quaternion.h 4.47 KB
``````#ifndef TIRA_QUATERNION_H
#define TIRA_QUATERNION_H

#include <stim/math/matrix_sq.h>
#include <stim/cuda/cudatools/callable.h>

namespace tira {

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;
}

//calculate the quaternion length (norm)
CUDA_CALLABLE T norm() {
return sqrt(w*w + x * x + y * y + z * z);
}

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 l = r.len();
//if (l > 1) l = 1;					//we have seen degenerate cases where |r| > 1 (probably due to loss of precision in the cross product)
//T theta = asin(l);				//compute the angle of the rotation about r
//deal with a zero vector (both k and kn point in the same direction)
T cos_theta = from.dot(to);			//calculate the cosine between the two vectors
T theta = acos(cos_theta);			//calculate the angle between the two vectors
if(theta == (T)0){
return;
}

//create a quaternion to capture the rotation
CreateRotation(theta, r.norm());
}

CUDA_CALLABLE quaternion<T> operator *(quaternion<T> &param){

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_sq<T, 3> toMatrix3(){

matrix_sq<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_sq<T, 4> toMatrix4(){
matrix_sq<T, 4> R;
T s, wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;
s = sqrt(norm());
xx = x * x;		xy = x * y;		xz = x * z;
yy = y * y;		yz = y * z;
zz = z * z;
wx = w * x;		wy = w * y;		wz = w * z;

R(0, 0) = 1 - 2 * s * (yy + zz);
R(0, 1) = 2 * s * (xy - wz);
R(0, 2) = 2 * s * (xz + wy);
R(1, 0) = 2 * s * (xy + wz);
R(1, 1) = 1 - 2 * s * (xx + zz);
R(1, 2) = 2 * s * (yz - wx);
R(2, 0) = 2 * s * (xz - wy);
R(2, 1) = 2 * s * (yz + wx);
R(2, 2) = 1 - 2 * s * (xx + yy);

R(0, 3) = 0;
R(1, 3) = 0;
R(2, 3) = 0;
R(3, 0) = 0;
R(3, 1) = 0;
R(3, 2) = 0;
R(3, 3) = 1;

// 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 R;
}

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;
}

// create a pure quaternion from a vector
CUDA_CALLABLE quaternion(vec3<T> v){
w = 0; x = v[0]; y = v[1]; z = v[2];
}

CUDA_CALLABLE quaternion<T> conj(){
quaternion<T> c;
c.w = w;
c.x = -x;
c.y = -y;
c.z = -z;
return c;
}

};

}	//end rts namespace

#endif
``````