src/px/pmapgen.c

/* Copyright (c) 1995 Regents of the University of California */

#ifndef lint
static char SCCSid[] = "$SunId$ LBL";
#endif

/*
 * pmapgen.c: general routines for 2-D perspective mappings.
 * These routines are independent of the poly structure,
 * so we do not think in terms of texture and screen space.
 *
 * Paul Heckbert        5 Nov 85, 12 Dec 85
 */

static char rcsid[] = "$Header: pmapgen.c,v 2.0 88/10/12 21:58:33 ph Locked $";
#include <stdio.h>
#include "pmap.h"
#include "mx3.h"

#define TOLERANCE 1e-13
#define ZERO(x) ((x)<TOLERANCE && (x)>-TOLERANCE)

#define X(i) quad[i][0]         /* quadrilateral x and y */
#define Y(i) quad[i][1]

/*
 * pmap_quad_rect: find mapping between quadrilateral and rectangle.
 * The correspondence is:
 *
 *      quad[0] --> (u0,v0)
 *      quad[1] --> (u1,v0)
 *      quad[2] --> (u1,v1)
 *      quad[3] --> (u0,v1)
 *
 * This method of computing the adjoint numerically is cheaper than
 * computing it symbolically.
 */
        
pmap_quad_rect(u0, v0, u1, v1, quad, QR)
double u0, v0, u1, v1;          /* bounds of rectangle */
double quad[4][2];              /* vertices of quadrilateral */
double QR[3][3];                /* quad->rect transform (returned) */
{
    int ret;
    double du, dv;
    double RQ[3][3];            /* rect->quad transform */

    du = u1-u0;
    dv = v1-v0;
    if (du==0. || dv==0.) {
        fprintf(stderr, "pmap_quad_rect: null rectangle\n");
        return PMAP_BAD;
    }

    /* first find mapping from unit uv square to xy quadrilateral */
    ret = pmap_square_quad(quad, RQ);
    if (ret==PMAP_BAD) return PMAP_BAD;

    /* concatenate transform from uv rectangle (u0,v0,u1,v1) to unit square */
    RQ[0][0] /= du;
    RQ[1][0] /= dv;
    RQ[2][0] -= RQ[0][0]*u0 + RQ[1][0]*v0;
    RQ[0][1] /= du;
    RQ[1][1] /= dv;
    RQ[2][1] -= RQ[0][1]*u0 + RQ[1][1]*v0;
    RQ[0][2] /= du;
    RQ[1][2] /= dv;
    RQ[2][2] -= RQ[0][2]*u0 + RQ[1][2]*v0;

    /* now RQ is transform from uv rectangle to xy quadrilateral */
    /* QR = inverse transform, which maps xy to uv */
    if (mx3d_adjoint(RQ, QR)==0.)
        fprintf(stderr, "pmap_quad_rect: warning: determinant=0\n");
    return ret;
}

/*
 * pmap_square_quad: find mapping between unit square and quadrilateral.
 * The correspondence is:
 *
 *      (0,0) --> quad[0]
 *      (1,0) --> quad[1]
 *      (1,1) --> quad[2]
 *      (0,1) --> quad[3]
 */

pmap_square_quad(quad, SQ)
register double quad[4][2];     /* vertices of quadrilateral */
register double SQ[3][3];       /* square->quad transform */
{
    double px, py;

    px = X(0)-X(1)+X(2)-X(3);
    py = Y(0)-Y(1)+Y(2)-Y(3);

    if (ZERO(px) && ZERO(py)) {         /* affine */
        SQ[0][0] = X(1)-X(0);
        SQ[1][0] = X(2)-X(1);
        SQ[2][0] = X(0);
        SQ[0][1] = Y(1)-Y(0);
        SQ[1][1] = Y(2)-Y(1);
        SQ[2][1] = Y(0);
        SQ[0][2] = 0.;
        SQ[1][2] = 0.;
        SQ[2][2] = 1.;
        return PMAP_LINEAR;
    }
    else {                              /* perspective */
        double dx1, dx2, dy1, dy2, del;

        dx1 = X(1)-X(2);
        dx2 = X(3)-X(2);
        dy1 = Y(1)-Y(2);
        dy2 = Y(3)-Y(2);
        del = DET2(dx1,dx2, dy1,dy2);
        if (del==0.) {
            fprintf(stderr, "pmap_square_quad: bad mapping\n");
            return PMAP_BAD;
        }
        SQ[0][2] = DET2(px,dx2, py,dy2)/del;
        SQ[1][2] = DET2(dx1,px, dy1,py)/del;
        SQ[2][2] = 1.;
        SQ[0][0] = X(1)-X(0)+SQ[0][2]*X(1);
        SQ[1][0] = X(3)-X(0)+SQ[1][2]*X(3);
        SQ[2][0] = X(0);
        SQ[0][1] = Y(1)-Y(0)+SQ[0][2]*Y(1);
        SQ[1][1] = Y(3)-Y(0)+SQ[1][2]*Y(3);
        SQ[2][1] = Y(0);
        return PMAP_PERSP;
    }
}
Revision:	2.1
Committed:	Wed Oct 11 10:39:26 1995 UTC (30 years ago) by greg
Content type:	text/plain
Branch:	MAIN
Log Message:	Initial revision
#	User	Rev	Content
1	greg	2.1	/* Copyright (c) 1995 Regents of the University of California */
2
3			#ifndef lint
4			static char SCCSid[] = "$SunId$ LBL";
5			#endif
6
7			/*
8			* pmapgen.c: general routines for 2-D perspective mappings.
9			* These routines are independent of the poly structure,
10			* so we do not think in terms of texture and screen space.
11			*
12			* Paul Heckbert 5 Nov 85, 12 Dec 85
13			*/
14
15			static char rcsid[] = "$Header: pmapgen.c,v 2.0 88/10/12 21:58:33 ph Locked $";
16			#include <stdio.h>
17			#include "pmap.h"
18			#include "mx3.h"
19
20			#define TOLERANCE 1e-13
21			#define ZERO(x) ((x)<TOLERANCE && (x)>-TOLERANCE)
22
23			#define X(i) quad[i][0] /* quadrilateral x and y */
24			#define Y(i) quad[i][1]
25
26			/*
27			* pmap_quad_rect: find mapping between quadrilateral and rectangle.
28			* The correspondence is:
29			*
30			* quad[0] --> (u0,v0)
31			* quad[1] --> (u1,v0)
32			* quad[2] --> (u1,v1)
33			* quad[3] --> (u0,v1)
34			*
35			* This method of computing the adjoint numerically is cheaper than
36			* computing it symbolically.
37			*/
38
39			pmap_quad_rect(u0, v0, u1, v1, quad, QR)
40			double u0, v0, u1, v1; /* bounds of rectangle */
41			double quad[4][2]; /* vertices of quadrilateral */
42			double QR[3][3]; /* quad->rect transform (returned) */
43			{
44			int ret;
45			double du, dv;
46			double RQ[3][3]; /* rect->quad transform */
47
48			du = u1-u0;
49			dv = v1-v0;
50			if (du==0. \|\| dv==0.) {
51			fprintf(stderr, "pmap_quad_rect: null rectangle\n");
52			return PMAP_BAD;
53			}
54
55			/* first find mapping from unit uv square to xy quadrilateral */
56			ret = pmap_square_quad(quad, RQ);
57			if (ret==PMAP_BAD) return PMAP_BAD;
58
59			/* concatenate transform from uv rectangle (u0,v0,u1,v1) to unit square */
60			RQ[0][0] /= du;
61			RQ[1][0] /= dv;
62			RQ[2][0] -= RQ[0][0]u0 + RQ[1][0]v0;
63			RQ[0][1] /= du;
64			RQ[1][1] /= dv;
65			RQ[2][1] -= RQ[0][1]u0 + RQ[1][1]v0;
66			RQ[0][2] /= du;
67			RQ[1][2] /= dv;
68			RQ[2][2] -= RQ[0][2]u0 + RQ[1][2]v0;
69
70			/* now RQ is transform from uv rectangle to xy quadrilateral */
71			/* QR = inverse transform, which maps xy to uv */
72			if (mx3d_adjoint(RQ, QR)==0.)
73			fprintf(stderr, "pmap_quad_rect: warning: determinant=0\n");
74			return ret;
75			}
76
77			/*
78			* pmap_square_quad: find mapping between unit square and quadrilateral.
79			* The correspondence is:
80			*
81			* (0,0) --> quad[0]
82			* (1,0) --> quad[1]
83			* (1,1) --> quad[2]
84			* (0,1) --> quad[3]
85			*/
86
87			pmap_square_quad(quad, SQ)
88			register double quad[4][2]; /* vertices of quadrilateral */
89			register double SQ[3][3]; /* square->quad transform */
90			{
91			double px, py;
92
93			px = X(0)-X(1)+X(2)-X(3);
94			py = Y(0)-Y(1)+Y(2)-Y(3);
95
96			if (ZERO(px) && ZERO(py)) { /* affine */
97			SQ[0][0] = X(1)-X(0);
98			SQ[1][0] = X(2)-X(1);
99			SQ[2][0] = X(0);
100			SQ[0][1] = Y(1)-Y(0);
101			SQ[1][1] = Y(2)-Y(1);
102			SQ[2][1] = Y(0);
103			SQ[0][2] = 0.;
104			SQ[1][2] = 0.;
105			SQ[2][2] = 1.;
106			return PMAP_LINEAR;
107			}
108			else { /* perspective */
109			double dx1, dx2, dy1, dy2, del;
110
111			dx1 = X(1)-X(2);
112			dx2 = X(3)-X(2);
113			dy1 = Y(1)-Y(2);
114			dy2 = Y(3)-Y(2);
115			del = DET2(dx1,dx2, dy1,dy2);
116			if (del==0.) {
117			fprintf(stderr, "pmap_square_quad: bad mapping\n");
118			return PMAP_BAD;
119			}
120			SQ[0][2] = DET2(px,dx2, py,dy2)/del;
121			SQ[1][2] = DET2(dx1,px, dy1,py)/del;
122			SQ[2][2] = 1.;
123			SQ[0][0] = X(1)-X(0)+SQ[0][2]*X(1);
124			SQ[1][0] = X(3)-X(0)+SQ[1][2]*X(3);
125			SQ[2][0] = X(0);
126			SQ[0][1] = Y(1)-Y(0)+SQ[0][2]*Y(1);
127			SQ[1][1] = Y(3)-Y(0)+SQ[1][2]*Y(3);
128			SQ[2][1] = Y(0);
129			return PMAP_PERSP;
130			}
131			}