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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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|
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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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|
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#define TOLERANCE 1e-13 |
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#define ZERO(x) ((x)<TOLERANCE && (x)>-TOLERANCE) |
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|
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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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/* |
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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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|
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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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|
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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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|
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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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|
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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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|
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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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/* |
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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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|
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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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|
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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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|
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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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|
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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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} |
