3D geometry

1 files changed, 169 insertions, 0 deletions

diff --git a/src/libgeometry/tstack.c b/src/libgeometry/tstack.c
new file mode 100644
index 00000000..bc41c4ac
--- /dev/null
+++ b/src/libgeometry/tstack.c
@@ -0,0 +1,169 @@
+/*% cc -gpc %
+ * These transformation routines maintain stacks of transformations
+ * and their inverses.  
+ * t=pushmat(t)		push matrix stack
+ * t=popmat(t)		pop matrix stack
+ * rot(t, a, axis)	multiply stack top by rotation
+ * qrot(t, q)		multiply stack top by rotation, q is unit quaternion
+ * scale(t, x, y, z)	multiply stack top by scale
+ * move(t, x, y, z)	multiply stack top by translation
+ * xform(t, m)		multiply stack top by m
+ * ixform(t, m, inv)	multiply stack top by m.  inv is the inverse of m.
+ * look(t, e, l, u)	multiply stack top by viewing transformation
+ * persp(t, fov, n, f)	multiply stack top by perspective transformation
+ * viewport(t, r, aspect)
+ *			multiply stack top by window->viewport transformation.
+ */
+#include <u.h>
+#include <libc.h>
+#include <draw.h>
+#include <geometry.h>
+Space *pushmat(Space *t){
+	Space *v;
+	v=malloc(sizeof(Space));
+	if(t==0){
+		ident(v->t);
+		ident(v->tinv);
+	}
+	else
+		*v=*t;
+	v->next=t;
+	return v;
+}
+Space *popmat(Space *t){
+	Space *v;
+	if(t==0) return 0;
+	v=t->next;
+	free(t);
+	return v;
+}
+void rot(Space *t, double theta, int axis){
+	double s=sin(radians(theta)), c=cos(radians(theta));
+	Matrix m, inv;
+	int i=(axis+1)%3, j=(axis+2)%3;
+	ident(m);
+	m[i][i] = c;
+	m[i][j] = -s;
+	m[j][i] = s;
+	m[j][j] = c;
+	ident(inv);
+	inv[i][i] = c;
+	inv[i][j] = s;
+	inv[j][i] = -s;
+	inv[j][j] = c;
+	ixform(t, m, inv);
+}
+void qrot(Space *t, Quaternion q){
+	Matrix m, inv;
+	int i, j;
+	qtom(m, q);
+	for(i=0;i!=4;i++) for(j=0;j!=4;j++) inv[i][j]=m[j][i];
+	ixform(t, m, inv);
+}
+void scale(Space *t, double x, double y, double z){
+	Matrix m, inv;
+	ident(m);
+	m[0][0]=x;
+	m[1][1]=y;
+	m[2][2]=z;
+	ident(inv);
+	inv[0][0]=1/x;
+	inv[1][1]=1/y;
+	inv[2][2]=1/z;
+	ixform(t, m, inv);
+}
+void move(Space *t, double x, double y, double z){
+	Matrix m, inv;
+	ident(m);
+	m[0][3]=x;
+	m[1][3]=y;
+	m[2][3]=z;
+	ident(inv);
+	inv[0][3]=-x;
+	inv[1][3]=-y;
+	inv[2][3]=-z;
+	ixform(t, m, inv);
+}
+void xform(Space *t, Matrix m){
+	Matrix inv;
+	if(invertmat(m, inv)==0) return;
+	ixform(t, m, inv);
+}
+void ixform(Space *t, Matrix m, Matrix inv){
+	matmul(t->t, m);
+	matmulr(t->tinv, inv);
+}
+/*
+ * multiply the top of the matrix stack by a view-pointing transformation
+ * with the eyepoint at e, looking at point l, with u at the top of the screen.
+ * The coordinate system is deemed to be right-handed.
+ * The generated transformation transforms this view into a view from
+ * the origin, looking in the positive y direction, with the z axis pointing up,
+ * and x to the right.
+ */
+void look(Space *t, Point3 e, Point3 l, Point3 u){
+	Matrix m, inv;
+	Point3 r;
+	l=unit3(sub3(l, e));
+	u=unit3(vrem3(sub3(u, e), l));
+	r=cross3(l, u);
+	/* make the matrix to transform from (rlu) space to (xyz) space */
+	ident(m);
+	m[0][0]=r.x; m[0][1]=r.y; m[0][2]=r.z;
+	m[1][0]=l.x; m[1][1]=l.y; m[1][2]=l.z;
+	m[2][0]=u.x; m[2][1]=u.y; m[2][2]=u.z;
+	ident(inv);
+	inv[0][0]=r.x; inv[0][1]=l.x; inv[0][2]=u.x;
+	inv[1][0]=r.y; inv[1][1]=l.y; inv[1][2]=u.y;
+	inv[2][0]=r.z; inv[2][1]=l.z; inv[2][2]=u.z;
+	ixform(t, m, inv);
+	move(t, -e.x, -e.y, -e.z);
+}
+/*
+ * generate a transformation that maps the frustum with apex at the origin,
+ * apex angle=fov and clipping planes y=n and y=f into the double-unit cube.
+ * plane y=n maps to y'=-1, y=f maps to y'=1
+ */
+int persp(Space *t, double fov, double n, double f){
+	Matrix m;
+	double z;
+	if(n<=0 || f<=n || fov<=0 || 180<=fov) /* really need f!=n && sin(v)!=0 */
+		return -1;
+	z=1/tan(radians(fov)/2);
+	m[0][0]=z; m[0][1]=0;           m[0][2]=0; m[0][3]=0;
+	m[1][0]=0; m[1][1]=(f+n)/(f-n); m[1][2]=0; m[1][3]=f*(1-m[1][1]);
+	m[2][0]=0; m[2][1]=0;           m[2][2]=z; m[2][3]=0;
+	m[3][0]=0; m[3][1]=1;           m[3][2]=0; m[3][3]=0;
+	xform(t, m);
+	return 0;
+}
+/*
+ * Map the unit-cube window into the given screen viewport.
+ * r has min at the top left, max just outside the lower right.  Aspect is the
+ * aspect ratio (dx/dy) of the viewport's pixels (not of the whole viewport!)
+ * The whole window is transformed to fit centered inside the viewport with equal
+ * slop on either top and bottom or left and right, depending on the viewport's
+ * aspect ratio.
+ * The window is viewed down the y axis, with x to the left and z up.  The viewport
+ * has x increasing to the right and y increasing down.  The window's y coordinates
+ * are mapped, unchanged, into the viewport's z coordinates.
+ */
+void viewport(Space *t, Rectangle r, double aspect){
+	Matrix m;
+	double xc, yc, wid, hgt, scale;
+	xc=.5*(r.min.x+r.max.x);
+	yc=.5*(r.min.y+r.max.y);
+	wid=(r.max.x-r.min.x)*aspect;
+	hgt=r.max.y-r.min.y;
+	scale=.5*(wid<hgt?wid:hgt);
+	ident(m);
+	m[0][0]=scale;
+	m[0][3]=xc;
+	m[1][1]=0;
+	m[1][2]=-scale;
+	m[1][3]=yc;
+	m[2][1]=1;
+	m[2][2]=0;
+	/* should get inverse by hand */
+	xform(t, m);
+}