1 /*
2  * The following routines transform points and planes from one space
3  * to another.  Points and planes are represented by their
4  * homogeneous coordinates, stored in variables of type Point3.
5  */
6 #include <u.h>
7 #include <libc.h>
8 #include <draw.h>
9 #include <geometry.h>
10 /*
11  * Transform point p.
12  */
13 Point3 xformpoint(Point3 p, Space *to, Space *from){
14 	Point3 q, r;
15 	register double *m;
16 	if(from){
17 		m=&from->t[0][0];
18 		q.x=*m++*p.x; q.x+=*m++*p.y; q.x+=*m++*p.z; q.x+=*m++*p.w;
19 		q.y=*m++*p.x; q.y+=*m++*p.y; q.y+=*m++*p.z; q.y+=*m++*p.w;
20 		q.z=*m++*p.x; q.z+=*m++*p.y; q.z+=*m++*p.z; q.z+=*m++*p.w;
21 		q.w=*m++*p.x; q.w+=*m++*p.y; q.w+=*m++*p.z; q.w+=*m  *p.w;
22 	}
23 	else
24 		q=p;
25 	if(to){
26 		m=&to->tinv[0][0];
27 		r.x=*m++*q.x; r.x+=*m++*q.y; r.x+=*m++*q.z; r.x+=*m++*q.w;
28 		r.y=*m++*q.x; r.y+=*m++*q.y; r.y+=*m++*q.z; r.y+=*m++*q.w;
29 		r.z=*m++*q.x; r.z+=*m++*q.y; r.z+=*m++*q.z; r.z+=*m++*q.w;
30 		r.w=*m++*q.x; r.w+=*m++*q.y; r.w+=*m++*q.z; r.w+=*m  *q.w;
31 	}
32 	else
33 		r=q;
34 	return r;
35 }
36 /*
37  * Transform point p with perspective division.
38  */
39 Point3 xformpointd(Point3 p, Space *to, Space *from){
40 	p=xformpoint(p, to, from);
41 	if(p.w!=0){
42 		p.x/=p.w;
43 		p.y/=p.w;
44 		p.z/=p.w;
45 		p.w=1;
46 	}
47 	return p;
48 }
49 /*
50  * Transform plane p -- same as xformpoint, except multiply on the
51  * other side by the inverse matrix.
52  */
53 Point3 xformplane(Point3 p, Space *to, Space *from){
54 	Point3 q, r;
55 	register double *m;
56 	if(from){
57 		m=&from->tinv[0][0];
58 		q.x =*m++*p.x; q.y =*m++*p.x; q.z =*m++*p.x; q.w =*m++*p.x;
59 		q.x+=*m++*p.y; q.y+=*m++*p.y; q.z+=*m++*p.y; q.w+=*m++*p.y;
60 		q.x+=*m++*p.z; q.y+=*m++*p.z; q.z+=*m++*p.z; q.w+=*m++*p.z;
61 		q.x+=*m++*p.w; q.y+=*m++*p.w; q.z+=*m++*p.w; q.w+=*m  *p.w;
62 	}
63 	else
64 		q=p;
65 	if(to){
66 		m=&to->t[0][0];
67 		r.x =*m++*q.x; r.y =*m++*q.x; r.z =*m++*q.x; r.w =*m++*q.x;
68 		r.x+=*m++*q.y; r.y+=*m++*q.y; r.z+=*m++*q.y; r.w+=*m++*q.y;
69 		r.x+=*m++*q.z; r.y+=*m++*q.z; r.z+=*m++*q.z; r.w+=*m++*q.z;
70 		r.x+=*m++*q.w; r.y+=*m++*q.w; r.z+=*m++*q.w; r.w+=*m  *q.w;
71 	}
72 	else
73 		r=q;
74 	return r;
75 }