3D geometry
diff --git a/src/libgeometry/quaternion.c b/src/libgeometry/quaternion.c
new file mode 100644
index 0000000..1f920f5
--- /dev/null
+++ b/src/libgeometry/quaternion.c
@@ -0,0 +1,242 @@
+/*
+ * 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);
+}
