/*
* Copyright (c) 2002-2008 LWJGL Project
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* * Neither the name of 'LWJGL' nor the names of
* its contributors may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Portions Copyright (C) 2003-2006 Sun Microsystems, Inc.
* All rights reserved.
*/
/*
** 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 1.1 (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
*/
package org.lwjgl.util.glu.tessellation;
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);
}
}