1 /*% cc -gpc %
2 * These transformation routines maintain stacks of transformations
3 * and their inverses.
4 * t=pushmat(t) push matrix stack
5 * t=popmat(t) pop matrix stack
6 * rot(t, a, axis) multiply stack top by rotation
7 * qrot(t, q) multiply stack top by rotation, q is unit quaternion
8 * scale(t, x, y, z) multiply stack top by scale
9 * move(t, x, y, z) multiply stack top by translation
10 * xform(t, m) multiply stack top by m
11 * ixform(t, m, inv) multiply stack top by m. inv is the inverse of m.
12 * look(t, e, l, u) multiply stack top by viewing transformation
13 * persp(t, fov, n, f) multiply stack top by perspective transformation
14 * viewport(t, r, aspect)
15 * multiply stack top by window->viewport transformation.
16 */
17 #include <u.h>
18 #include <libc.h>
19 #include <draw.h>
20 #include <geometry.h>
pushmat(Space * t)21 Space *pushmat(Space *t){
22 Space *v;
23 v=malloc(sizeof(Space));
24 if(t==0){
25 ident(v->t);
26 ident(v->tinv);
27 }
28 else
29 *v=*t;
30 v->next=t;
31 return v;
32 }
popmat(Space * t)33 Space *popmat(Space *t){
34 Space *v;
35 if(t==0) return 0;
36 v=t->next;
37 free(t);
38 return v;
39 }
rot(Space * t,double theta,int axis)40 void rot(Space *t, double theta, int axis){
41 double s=sin(radians(theta)), c=cos(radians(theta));
42 Matrix m, inv;
43 int i=(axis+1)%3, j=(axis+2)%3;
44 ident(m);
45 m[i][i] = c;
46 m[i][j] = -s;
47 m[j][i] = s;
48 m[j][j] = c;
49 ident(inv);
50 inv[i][i] = c;
51 inv[i][j] = s;
52 inv[j][i] = -s;
53 inv[j][j] = c;
54 ixform(t, m, inv);
55 }
qrot(Space * t,Quaternion q)56 void qrot(Space *t, Quaternion q){
57 Matrix m, inv;
58 int i, j;
59 qtom(m, q);
60 for(i=0;i!=4;i++) for(j=0;j!=4;j++) inv[i][j]=m[j][i];
61 ixform(t, m, inv);
62 }
scale(Space * t,double x,double y,double z)63 void scale(Space *t, double x, double y, double z){
64 Matrix m, inv;
65 ident(m);
66 m[0][0]=x;
67 m[1][1]=y;
68 m[2][2]=z;
69 ident(inv);
70 inv[0][0]=1/x;
71 inv[1][1]=1/y;
72 inv[2][2]=1/z;
73 ixform(t, m, inv);
74 }
move(Space * t,double x,double y,double z)75 void move(Space *t, double x, double y, double z){
76 Matrix m, inv;
77 ident(m);
78 m[0][3]=x;
79 m[1][3]=y;
80 m[2][3]=z;
81 ident(inv);
82 inv[0][3]=-x;
83 inv[1][3]=-y;
84 inv[2][3]=-z;
85 ixform(t, m, inv);
86 }
xform(Space * t,Matrix m)87 void xform(Space *t, Matrix m){
88 Matrix inv;
89 if(invertmat(m, inv)==0) return;
90 ixform(t, m, inv);
91 }
ixform(Space * t,Matrix m,Matrix inv)92 void ixform(Space *t, Matrix m, Matrix inv){
93 matmul(t->t, m);
94 matmulr(t->tinv, inv);
95 }
96 /*
97 * multiply the top of the matrix stack by a view-pointing transformation
98 * with the eyepoint at e, looking at point l, with u at the top of the screen.
99 * The coordinate system is deemed to be right-handed.
100 * The generated transformation transforms this view into a view from
101 * the origin, looking in the positive y direction, with the z axis pointing up,
102 * and x to the right.
103 */
look(Space * t,Point3 e,Point3 l,Point3 u)104 void look(Space *t, Point3 e, Point3 l, Point3 u){
105 Matrix m, inv;
106 Point3 r;
107 l=unit3(sub3(l, e));
108 u=unit3(vrem3(sub3(u, e), l));
109 r=cross3(l, u);
110 /* make the matrix to transform from (rlu) space to (xyz) space */
111 ident(m);
112 m[0][0]=r.x; m[0][1]=r.y; m[0][2]=r.z;
113 m[1][0]=l.x; m[1][1]=l.y; m[1][2]=l.z;
114 m[2][0]=u.x; m[2][1]=u.y; m[2][2]=u.z;
115 ident(inv);
116 inv[0][0]=r.x; inv[0][1]=l.x; inv[0][2]=u.x;
117 inv[1][0]=r.y; inv[1][1]=l.y; inv[1][2]=u.y;
118 inv[2][0]=r.z; inv[2][1]=l.z; inv[2][2]=u.z;
119 ixform(t, m, inv);
120 move(t, -e.x, -e.y, -e.z);
121 }
122 /*
123 * generate a transformation that maps the frustum with apex at the origin,
124 * apex angle=fov and clipping planes y=n and y=f into the double-unit cube.
125 * plane y=n maps to y'=-1, y=f maps to y'=1
126 */
persp(Space * t,double fov,double n,double f)127 int persp(Space *t, double fov, double n, double f){
128 Matrix m;
129 double z;
130 if(n<=0 || f<=n || fov<=0 || 180<=fov) /* really need f!=n && sin(v)!=0 */
131 return -1;
132 z=1/tan(radians(fov)/2);
133 m[0][0]=z; m[0][1]=0; m[0][2]=0; m[0][3]=0;
134 m[1][0]=0; m[1][1]=(f+n)/(f-n); m[1][2]=0; m[1][3]=f*(1-m[1][1]);
135 m[2][0]=0; m[2][1]=0; m[2][2]=z; m[2][3]=0;
136 m[3][0]=0; m[3][1]=1; m[3][2]=0; m[3][3]=0;
137 xform(t, m);
138 return 0;
139 }
140 /*
141 * Map the unit-cube window into the given screen viewport.
142 * r has min at the top left, max just outside the lower right. Aspect is the
143 * aspect ratio (dx/dy) of the viewport's pixels (not of the whole viewport!)
144 * The whole window is transformed to fit centered inside the viewport with equal
145 * slop on either top and bottom or left and right, depending on the viewport's
146 * aspect ratio.
147 * The window is viewed down the y axis, with x to the left and z up. The viewport
148 * has x increasing to the right and y increasing down. The window's y coordinates
149 * are mapped, unchanged, into the viewport's z coordinates.
150 */
viewport(Space * t,Rectangle r,double aspect)151 void viewport(Space *t, Rectangle r, double aspect){
152 Matrix m;
153 double xc, yc, wid, hgt, scale;
154 xc=.5*(r.min.x+r.max.x);
155 yc=.5*(r.min.y+r.max.y);
156 wid=(r.max.x-r.min.x)*aspect;
157 hgt=r.max.y-r.min.y;
158 scale=.5*(wid<hgt?wid:hgt);
159 ident(m);
160 m[0][0]=scale;
161 m[0][3]=xc;
162 m[1][1]=0;
163 m[1][2]=-scale;
164 m[1][3]=yc;
165 m[2][1]=1;
166 m[2][2]=0;
167 /* should get inverse by hand */
168 xform(t, m);
169 }
170