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>
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 }
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 }
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 }
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 }
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 }
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 }
87 void xform(Space *t, Matrix m){
88 	Matrix inv;
89 	if(invertmat(m, inv)==0) return;
90 	ixform(t, m, inv);
91 }
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  */
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  */
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  */
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 }