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#ifndef lint
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static const char RCSid[] = "$Id: pmapgen.c,v 2.3 2003/02/22 02:07:27 greg Exp $";
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#endif
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/*
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* pmapgen.c: general routines for 2-D perspective mappings.
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* These routines are independent of the poly structure,
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* so we do not think in terms of texture and screen space.
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*
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* Paul Heckbert 5 Nov 85, 12 Dec 85
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*/
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#include <stdio.h>
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#include "pmap.h"
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#include "mx3.h"
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#define TOLERANCE 1e-13
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#define ZERO(x) ((x)<TOLERANCE && (x)>-TOLERANCE)
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#define X(i) qdrl[i][0] /* quadrilateral x and y */
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#define Y(i) qdrl[i][1]
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/*
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* pmap_quad_rect: find mapping between quadrilateral and rectangle.
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* The correspondence is:
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*
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* qdrl[0] --> (u0,v0)
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* qdrl[1] --> (u1,v0)
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* qdrl[2] --> (u1,v1)
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* qdrl[3] --> (u0,v1)
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*
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* This method of computing the adjoint numerically is cheaper than
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* computing it symbolically.
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*/
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extern int
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pmap_quad_rect(
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double u0, /* bounds of rectangle */
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double v0,
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double u1,
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double v1,
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double qdrl[4][2], /* vertices of quadrilateral */
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double QR[3][3] /* qdrl->rect transform (returned) */
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)
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{
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int ret;
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double du, dv;
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double RQ[3][3]; /* rect->qdrl transform */
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du = u1-u0;
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dv = v1-v0;
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if (du==0. || dv==0.) {
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fprintf(stderr, "pmap_quad_rect: null rectangle\n");
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return PMAP_BAD;
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}
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/* first find mapping from unit uv square to xy quadrilateral */
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ret = pmap_square_quad(qdrl, RQ);
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if (ret==PMAP_BAD) return PMAP_BAD;
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/* concatenate transform from uv rectangle (u0,v0,u1,v1) to unit square */
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RQ[0][0] /= du;
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RQ[1][0] /= dv;
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RQ[2][0] -= RQ[0][0]*u0 + RQ[1][0]*v0;
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RQ[0][1] /= du;
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RQ[1][1] /= dv;
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RQ[2][1] -= RQ[0][1]*u0 + RQ[1][1]*v0;
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RQ[0][2] /= du;
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RQ[1][2] /= dv;
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RQ[2][2] -= RQ[0][2]*u0 + RQ[1][2]*v0;
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/* now RQ is transform from uv rectangle to xy quadrilateral */
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/* QR = inverse transform, which maps xy to uv */
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if (mx3d_adjoint(RQ, QR)==0.)
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fprintf(stderr, "pmap_quad_rect: warning: determinant=0\n");
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return ret;
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}
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/*
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* pmap_square_quad: find mapping between unit square and quadrilateral.
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* The correspondence is:
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*
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* (0,0) --> qdrl[0]
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* (1,0) --> qdrl[1]
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* (1,1) --> qdrl[2]
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* (0,1) --> qdrl[3]
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*/
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extern int
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pmap_square_quad(
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register double qdrl[4][2], /* vertices of quadrilateral */
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register double SQ[3][3] /* square->qdrl transform */
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)
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{
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double px, py;
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px = X(0)-X(1)+X(2)-X(3);
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py = Y(0)-Y(1)+Y(2)-Y(3);
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if (ZERO(px) && ZERO(py)) { /* affine */
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SQ[0][0] = X(1)-X(0);
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SQ[1][0] = X(2)-X(1);
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SQ[2][0] = X(0);
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SQ[0][1] = Y(1)-Y(0);
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SQ[1][1] = Y(2)-Y(1);
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SQ[2][1] = Y(0);
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SQ[0][2] = 0.;
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SQ[1][2] = 0.;
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SQ[2][2] = 1.;
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return PMAP_LINEAR;
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}
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else { /* perspective */
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double dx1, dx2, dy1, dy2, del;
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dx1 = X(1)-X(2);
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dx2 = X(3)-X(2);
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dy1 = Y(1)-Y(2);
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dy2 = Y(3)-Y(2);
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del = DET2(dx1,dx2, dy1,dy2);
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if (del==0.) {
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fprintf(stderr, "pmap_square_quad: bad mapping\n");
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return PMAP_BAD;
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}
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SQ[0][2] = DET2(px,dx2, py,dy2)/del;
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SQ[1][2] = DET2(dx1,px, dy1,py)/del;
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SQ[2][2] = 1.;
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SQ[0][0] = X(1)-X(0)+SQ[0][2]*X(1);
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SQ[1][0] = X(3)-X(0)+SQ[1][2]*X(3);
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SQ[2][0] = X(0);
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SQ[0][1] = Y(1)-Y(0)+SQ[0][2]*Y(1);
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SQ[1][1] = Y(3)-Y(0)+SQ[1][2]*Y(3);
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SQ[2][1] = Y(0);
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return PMAP_PERSP;
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}
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}
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