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/* * Portions Copyright (C) 2003-2006 Sun Microsystems, Inc. * All rights reserved./*from ww w . ja v a 2 s . c o m*/ */ /* ** License Applicability. Except to the extent portions of this file are ** made subject to an alternative license as permitted in the SGI Free ** Software License B, Version 2.0 (the "License"), the contents of this ** file are subject only to the provisions of the License. You may not use ** this file except in compliance with the License. You may obtain a copy ** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600 ** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at: ** ** http://oss.sgi.com/projects/FreeB ** ** Note that, as provided in the License, the Software is distributed on an ** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS ** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND ** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A ** PARTICULAR PURPOSE, AND NON-INFRINGEMENT. ** ** NOTE: The Original Code (as defined below) has been licensed to Sun ** Microsystems, Inc. ("Sun") under the SGI Free Software License B ** (Version 1.1), shown above ("SGI License"). Pursuant to Section ** 3.2(3) of the SGI License, Sun is distributing the Covered Code to ** you under an alternative license ("Alternative License"). This ** Alternative License includes all of the provisions of the SGI License ** except that Section 2.2 and 11 are omitted. Any differences between ** the Alternative License and the SGI License are offered solely by Sun ** and not by SGI. ** ** Original Code. The Original Code is: OpenGL Sample Implementation, ** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics, ** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc. ** Copyright in any portions created by third parties is as indicated ** elsewhere herein. All Rights Reserved. ** ** Additional Notice Provisions: The application programming interfaces ** established by SGI in conjunction with the Original Code are The ** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released ** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version ** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X ** Window System(R) (Version 1.3), released October 19, 1998. This software ** was created using the OpenGL(R) version 1.2.1 Sample Implementation ** published by SGI, but has not been independently verified as being ** compliant with the OpenGL(R) version 1.2.1 Specification. ** ** Author: Eric Veach, July 1994 ** Java Port: Pepijn Van Eeckhoudt, July 2003 ** Java Port: Nathan Parker Burg, August 2003 ** Processing integration: Andres Colubri, February 2012 */ package com.processing.opengl.tess; class Geom { private Geom() { } /* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w), * evaluates the t-coord of the edge uw at the s-coord of the vertex v. * Returns v->t - (uw)(v->s), ie. the signed distance from uw to v. * If uw is vertical (and thus passes thru v), the result is zero. * * The calculation is extremely accurate and stable, even when v * is very close to u or w. In particular if we set v->t = 0 and * let r be the negated result (this evaluates (uw)(v->s)), then * r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t). */ static double EdgeEval(GLUvertex u, GLUvertex v, GLUvertex w) { double gapL, gapR; assert (VertLeq(u, v) && VertLeq(v, w)); gapL = v.s - u.s; gapR = w.s - v.s; if (gapL + gapR > 0) { if (gapL < gapR) { return (v.t - u.t) + (u.t - w.t) * (gapL / (gapL + gapR)); } else { return (v.t - w.t) + (w.t - u.t) * (gapR / (gapL + gapR)); } } /* vertical line */ return 0; } static double EdgeSign(GLUvertex u, GLUvertex v, GLUvertex w) { double gapL, gapR; assert (VertLeq(u, v) && VertLeq(v, w)); gapL = v.s - u.s; gapR = w.s - v.s; if (gapL + gapR > 0) { return (v.t - w.t) * gapL + (v.t - u.t) * gapR; } /* vertical line */ return 0; } /*********************************************************************** * Define versions of EdgeSign, EdgeEval with s and t transposed. */ static double TransEval(GLUvertex u, GLUvertex v, GLUvertex w) { /* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w), * evaluates the t-coord of the edge uw at the s-coord of the vertex v. * Returns v->s - (uw)(v->t), ie. the signed distance from uw to v. * If uw is vertical (and thus passes thru v), the result is zero. * * The calculation is extremely accurate and stable, even when v * is very close to u or w. In particular if we set v->s = 0 and * let r be the negated result (this evaluates (uw)(v->t)), then * r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s). */ double gapL, gapR; assert (TransLeq(u, v) && TransLeq(v, w)); gapL = v.t - u.t; gapR = w.t - v.t; if (gapL + gapR > 0) { if (gapL < gapR) { return (v.s - u.s) + (u.s - w.s) * (gapL / (gapL + gapR)); } else { return (v.s - w.s) + (w.s - u.s) * (gapR / (gapL + gapR)); } } /* vertical line */ return 0; } static double TransSign(GLUvertex u, GLUvertex v, GLUvertex w) { /* Returns a number whose sign matches TransEval(u,v,w) but which * is cheaper to evaluate. Returns > 0, == 0 , or < 0 * as v is above, on, or below the edge uw. */ double gapL, gapR; assert (TransLeq(u, v) && TransLeq(v, w)); gapL = v.t - u.t; gapR = w.t - v.t; if (gapL + gapR > 0) { return (v.s - w.s) * gapL + (v.s - u.s) * gapR; } /* vertical line */ return 0; } static boolean VertCCW(GLUvertex u, GLUvertex v, GLUvertex w) { /* For almost-degenerate situations, the results are not reliable. * Unless the floating-point arithmetic can be performed without * rounding errors, *any* implementation will give incorrect results * on some degenerate inputs, so the client must have some way to * handle this situation. */ return (u.s * (v.t - w.t) + v.s * (w.t - u.t) + w.s * (u.t - v.t)) >= 0; } /* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b), * or (x+y)/2 if a==b==0. It requires that a,b >= 0, and enforces * this in the rare case that one argument is slightly negative. * The implementation is extremely stable numerically. * In particular it guarantees that the result r satisfies * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate * even when a and b differ greatly in magnitude. */ static double Interpolate(double a, double x, double b, double y) { a = (a < 0) ? 0 : a; b = (b < 0) ? 0 : b; if (a <= b) { if (b == 0) { return (x + y) / 2.0; } else { return (x + (y - x) * (a / (a + b))); } } else { return (y + (x - y) * (b / (a + b))); } } static void EdgeIntersect(GLUvertex o1, GLUvertex d1, GLUvertex o2, GLUvertex d2, GLUvertex v) /* Given edges (o1,d1) and (o2,d2), compute their point of intersection. * The computed point is guaranteed to lie in the intersection of the * bounding rectangles defined by each edge. */ { double z1, z2; /* This is certainly not the most efficient way to find the intersection * of two line segments, but it is very numerically stable. * * Strategy: find the two middle vertices in the VertLeq ordering, * and interpolate the intersection s-value from these. Then repeat * using the TransLeq ordering to find the intersection t-value. */ if (!VertLeq(o1, d1)) { GLUvertex temp = o1; o1 = d1; d1 = temp; } if (!VertLeq(o2, d2)) { GLUvertex temp = o2; o2 = d2; d2 = temp; } if (!VertLeq(o1, o2)) { GLUvertex temp = o1; o1 = o2; o2 = temp; temp = d1; d1 = d2; d2 = temp; } if (!VertLeq(o2, d1)) { /* Technically, no intersection -- do our best */ v.s = (o2.s + d1.s) / 2.0; } else if (VertLeq(d1, d2)) { /* Interpolate between o2 and d1 */ z1 = EdgeEval(o1, o2, d1); z2 = EdgeEval(o2, d1, d2); if (z1 + z2 < 0) { z1 = -z1; z2 = -z2; } v.s = Interpolate(z1, o2.s, z2, d1.s); } else { /* Interpolate between o2 and d2 */ z1 = EdgeSign(o1, o2, d1); z2 = -EdgeSign(o1, d2, d1); if (z1 + z2 < 0) { z1 = -z1; z2 = -z2; } v.s = Interpolate(z1, o2.s, z2, d2.s); } /* Now repeat the process for t */ if (!TransLeq(o1, d1)) { GLUvertex temp = o1; o1 = d1; d1 = temp; } if (!TransLeq(o2, d2)) { GLUvertex temp = o2; o2 = d2; d2 = temp; } if (!TransLeq(o1, o2)) { GLUvertex temp = o2; o2 = o1; o1 = temp; temp = d2; d2 = d1; d1 = temp; } if (!TransLeq(o2, d1)) { /* Technically, no intersection -- do our best */ v.t = (o2.t + d1.t) / 2.0; } else if (TransLeq(d1, d2)) { /* Interpolate between o2 and d1 */ z1 = TransEval(o1, o2, d1); z2 = TransEval(o2, d1, d2); if (z1 + z2 < 0) { z1 = -z1; z2 = -z2; } v.t = Interpolate(z1, o2.t, z2, d1.t); } else { /* Interpolate between o2 and d2 */ z1 = TransSign(o1, o2, d1); z2 = -TransSign(o1, d2, d1); if (z1 + z2 < 0) { z1 = -z1; z2 = -z2; } v.t = Interpolate(z1, o2.t, z2, d2.t); } } static boolean VertEq(GLUvertex u, GLUvertex v) { return u.s == v.s && u.t == v.t; } static boolean VertLeq(GLUvertex u, GLUvertex v) { return u.s < v.s || (u.s == v.s && u.t <= v.t); } /* Versions of VertLeq, EdgeSign, EdgeEval with s and t transposed. */ static boolean TransLeq(GLUvertex u, GLUvertex v) { return u.t < v.t || (u.t == v.t && u.s <= v.s); } static boolean EdgeGoesLeft(GLUhalfEdge e) { return VertLeq(e.Sym.Org, e.Org); } static boolean EdgeGoesRight(GLUhalfEdge e) { return VertLeq(e.Org, e.Sym.Org); } static double VertL1dist(GLUvertex u, GLUvertex v) { return Math.abs(u.s - v.s) + Math.abs(u.t - v.t); } /***********************************************************************/ // Compute the cosine of the angle between the edges between o and // v1 and between o and v2 static double EdgeCos(GLUvertex o, GLUvertex v1, GLUvertex v2) { double ov1s = v1.s - o.s; double ov1t = v1.t - o.t; double ov2s = v2.s - o.s; double ov2t = v2.t - o.t; double dotp = ov1s * ov2s + ov1t * ov2t; double len = Math.sqrt(ov1s * ov1s + ov1t * ov1t) * Math.sqrt(ov2s * ov2s + ov2t * ov2t); if (len > 0.0) { dotp /= len; } return dotp; } static final double EPSILON = 1.0e-5; static final double ONE_MINUS_EPSILON = 1.0 - EPSILON; }