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dualQuaternionMath.cpp
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199 lines (180 loc) · 6.46 KB
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#include "dualQuaternionMath.h"
namespace oxyde {
namespace DQ {
//dual_quaternion_product = lambda((qs, qx, qy, qz), (dqs, dqx, dqy, dqz)), ((gs, gx, gy, gz), (dgs, dgx, dgy, dgz)) : ((gs*qs - gx*qx - gy*qy - gz*qz, gs*qx + gx*qs - gy*qz + gz*qy, gs*qy + gx*qz + gy*qs - gz*qx, gs*qz - gx*qy + gy*qx + gz*qs), (dgs*qs - dgx*qx - dgy*qy - dgz*qz + dqs*gs - dqx*gx - dqy*gy - dqz*gz, dgs*qx + dgx*qs - dgy*qz + dgz*qy + dqs*gx + dqx*gs + dqy*gz - dqz*gy, dgs*qy + dgx*qz + dgy*qs - dgz*qx + dqs*gy - dqx*gz + dqy*gs + dqz*gx, dgs*qz - dgx*qy + dgy*qx + dgz*qs + dqs*gz + dqx*gy - dqy*gx + dqz*gs))
void dual_quaternion_product(DUALQUAARG(q),
DUALQUAARG(g),
DUALQUAARG(o)) {
os = gs*qs - gx*qx - gy*qy - gz*qz;
ox = gs*qx + gx*qs - gy*qz + gz*qy;
oy = gs*qy + gx*qz + gy*qs - gz*qx;
oz = gs*qz - gx*qy + gy*qx + gz*qs;
dos = dgs*qs - dgx*qx - dgy*qy - dgz*qz + dqs*gs - dqx*gx - dqy*gy - dqz*gz;
dox = dgs*qx + dgx*qs - dgy*qz + dgz*qy + dqs*gx + dqx*gs + dqy*gz - dqz*gy;
doy = dgs*qy + dgx*qz + dgy*qs - dgz*qx + dqs*gy - dqx*gz + dqy*gs + dqz*gx;
doz = dgs*qz - dgx*qy + dgy*qx + dgz*qs + dqs*gz + dqx*gy - dqy*gx + dqz*gs;
}
//dual_quaternion_sum = lambda((qs, qx, qy, qz), (dqs, dqx, dqy, dqz)), ((gs, gx, gy, gz), (dgs, dgx, dgy, dgz)) : ((qs + gs, qx + gx, qy + gy, qz + gz), (dqs + dgs, dqx + dgx, dqy + dgy, dqz + dgz))
void dual_quaternion_sum(DUALQUAARG(q),
DUALQUAARG(g),
DUALQUAARG(o)) {
os = qs + gs;
ox = qx + gx;
oy = qy + gy;
oz = qz + gz;
dos = dqs + dgs;
dox = dqx + dgx;
doy = dqy + dgy;
doz = dqz + dgz;
}
//dual_quaternion_product_by_scalar = lambda((qs, qx, qy, qz), (dqs, dqx, dqy, dqz)), w : ((qs*w, qx*w, qy*w, qz*w), (dqs*w, dqx*w, dqy*w, dqz*w))
void dual_quaternion_product_by_scalar(DUALQUAARG(q), float w, DUALQUAARG(o)) {
os = qs*w;
ox = qx*w;
oy = qy*w;
oz = qz*w;
dos = dqs*w;
dox = dqx*w;
doy = dqy*w;
doz = dqz*w;
}
//dual_quaternion_conjugate = lambda((qs, qx, qy, qz), (dqs, dqx, dqy, dqz)) : ((qs, -qx, -qy, -qz), (dqs, -dqx, -dqy, -dqz))
void dual_quaternion_conjugate(DUALQUAARG(q), DUALQUAARG(o)) {
os = qs;
ox = -qx;
oy = -qy;
oz = -qz;
dos = dqs;
dox = -dqx;
doy = -dqy;
doz = -dqz;
}
//dual_quaternion_norm = lambda quat : np.sqrt(dual_quaternion_product(quat, dual_quaternion_conjugate(quat))[0][0])
float dual_quaternion_norm(DUALQUAARG(q)) {
//// X = dual_quaternion_conjugate(quat)
DUALQUAVAR(conj);
dual_quaternion_conjugate(DUALQUACOMP(q), DUALQUACOMP(conj));
//// Y = dual_quaternion_product(quat, X)
DUALQUAVAR(o);
dual_quaternion_product(DUALQUACOMP(q), DUALQUACOMP(conj), DUALQUACOMP(o));
//// np.sqrt(Y[0][0])
//return sqrt(ox);
return sqrt(qs*qs + qx*qx + qy*qy + qz*qz);
}
//dual_quaternion_epsilon = lambda((qs, qx, qy, qz), (dqs, dqx, dqy, dqz)) : ((qs, qx, qy, qz), (-dqs, -dqx, -dqy, -dqz))
void dual_quaternion_epsilon(DUALQUAARG(q), DUALQUAARG(o)) {
os = qs;
ox = qx;
oy = qy;
oz = qz;
dos = -dqs;
dox = -dqx;
doy = -dqy;
doz = -dqz;
}
//dual_quaternion_complement = lambda((qs, qx, qy, qz), (dqs, dqx, dqy, dqz)) : ((-qs, -qx, -qy, -qz), (-dqs, -dqx, -dqy, -dqz))
void dual_quaternion_complement(DUALQUAARG(q), DUALQUAARG(o)) {
os = -qs;
ox = -qx;
oy = -qy;
oz = -qz;
dos = -dqs;
dox = -dqx;
doy = -dqy;
doz = -dqz;
}
//dual_Versor = lambda theta, (ux, uy, uz), s, (mx, my, mz) : ((np.cos(theta / 2.0), ux*np.sin(theta / 2.0), uy*np.sin(theta / 2.0), uz*np.sin(theta / 2.0)), (-s*np.sin(theta / 2.0) / 4.0, mx*np.sin(theta / 2.0) + s*ux*np.cos(theta / 2.0) / 4.0, my*np.sin(theta / 2.0) + s*uy*np.cos(theta / 2.0) / 4.0, mz*np.sin(theta / 2.0) + s*uz*np.cos(theta / 2.0) / 4.0))
void dual_Versor(float theta, float nx, float ny, float nz, float slide, float mx, float my, float mz, DUALQUAARG(o)) {
//os = cos(theta / 2.0);
//ox = ux*sin(theta / 2.0);
//oy = uy*sin(theta / 2.0);
//oz = uz*sin(theta / 2.0);
//dos = -s*sin(theta / 2.0) / 4.0;
//dox = mx*sin(theta / 2.0) + (s*ux*cos(theta / 2.0) / 4.0);
//doy = my*sin(theta / 2.0) + (s*uy*cos(theta / 2.0) / 4.0);
//doz = mz*sin(theta / 2.0) + (s*uz*cos(theta / 2.0) / 4.0);
float cosHalfTheta = cos(theta / 2.0);
float sinHalfTheta = sin(theta / 2.0);
os = cosHalfTheta;
ox = nx*sinHalfTheta;
oy = ny*sinHalfTheta;
oz = nz*sinHalfTheta;
dos = (sinHalfTheta*slide) / 2.;
dox = mx*sinHalfTheta - (cosHalfTheta*nx*slide) / 2.;
doy = my*sinHalfTheta - (cosHalfTheta*ny*slide) / 2.;
doz = mz*sinHalfTheta - (cosHalfTheta*nz*slide) / 2.;
}
//pure_Real_quaternion = lambda(qs, qx, qy, qz) : ((qs, qx, qy, qz), (0, 0, 0, 0))
void pure_Real_quaternion(float qs, float qx, float qy, float qz, DUALQUAARG(o)) {
os = qs;
ox = qx;
oy = qy;
oz = qz;
dos = 0;
dox = 0;
doy = 0;
doz = 0;
}
//point_quaternion = lambda(px, py, pz) : ((1, 0, 0, 0), (0, px, py, pz))
void point_quaternion(float px, float py, float pz, DUALQUAARG(o)) {
os = 1;
ox = 0;
oy = 0;
oz = 0;
dos = 0;
dox = px;
doy = py;
doz = pz;
}
void vector_quaternion(float vx, float vy, float vz, DUALQUAARG(o)) {
os = 0;
ox = 0;
oy = 0;
oz = 0;
dos = 0;
dox = vx;
doy = vy;
doz = vz;
}
//translation_quaternion = lambda(dx, dy, dz) : ((1, 0, 0, 0), (0, -dx / 2, -dy / 2, -dz / 2))
void translation_quaternion(float dx, float dy, float dz, DUALQUAARG(o)) {
os = 1;
ox = 0;
oy = 0;
oz = 0;
dos = 0;
dox = -dx / 2.0;
doy = -dy / 2.0;
doz = -dz / 2.0;
}
//line_quaternion = lambda(vx, vy, vz), (rx, ry, rz) : ((0, vx, vy, vz), (0, rx, ry, rz))
void line_quaternion(float vx, float vy, float vz, float rx, float ry, float rz, DUALQUAARG(o)) {
os = 0;
ox = vx;
oy = vy;
oz = vz;
dos = 0;
dox = rx;
doy = ry;
doz = rz;
}
//dual_quaternion_dot_product = lambda((qs, qx, qy, qz), (dqs, dqx, dqy, dqz)), ((gs, gx, gy, gz), (dgs, dgx, dgy, dgz)) : (gs*qs + gx*qx + gy*qy + gz*qz, dgs*qs + dgx*qx + dgy*qy + dgz*qz + dqs*gs + dqx*gx + dqy*gy + dqz*gz)
void dual_quaternion_dot_product(DUALQUAARG(q),
DUALQUAARG(g),
float &r, float &d) {
r = gs*qs + gx*qx + gy*qy + gz*qz;
d = dgs*qs + dgx*qx + dgy*qy + dgz*qz + dqs*gs + dqx*gx + dqy*gy + dqz*gz;
}
//dual_quaternion_unity = lambda : ((1.0, 0.0, 0.0, 0.0), (0.0, 0.0, 0.0, 0.0))
void dual_quaternion_unity(DUALQUAARG(o)) {
os = 1.0;
ox = 0.0;
oy = 0.0;
oz = 0.0;
dos = 0.0;
dox = 0.0;
doy = 0.0;
doz = 0.0;
}
}
}