RTS_QUATERNION_H
#include <stim/math/matrix.h>
#include <stim/cuda/cudatools/callable.h>
namespace stim{
template<typename T>
class quaternion
{
public:
T w;
T x;
T y;
T z;
CUDA_CALLABLE void normalize(){
double length=sqrt(w*w + x*x + y*y + z*z);
w=w/length;
x=x/length;
y=y/length;
z=z/length;
}
CUDA_CALLABLE void CreateRotation(T theta, T ux, T uy, T uz){
vec3<T> u(ux, uy, uz);
CreateRotation(theta, u);
}
CUDA_CALLABLE void CreateRotation(T theta, vec3<T> u){
vec3<T> u_hat = u.norm();
//assign the given Euler rotation to this quaternion
w = (T)cos(theta/2);
x = u_hat[0]*(T)sin(theta/2);
y = u_hat[1]*(T)sin(theta/2);
z = u_hat[2]*(T)sin(theta/2);
}
CUDA_CALLABLE void CreateRotation(vec3<T> from, vec3<T> to){
from = from.norm();
to = to.norm();
vec3<T> r = from.cross(to); //compute the rotation vector
T theta = asin(r.len()); //compute the angle of the rotation about r
//deal with a zero vector (both k and kn point in the same direction)
if(theta == (T)0){
return;
}
//create a quaternion to capture the rotation
CreateRotation(theta, r.norm());
}
CUDA_CALLABLE quaternion<T> operator *(quaternion<T> ¶m){
float A, B, C, D, E, F, G, H;
A = (w + x)*(param.w + param.x);
B = (z - y)*(param.y - param.z);
C = (w - x)*(param.y + param.z);
D = (y + z)*(param.w - param.x);
E = (x + z)*(param.x + param.y);
F = (x - z)*(param.x - param.y);
G = (w + y)*(param.w - param.z);
H = (w - y)*(param.w + param.z);
quaternion<T> result;
result.w = B + (-E - F + G + H) /2;
result.x = A - (E + F + G + H)/2;
result.y = C + (E - F + G - H)/2;
result.z = D + (E - F - G + H)/2;
return result;
}
CUDA_CALLABLE matrix<T, 3> toMatrix3(){
matrix<T, 3> result;
T wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;
// calculate coefficients
x2 = x + x; y2 = y + y;
z2 = z + z;
xx = x * x2; xy = x * y2; xz = x * z2;
yy = y * y2; yz = y * z2; zz = z * z2;
wx = w * x2; wy = w * y2; wz = w * z2;
result(0, 0) = 1 - (yy + zz);
result(0, 1) = xy - wz;
result(0, 2) = xz + wy;
result(1, 0) = xy + wz;
result(1, 1) = 1 - (xx + zz);
result(1, 2) = yz - wx;
result(2, 0) = xz - wy;
result(2, 1) = yz + wx;
result(2, 2) = 1 - (xx + yy);
return result;
}
CUDA_CALLABLE matrix<T, 4> toMatrix4(){
matrix<T, 4> result;
T wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;
// calculate coefficients
x2 = x + x; y2 = y + y;
z2 = z + z;
xx = x * x2; xy = x * y2; xz = x * z2;
yy = y * y2; yz = y * z2; zz = z * z2;
wx = w * x2; wy = w * y2; wz = w * z2;
result(0, 0) = 1 - (yy + zz);
result(0, 1) = xy - wz;
result(0, 2) = xz + wy;
result(1, 0) = xy + wz;
result(1, 1) = 1 - (xx + zz);
result(1, 2) = yz - wx;
result(2, 0) = xz - wy;
result(2, 1) = yz + wx;
result(2, 2) = 1 - (xx + yy);
result(3, 3) = 1;
return result;
}
CUDA_CALLABLE quaternion(){
w=0; x=0; y=0; z=0;
}
CUDA_CALLABLE quaternion(T c, T i, T j, T k){
w=c; x=i; y=j; z=k;
}
};
} //end rts namespace
#endif