ref: 71a993b4ca2c455f491aad669e3a4ac2979f6bb8
dir: /sys/src/libgeometry/quaternion.c/
/*
* Quaternion arithmetic:
* qadd(q, r) returns q+r
* qsub(q, r) returns q-r
* qneg(q) returns -q
* qmul(q, r) returns q*r
* qdiv(q, r) returns q/r, can divide check.
* qinv(q) returns 1/q, can divide check.
* double qlen(p) returns modulus of p
* qunit(q) returns a unit quaternion parallel to q
* The following only work on unit quaternions and rotation matrices:
* slerp(q, r, a) returns q*(r*q^-1)^a
* qmid(q, r) slerp(q, r, .5)
* qsqrt(q) qmid(q, (Quaternion){1,0,0,0})
* qtom(m, q) converts a unit quaternion q into a rotation matrix m
* mtoq(m) returns a quaternion equivalent to a rotation matrix m
*/
#include <u.h>
#include <libc.h>
#include <draw.h>
#include <geometry.h>
void qtom(Matrix m, Quaternion q){
#ifndef new
m[0][0]=1-2*(q.j*q.j+q.k*q.k);
m[0][1]=2*(q.i*q.j+q.r*q.k);
m[0][2]=2*(q.i*q.k-q.r*q.j);
m[0][3]=0;
m[1][0]=2*(q.i*q.j-q.r*q.k);
m[1][1]=1-2*(q.i*q.i+q.k*q.k);
m[1][2]=2*(q.j*q.k+q.r*q.i);
m[1][3]=0;
m[2][0]=2*(q.i*q.k+q.r*q.j);
m[2][1]=2*(q.j*q.k-q.r*q.i);
m[2][2]=1-2*(q.i*q.i+q.j*q.j);
m[2][3]=0;
m[3][0]=0;
m[3][1]=0;
m[3][2]=0;
m[3][3]=1;
#else
/*
* Transcribed from Ken Shoemake's new code -- not known to work
*/
double Nq = q.r*q.r+q.i*q.i+q.j*q.j+q.k*q.k;
double s = (Nq > 0.0) ? (2.0 / Nq) : 0.0;
double xs = q.i*s, ys = q.j*s, zs = q.k*s;
double wx = q.r*xs, wy = q.r*ys, wz = q.r*zs;
double xx = q.i*xs, xy = q.i*ys, xz = q.i*zs;
double yy = q.j*ys, yz = q.j*zs, zz = q.k*zs;
m[0][0] = 1.0 - (yy + zz); m[1][0] = xy + wz; m[2][0] = xz - wy;
m[0][1] = xy - wz; m[1][1] = 1.0 - (xx + zz); m[2][1] = yz + wx;
m[0][2] = xz + wy; m[1][2] = yz - wx; m[2][2] = 1.0 - (xx + yy);
m[0][3] = m[1][3] = m[2][3] = m[3][0] = m[3][1] = m[3][2] = 0.0;
m[3][3] = 1.0;
#endif
}
Quaternion mtoq(Matrix mat){
#ifndef new
#define EPS 1.387778780781445675529539585113525e-17 /* 2^-56 */
double t;
Quaternion q;
q.r=0.;
q.i=0.;
q.j=0.;
q.k=1.;
if((t=.25*(1+mat[0][0]+mat[1][1]+mat[2][2]))>EPS){
q.r=sqrt(t);
t=4*q.r;
q.i=(mat[1][2]-mat[2][1])/t;
q.j=(mat[2][0]-mat[0][2])/t;
q.k=(mat[0][1]-mat[1][0])/t;
}
else if((t=-.5*(mat[1][1]+mat[2][2]))>EPS){
q.i=sqrt(t);
t=2*q.i;
q.j=mat[0][1]/t;
q.k=mat[0][2]/t;
}
else if((t=.5*(1-mat[2][2]))>EPS){
q.j=sqrt(t);
q.k=mat[1][2]/(2*q.j);
}
return q;
#else
/*
* Transcribed from Ken Shoemake's new code -- not known to work
*/
/* This algorithm avoids near-zero divides by looking for a large
* component -- first r, then i, j, or k. When the trace is greater than zero,
* |r| is greater than 1/2, which is as small as a largest component can be.
* Otherwise, the largest diagonal entry corresponds to the largest of |i|,
* |j|, or |k|, one of which must be larger than |r|, and at least 1/2.
*/
Quaternion qu;
double tr, s;
tr = mat[0][0] + mat[1][1] + mat[2][2];
if (tr >= 0.0) {
s = sqrt(tr + mat[3][3]);
qu.r = s*0.5;
s = 0.5 / s;
qu.i = (mat[2][1] - mat[1][2]) * s;
qu.j = (mat[0][2] - mat[2][0]) * s;
qu.k = (mat[1][0] - mat[0][1]) * s;
}
else {
int i = 0;
if (mat[1][1] > mat[0][0]) i = 1;
if (mat[2][2] > mat[i][i]) i = 2;
switch(i){
case 0:
s = sqrt( (mat[0][0] - (mat[1][1]+mat[2][2])) + mat[3][3] );
qu.i = s*0.5;
s = 0.5 / s;
qu.j = (mat[0][1] + mat[1][0]) * s;
qu.k = (mat[2][0] + mat[0][2]) * s;
qu.r = (mat[2][1] - mat[1][2]) * s;
break;
case 1:
s = sqrt( (mat[1][1] - (mat[2][2]+mat[0][0])) + mat[3][3] );
qu.j = s*0.5;
s = 0.5 / s;
qu.k = (mat[1][2] + mat[2][1]) * s;
qu.i = (mat[0][1] + mat[1][0]) * s;
qu.r = (mat[0][2] - mat[2][0]) * s;
break;
case 2:
s = sqrt( (mat[2][2] - (mat[0][0]+mat[1][1])) + mat[3][3] );
qu.k = s*0.5;
s = 0.5 / s;
qu.i = (mat[2][0] + mat[0][2]) * s;
qu.j = (mat[1][2] + mat[2][1]) * s;
qu.r = (mat[1][0] - mat[0][1]) * s;
break;
}
}
if (mat[3][3] != 1.0){
s=1/sqrt(mat[3][3]);
qu.r*=s;
qu.i*=s;
qu.j*=s;
qu.k*=s;
}
return (qu);
#endif
}
Quaternion qadd(Quaternion q, Quaternion r){
q.r+=r.r;
q.i+=r.i;
q.j+=r.j;
q.k+=r.k;
return q;
}
Quaternion qsub(Quaternion q, Quaternion r){
q.r-=r.r;
q.i-=r.i;
q.j-=r.j;
q.k-=r.k;
return q;
}
Quaternion qneg(Quaternion q){
q.r=-q.r;
q.i=-q.i;
q.j=-q.j;
q.k=-q.k;
return q;
}
Quaternion qmul(Quaternion q, Quaternion r){
Quaternion s;
s.r=q.r*r.r-q.i*r.i-q.j*r.j-q.k*r.k;
s.i=q.r*r.i+r.r*q.i+q.j*r.k-q.k*r.j;
s.j=q.r*r.j+r.r*q.j+q.k*r.i-q.i*r.k;
s.k=q.r*r.k+r.r*q.k+q.i*r.j-q.j*r.i;
return s;
}
Quaternion qdiv(Quaternion q, Quaternion r){
return qmul(q, qinv(r));
}
Quaternion qunit(Quaternion q){
double l=qlen(q);
q.r/=l;
q.i/=l;
q.j/=l;
q.k/=l;
return q;
}
/*
* Bug?: takes no action on divide check
*/
Quaternion qinv(Quaternion q){
double l=q.r*q.r+q.i*q.i+q.j*q.j+q.k*q.k;
q.r/=l;
q.i=-q.i/l;
q.j=-q.j/l;
q.k=-q.k/l;
return q;
}
double qlen(Quaternion p){
return sqrt(p.r*p.r+p.i*p.i+p.j*p.j+p.k*p.k);
}
Quaternion slerp(Quaternion q, Quaternion r, double a){
double u, v, ang, s;
double dot=q.r*r.r+q.i*r.i+q.j*r.j+q.k*r.k;
ang=dot<-1?PI:dot>1?0:acos(dot); /* acos gives NaN for dot slightly out of range */
s=sin(ang);
if(s==0) return ang<PI/2?q:r;
u=sin((1-a)*ang)/s;
v=sin(a*ang)/s;
q.r=u*q.r+v*r.r;
q.i=u*q.i+v*r.i;
q.j=u*q.j+v*r.j;
q.k=u*q.k+v*r.k;
return q;
}
/*
* Only works if qlen(q)==qlen(r)==1
*/
Quaternion qmid(Quaternion q, Quaternion r){
double l;
q=qadd(q, r);
l=qlen(q);
if(l<1e-12){
q.r=r.i;
q.i=-r.r;
q.j=r.k;
q.k=-r.j;
}
else{
q.r/=l;
q.i/=l;
q.j/=l;
q.k/=l;
}
return q;
}
/*
* Only works if qlen(q)==1
*/
static Quaternion qident={1,0,0,0};
Quaternion qsqrt(Quaternion q){
return qmid(q, qident);
}