1 |
#ifndef lint |
2 |
static const char RCSid[] = "$Id: pmapgen.c,v 2.3 2003/02/22 02:07:27 greg Exp $"; |
3 |
#endif |
4 |
/* |
5 |
* pmapgen.c: general routines for 2-D perspective mappings. |
6 |
* These routines are independent of the poly structure, |
7 |
* so we do not think in terms of texture and screen space. |
8 |
* |
9 |
* Paul Heckbert 5 Nov 85, 12 Dec 85 |
10 |
*/ |
11 |
|
12 |
#include <stdio.h> |
13 |
#include "pmap.h" |
14 |
#include "mx3.h" |
15 |
|
16 |
#define TOLERANCE 1e-13 |
17 |
#define ZERO(x) ((x)<TOLERANCE && (x)>-TOLERANCE) |
18 |
|
19 |
#define X(i) qdrl[i][0] /* quadrilateral x and y */ |
20 |
#define Y(i) qdrl[i][1] |
21 |
|
22 |
/* |
23 |
* pmap_quad_rect: find mapping between quadrilateral and rectangle. |
24 |
* The correspondence is: |
25 |
* |
26 |
* qdrl[0] --> (u0,v0) |
27 |
* qdrl[1] --> (u1,v0) |
28 |
* qdrl[2] --> (u1,v1) |
29 |
* qdrl[3] --> (u0,v1) |
30 |
* |
31 |
* This method of computing the adjoint numerically is cheaper than |
32 |
* computing it symbolically. |
33 |
*/ |
34 |
|
35 |
extern int |
36 |
pmap_quad_rect( |
37 |
double u0, /* bounds of rectangle */ |
38 |
double v0, |
39 |
double u1, |
40 |
double v1, |
41 |
double qdrl[4][2], /* vertices of quadrilateral */ |
42 |
double QR[3][3] /* qdrl->rect transform (returned) */ |
43 |
) |
44 |
{ |
45 |
int ret; |
46 |
double du, dv; |
47 |
double RQ[3][3]; /* rect->qdrl transform */ |
48 |
|
49 |
du = u1-u0; |
50 |
dv = v1-v0; |
51 |
if (du==0. || dv==0.) { |
52 |
fprintf(stderr, "pmap_quad_rect: null rectangle\n"); |
53 |
return PMAP_BAD; |
54 |
} |
55 |
|
56 |
/* first find mapping from unit uv square to xy quadrilateral */ |
57 |
ret = pmap_square_quad(qdrl, RQ); |
58 |
if (ret==PMAP_BAD) return PMAP_BAD; |
59 |
|
60 |
/* concatenate transform from uv rectangle (u0,v0,u1,v1) to unit square */ |
61 |
RQ[0][0] /= du; |
62 |
RQ[1][0] /= dv; |
63 |
RQ[2][0] -= RQ[0][0]*u0 + RQ[1][0]*v0; |
64 |
RQ[0][1] /= du; |
65 |
RQ[1][1] /= dv; |
66 |
RQ[2][1] -= RQ[0][1]*u0 + RQ[1][1]*v0; |
67 |
RQ[0][2] /= du; |
68 |
RQ[1][2] /= dv; |
69 |
RQ[2][2] -= RQ[0][2]*u0 + RQ[1][2]*v0; |
70 |
|
71 |
/* now RQ is transform from uv rectangle to xy quadrilateral */ |
72 |
/* QR = inverse transform, which maps xy to uv */ |
73 |
if (mx3d_adjoint(RQ, QR)==0.) |
74 |
fprintf(stderr, "pmap_quad_rect: warning: determinant=0\n"); |
75 |
return ret; |
76 |
} |
77 |
|
78 |
/* |
79 |
* pmap_square_quad: find mapping between unit square and quadrilateral. |
80 |
* The correspondence is: |
81 |
* |
82 |
* (0,0) --> qdrl[0] |
83 |
* (1,0) --> qdrl[1] |
84 |
* (1,1) --> qdrl[2] |
85 |
* (0,1) --> qdrl[3] |
86 |
*/ |
87 |
|
88 |
extern int |
89 |
pmap_square_quad( |
90 |
register double qdrl[4][2], /* vertices of quadrilateral */ |
91 |
register double SQ[3][3] /* square->qdrl transform */ |
92 |
) |
93 |
{ |
94 |
double px, py; |
95 |
|
96 |
px = X(0)-X(1)+X(2)-X(3); |
97 |
py = Y(0)-Y(1)+Y(2)-Y(3); |
98 |
|
99 |
if (ZERO(px) && ZERO(py)) { /* affine */ |
100 |
SQ[0][0] = X(1)-X(0); |
101 |
SQ[1][0] = X(2)-X(1); |
102 |
SQ[2][0] = X(0); |
103 |
SQ[0][1] = Y(1)-Y(0); |
104 |
SQ[1][1] = Y(2)-Y(1); |
105 |
SQ[2][1] = Y(0); |
106 |
SQ[0][2] = 0.; |
107 |
SQ[1][2] = 0.; |
108 |
SQ[2][2] = 1.; |
109 |
return PMAP_LINEAR; |
110 |
} |
111 |
else { /* perspective */ |
112 |
double dx1, dx2, dy1, dy2, del; |
113 |
|
114 |
dx1 = X(1)-X(2); |
115 |
dx2 = X(3)-X(2); |
116 |
dy1 = Y(1)-Y(2); |
117 |
dy2 = Y(3)-Y(2); |
118 |
del = DET2(dx1,dx2, dy1,dy2); |
119 |
if (del==0.) { |
120 |
fprintf(stderr, "pmap_square_quad: bad mapping\n"); |
121 |
return PMAP_BAD; |
122 |
} |
123 |
SQ[0][2] = DET2(px,dx2, py,dy2)/del; |
124 |
SQ[1][2] = DET2(dx1,px, dy1,py)/del; |
125 |
SQ[2][2] = 1.; |
126 |
SQ[0][0] = X(1)-X(0)+SQ[0][2]*X(1); |
127 |
SQ[1][0] = X(3)-X(0)+SQ[1][2]*X(3); |
128 |
SQ[2][0] = X(0); |
129 |
SQ[0][1] = Y(1)-Y(0)+SQ[0][2]*Y(1); |
130 |
SQ[1][1] = Y(3)-Y(0)+SQ[1][2]*Y(3); |
131 |
SQ[2][1] = Y(0); |
132 |
return PMAP_PERSP; |
133 |
} |
134 |
} |