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/*
* 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 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 processing.lwjgl.tess;
class Normal {
private Normal() {
}
static boolean SLANTED_SWEEP = false;
static double S_UNIT_X; /* Pre-normalized */
static double S_UNIT_Y;
private static final boolean TRUE_PROJECT = false;
static {
if (SLANTED_SWEEP) {
/* The "feature merging" is not intended to be complete. There are
* special cases where edges are nearly parallel to the sweep line
* which are not implemented. The algorithm should still behave
* robustly (ie. produce a reasonable tesselation) in the presence
* of such edges, however it may miss features which could have been
* merged. We could minimize this effect by choosing the sweep line
* direction to be something unusual (ie. not parallel to one of the
* coordinate axes).
*/
S_UNIT_X = 0.50941539564955385; /* Pre-normalized */
S_UNIT_Y = 0.86052074622010633;
} else {
S_UNIT_X = 1.0;
S_UNIT_Y = 0.0;
}
}
private static double Dot(double[] u, double[] v) {
return (u[0] * v[0] + u[1] * v[1] + u[2] * v[2]);
}
static void Normalize(double[] v) {
double len = v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
assert (len > 0);
len = Math.sqrt(len);
v[0] /= len;
v[1] /= len;
v[2] /= len;
}
static int LongAxis(double[] v) {
int i = 0;
if (Math.abs(v[1]) > Math.abs(v[0])) {
i = 1;
}
if (Math.abs(v[2]) > Math.abs(v[i])) {
i = 2;
}
return i;
}
static void ComputeNormal(GLUtessellatorImpl tess, double[] norm) {
GLUvertex v, v1, v2;
double c, tLen2, maxLen2;
double[] maxVal, minVal, d1, d2, tNorm;
GLUvertex[] maxVert, minVert;
GLUvertex vHead = tess.mesh.vHead;
int i;
maxVal = new double[3];
minVal = new double[3];
minVert = new GLUvertex[3];
maxVert = new GLUvertex[3];
d1 = new double[3];
d2 = new double[3];
tNorm = new double[3];
maxVal[0] = maxVal[1] = maxVal[2] = -2 * PGLU.GLU_TESS_MAX_COORD;
minVal[0] = minVal[1] = minVal[2] = 2 * PGLU.GLU_TESS_MAX_COORD;
for (v = vHead.next; v != vHead; v = v.next) {
for (i = 0; i < 3; ++i) {
c = v.coords[i];
if (c < minVal[i]) {
minVal[i] = c;
minVert[i] = v;
}
if (c > maxVal[i]) {
maxVal[i] = c;
maxVert[i] = v;
}
}
}
/* Find two vertices separated by at least 1/sqrt(3) of the maximum
* distance between any two vertices
*/
i = 0;
if (maxVal[1] - minVal[1] > maxVal[0] - minVal[0]) {
i = 1;
}
if (maxVal[2] - minVal[2] > maxVal[i] - minVal[i]) {
i = 2;
}
if (minVal[i] >= maxVal[i]) {
/* All vertices are the same -- normal doesn't matter */
norm[0] = 0;
norm[1] = 0;
norm[2] = 1;
return;
}
/* Look for a third vertex which forms the triangle with maximum area
* (Length of normal == twice the triangle area)
*/
maxLen2 = 0;
v1 = minVert[i];
v2 = maxVert[i];
d1[0] = v1.coords[0] - v2.coords[0];
d1[1] = v1.coords[1] - v2.coords[1];
d1[2] = v1.coords[2] - v2.coords[2];
for (v = vHead.next; v != vHead; v = v.next) {
d2[0] = v.coords[0] - v2.coords[0];
d2[1] = v.coords[1] - v2.coords[1];
d2[2] = v.coords[2] - v2.coords[2];
tNorm[0] = d1[1] * d2[2] - d1[2] * d2[1];
tNorm[1] = d1[2] * d2[0] - d1[0] * d2[2];
tNorm[2] = d1[0] * d2[1] - d1[1] * d2[0];
tLen2 = tNorm[0] * tNorm[0] + tNorm[1] * tNorm[1] + tNorm[2] * tNorm[2];
if (tLen2 > maxLen2) {
maxLen2 = tLen2;
norm[0] = tNorm[0];
norm[1] = tNorm[1];
norm[2] = tNorm[2];
}
}
if (maxLen2 <= 0) {
/* All points lie on a single line -- any decent normal will do */
norm[0] = norm[1] = norm[2] = 0;
norm[LongAxis(d1)] = 1;
}
}
static void CheckOrientation(GLUtessellatorImpl tess) {
double area;
GLUface f, fHead = tess.mesh.fHead;
GLUvertex v, vHead = tess.mesh.vHead;
GLUhalfEdge e;
/* When we compute the normal automatically, we choose the orientation
* so that the the sum of the signed areas of all contours is non-negative.
*/
area = 0;
for (f = fHead.next; f != fHead; f = f.next) {
e = f.anEdge;
if (e.winding <= 0) continue;
do {
area += (e.Org.s - e.Sym.Org.s) * (e.Org.t + e.Sym.Org.t);
e = e.Lnext;
} while (e != f.anEdge);
}
if (area < 0) {
/* Reverse the orientation by flipping all the t-coordinates */
for (v = vHead.next; v != vHead; v = v.next) {
v.t = -v.t;
}
tess.tUnit[0] = -tess.tUnit[0];
tess.tUnit[1] = -tess.tUnit[1];
tess.tUnit[2] = -tess.tUnit[2];
}
}
/* Determine the polygon normal and project vertices onto the plane
* of the polygon.
*/
public static void __gl_projectPolygon(GLUtessellatorImpl tess) {
GLUvertex v, vHead = tess.mesh.vHead;
double w;
double[] norm = new double[3];
double[] sUnit, tUnit;
int i;
boolean computedNormal = false;
norm[0] = tess.normal[0];
norm[1] = tess.normal[1];
norm[2] = tess.normal[2];
if (norm[0] == 0 && norm[1] == 0 && norm[2] == 0) {
ComputeNormal(tess, norm);
computedNormal = true;
}
sUnit = tess.sUnit;
tUnit = tess.tUnit;
i = LongAxis(norm);
if (TRUE_PROJECT) {
/* Choose the initial sUnit vector to be approximately perpendicular
* to the normal.
*/
Normalize(norm);
sUnit[i] = 0;
sUnit[(i + 1) % 3] = S_UNIT_X;
sUnit[(i + 2) % 3] = S_UNIT_Y;
/* Now make it exactly perpendicular */
w = Dot(sUnit, norm);
sUnit[0] -= w * norm[0];
sUnit[1] -= w * norm[1];
sUnit[2] -= w * norm[2];
Normalize(sUnit);
/* Choose tUnit so that (sUnit,tUnit,norm) form a right-handed frame */
tUnit[0] = norm[1] * sUnit[2] - norm[2] * sUnit[1];
tUnit[1] = norm[2] * sUnit[0] - norm[0] * sUnit[2];
tUnit[2] = norm[0] * sUnit[1] - norm[1] * sUnit[0];
Normalize(tUnit);
} else {
/* Project perpendicular to a coordinate axis -- better numerically */
sUnit[i] = 0;
sUnit[(i + 1) % 3] = S_UNIT_X;
sUnit[(i + 2) % 3] = S_UNIT_Y;
tUnit[i] = 0;
tUnit[(i + 1) % 3] = (norm[i] > 0) ? -S_UNIT_Y : S_UNIT_Y;
tUnit[(i + 2) % 3] = (norm[i] > 0) ? S_UNIT_X : -S_UNIT_X;
}
/* Project the vertices onto the sweep plane */
for (v = vHead.next; v != vHead; v = v.next) {
v.s = Dot(v.coords, sUnit);
v.t = Dot(v.coords, tUnit);
}
if (computedNormal) {
CheckOrientation(tess);
}
}
}
