1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
|
#include <u.h>
#include <libc.h>
#include <draw.h>
#include <geometry.h>
#include <graphics.h>
static Point2
flatten(Camera *c, Point3 p)
{
Point2 p2;
Matrix S = {
Dx(c->viewport->r)/2, 0, 0,
0, Dy(c->viewport->r)/2, 0,
0, 0, 1,
}, T = {
1, 0, 1,
0, 1, 1,
0, 0, 1,
};
p2 = Pt2(p.x, p.y, p.w);
if(p2.w != 0)
p2 = divpt2(p2, p2.w);
mulm(S, T);
p2 = xform(p2, S);
return p2;
}
Point3
world2vcs(Camera *c, Point3 p)
{
return rframexform3(p, *c);
}
Point3
vcs2ndc(Camera *c, Point3 p)
{
return xform3(p, c->proj);
}
Point3
world2ndc(Camera *c, Point3 p)
{
return vcs2ndc(c, world2vcs(c, p));
}
/* requires p to be in NDC */
int
isclipping(Point3 p)
{
if(p.x > p.w || p.x < -p.w ||
p.y > p.w || p.y < -p.w ||
p.z > p.w || p.z < 0)
return 1;
return 0;
}
/* Liang-Barsky algorithm, requires p0, p1 to be in NDC */
int
clipline3(Point3 *p0, Point3 *p1)
{
Point3 q0, q1, v;
int m0, m1, i;
double ti, to, th;
double c0[3*2] = {
p0->w + p0->x, p0->w - p0->x, p0->w + p0->y,
p0->w - p0->y, p0->z, p0->w - p0->z,
}, c1[3*2] = {
p1->w + p1->x, p1->w - p1->x, p1->w + p1->y,
p1->w - p1->y, p1->z, p1->w - p1->z,
};
/* bit-encoded regions */
m0 = (c0[0] < 0) << 0 |
(c0[1] < 0) << 1 |
(c0[2] < 0) << 2 |
(c0[3] < 0) << 3 |
(c0[4] < 0) << 4 |
(c0[5] < 0) << 5;
m1 = (c1[0] < 0) << 0 |
(c1[1] < 0) << 1 |
(c1[2] < 0) << 2 |
(c1[3] < 0) << 3 |
(c1[4] < 0) << 4 |
(c1[5] < 0) << 5;
if((m0 & m1) != 0)
return 1; /* trivially rejected */
if((m0 | m1) == 0)
return 0; /* trivially accepted */
ti = 0;
to = 1;
for(i = 0; i < 3*2; i++){
if(c1[i] < 0){
th = c0[i] / (c0[i]-c1[i]);
if(th < to)
to = th;
}else if(c0[i] < 0){
th = c0[i] / (c0[i]-c1[i]);
if(th < ti)
ti = th;
}
if(ti > to)
return 1;
}
/* chop line to fit inside NDC */
q0 = *p0;
q1 = *p1;
v = subpt3(q1, q0);
if(m0 != 0)
*p0 = addpt3(q0, mulpt3(v, ti));
if(m1 != 0)
*p1 = addpt3(q0, mulpt3(v, to));
return 0;
}
Point
toviewport(Camera *c, Point3 p)
{
Point2 p2;
RFrame rf = {
c->viewport->r.min.x, c->viewport->r.max.y, 1,
1, 0, 0,
0, -1, 0
};
p2 = invrframexform(flatten(c, p), rf);
return Pt(p2.x, p2.y);
}
Point2
fromviewport(Camera *c, Point p)
{
RFrame rf = {
c->viewport->r.min.x, c->viewport->r.max.y, 1,
1, 0, 0,
0, -1, 0
};
return rframexform(Pt2(p.x,p.y,1), rf);
}
void
perspective(Matrix3 m, double fov, double a, double n, double f)
{
double cotan;
cotan = 1/tan(fov/2);
identity3(m);
m[0][0] = cotan/a;
m[1][1] = cotan;
m[2][2] = -(f+n)/(f-n);
m[2][3] = -2*f*n/(f-n);
m[3][2] = -1;
}
void
orthographic(Matrix3 m, double l, double r, double b, double t, double n, double f)
{
identity3(m);
m[0][0] = 2/(r - l);
m[1][1] = 2/(t - b);
m[2][2] = -2/(f - n);
m[0][3] = -(r + l)/(r - l);
m[1][3] = -(t + b)/(t - b);
m[2][3] = -(f + n)/(f - n);
}
void
line3(Camera *c, Point3 p0, Point3 p1, int end0, int end1, Image *src)
{
p0 = world2ndc(c, p0);
p1 = world2ndc(c, p1);
if(clipline3(&p0, &p1))
return;
line(c->viewport, toviewport(c, p0), toviewport(c, p1), end0, end1, 0, src, ZP);
}
Point
string3(Camera *c, Point3 p, Image *src, Font *f, char *s)
{
p = world2ndc(c, p);
if(isclipping(p))
return Pt(-1,-1);
return string(c->viewport, toviewport(c, p), src, ZP, f, s);
}
|
