3D geometry

1 files changed, 242 insertions, 0 deletions

diff --git a/src/libgeometry/quaternion.c b/src/libgeometry/quaternion.c
new file mode 100644
index 00000000..1f920f5a
--- /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);
+}