1207 lines
48 KiB
Java
1207 lines
48 KiB
Java
/*
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* Copyright (c) 1998, 2006, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation. Oracle designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Oracle in the LICENSE file that accompanied this code.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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package sun.awt.geom;
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import java.awt.geom.Rectangle2D;
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import java.awt.geom.QuadCurve2D;
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import java.awt.geom.CubicCurve2D;
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import java.awt.geom.PathIterator;
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import java.awt.geom.IllegalPathStateException;
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import java.util.Vector;
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public abstract class Curve {
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public static final int INCREASING = 1;
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public static final int DECREASING = -1;
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protected int direction;
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public static void insertMove(Vector curves, double x, double y) {
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curves.add(new Order0(x, y));
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}
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public static void insertLine(Vector curves,
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double x0, double y0,
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double x1, double y1)
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{
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if (y0 < y1) {
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curves.add(new Order1(x0, y0,
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x1, y1,
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INCREASING));
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} else if (y0 > y1) {
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curves.add(new Order1(x1, y1,
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x0, y0,
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DECREASING));
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} else {
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// Do not add horizontal lines
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}
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}
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public static void insertQuad(Vector curves,
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double x0, double y0,
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double coords[])
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{
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double y1 = coords[3];
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if (y0 > y1) {
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Order2.insert(curves, coords,
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coords[2], y1,
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coords[0], coords[1],
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x0, y0,
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DECREASING);
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} else if (y0 == y1 && y0 == coords[1]) {
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// Do not add horizontal lines
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return;
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} else {
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Order2.insert(curves, coords,
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x0, y0,
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coords[0], coords[1],
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coords[2], y1,
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INCREASING);
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}
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}
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public static void insertCubic(Vector curves,
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double x0, double y0,
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double coords[])
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{
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double y1 = coords[5];
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if (y0 > y1) {
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Order3.insert(curves, coords,
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coords[4], y1,
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coords[2], coords[3],
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coords[0], coords[1],
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x0, y0,
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DECREASING);
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} else if (y0 == y1 && y0 == coords[1] && y0 == coords[3]) {
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// Do not add horizontal lines
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return;
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} else {
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Order3.insert(curves, coords,
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x0, y0,
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coords[0], coords[1],
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coords[2], coords[3],
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coords[4], y1,
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INCREASING);
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}
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}
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/**
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* Calculates the number of times the given path
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* crosses the ray extending to the right from (px,py).
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* If the point lies on a part of the path,
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* then no crossings are counted for that intersection.
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* +1 is added for each crossing where the Y coordinate is increasing
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* -1 is added for each crossing where the Y coordinate is decreasing
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* The return value is the sum of all crossings for every segment in
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* the path.
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* The path must start with a SEG_MOVETO, otherwise an exception is
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* thrown.
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* The caller must check p[xy] for NaN values.
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* The caller may also reject infinite p[xy] values as well.
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*/
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public static int pointCrossingsForPath(PathIterator pi,
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double px, double py)
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{
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if (pi.isDone()) {
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return 0;
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}
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double coords[] = new double[6];
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if (pi.currentSegment(coords) != PathIterator.SEG_MOVETO) {
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throw new IllegalPathStateException("missing initial moveto "+
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"in path definition");
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}
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pi.next();
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double movx = coords[0];
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double movy = coords[1];
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double curx = movx;
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double cury = movy;
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double endx, endy;
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int crossings = 0;
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while (!pi.isDone()) {
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switch (pi.currentSegment(coords)) {
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case PathIterator.SEG_MOVETO:
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if (cury != movy) {
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crossings += pointCrossingsForLine(px, py,
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curx, cury,
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movx, movy);
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}
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movx = curx = coords[0];
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movy = cury = coords[1];
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break;
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case PathIterator.SEG_LINETO:
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endx = coords[0];
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endy = coords[1];
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crossings += pointCrossingsForLine(px, py,
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curx, cury,
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endx, endy);
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curx = endx;
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cury = endy;
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break;
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case PathIterator.SEG_QUADTO:
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endx = coords[2];
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endy = coords[3];
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crossings += pointCrossingsForQuad(px, py,
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curx, cury,
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coords[0], coords[1],
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endx, endy, 0);
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curx = endx;
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cury = endy;
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break;
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case PathIterator.SEG_CUBICTO:
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endx = coords[4];
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endy = coords[5];
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crossings += pointCrossingsForCubic(px, py,
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curx, cury,
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coords[0], coords[1],
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coords[2], coords[3],
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endx, endy, 0);
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curx = endx;
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cury = endy;
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break;
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case PathIterator.SEG_CLOSE:
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if (cury != movy) {
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crossings += pointCrossingsForLine(px, py,
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curx, cury,
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movx, movy);
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}
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curx = movx;
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cury = movy;
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break;
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}
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pi.next();
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}
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if (cury != movy) {
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crossings += pointCrossingsForLine(px, py,
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curx, cury,
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movx, movy);
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}
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return crossings;
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}
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/**
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* Calculates the number of times the line from (x0,y0) to (x1,y1)
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* crosses the ray extending to the right from (px,py).
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* If the point lies on the line, then no crossings are recorded.
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* +1 is returned for a crossing where the Y coordinate is increasing
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* -1 is returned for a crossing where the Y coordinate is decreasing
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*/
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public static int pointCrossingsForLine(double px, double py,
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double x0, double y0,
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double x1, double y1)
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{
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if (py < y0 && py < y1) return 0;
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if (py >= y0 && py >= y1) return 0;
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// assert(y0 != y1);
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if (px >= x0 && px >= x1) return 0;
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if (px < x0 && px < x1) return (y0 < y1) ? 1 : -1;
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double xintercept = x0 + (py - y0) * (x1 - x0) / (y1 - y0);
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if (px >= xintercept) return 0;
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return (y0 < y1) ? 1 : -1;
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}
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/**
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* Calculates the number of times the quad from (x0,y0) to (x1,y1)
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* crosses the ray extending to the right from (px,py).
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* If the point lies on a part of the curve,
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* then no crossings are counted for that intersection.
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* the level parameter should be 0 at the top-level call and will count
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* up for each recursion level to prevent infinite recursion
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* +1 is added for each crossing where the Y coordinate is increasing
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* -1 is added for each crossing where the Y coordinate is decreasing
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*/
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public static int pointCrossingsForQuad(double px, double py,
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double x0, double y0,
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double xc, double yc,
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double x1, double y1, int level)
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{
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if (py < y0 && py < yc && py < y1) return 0;
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if (py >= y0 && py >= yc && py >= y1) return 0;
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// Note y0 could equal y1...
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if (px >= x0 && px >= xc && px >= x1) return 0;
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if (px < x0 && px < xc && px < x1) {
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if (py >= y0) {
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if (py < y1) return 1;
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} else {
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// py < y0
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if (py >= y1) return -1;
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}
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// py outside of y01 range, and/or y0==y1
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return 0;
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}
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// double precision only has 52 bits of mantissa
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if (level > 52) return pointCrossingsForLine(px, py, x0, y0, x1, y1);
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double x0c = (x0 + xc) / 2;
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double y0c = (y0 + yc) / 2;
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double xc1 = (xc + x1) / 2;
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double yc1 = (yc + y1) / 2;
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xc = (x0c + xc1) / 2;
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yc = (y0c + yc1) / 2;
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if (Double.isNaN(xc) || Double.isNaN(yc)) {
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// [xy]c are NaN if any of [xy]0c or [xy]c1 are NaN
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// [xy]0c or [xy]c1 are NaN if any of [xy][0c1] are NaN
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// These values are also NaN if opposing infinities are added
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return 0;
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}
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return (pointCrossingsForQuad(px, py,
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x0, y0, x0c, y0c, xc, yc,
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level+1) +
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pointCrossingsForQuad(px, py,
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xc, yc, xc1, yc1, x1, y1,
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level+1));
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}
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/**
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* Calculates the number of times the cubic from (x0,y0) to (x1,y1)
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* crosses the ray extending to the right from (px,py).
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* If the point lies on a part of the curve,
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* then no crossings are counted for that intersection.
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* the level parameter should be 0 at the top-level call and will count
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* up for each recursion level to prevent infinite recursion
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* +1 is added for each crossing where the Y coordinate is increasing
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* -1 is added for each crossing where the Y coordinate is decreasing
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*/
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public static int pointCrossingsForCubic(double px, double py,
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double x0, double y0,
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double xc0, double yc0,
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double xc1, double yc1,
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double x1, double y1, int level)
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{
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if (py < y0 && py < yc0 && py < yc1 && py < y1) return 0;
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if (py >= y0 && py >= yc0 && py >= yc1 && py >= y1) return 0;
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// Note y0 could equal yc0...
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if (px >= x0 && px >= xc0 && px >= xc1 && px >= x1) return 0;
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if (px < x0 && px < xc0 && px < xc1 && px < x1) {
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if (py >= y0) {
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if (py < y1) return 1;
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} else {
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// py < y0
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if (py >= y1) return -1;
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}
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// py outside of y01 range, and/or y0==yc0
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return 0;
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}
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// double precision only has 52 bits of mantissa
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if (level > 52) return pointCrossingsForLine(px, py, x0, y0, x1, y1);
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double xmid = (xc0 + xc1) / 2;
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double ymid = (yc0 + yc1) / 2;
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xc0 = (x0 + xc0) / 2;
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yc0 = (y0 + yc0) / 2;
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xc1 = (xc1 + x1) / 2;
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yc1 = (yc1 + y1) / 2;
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double xc0m = (xc0 + xmid) / 2;
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double yc0m = (yc0 + ymid) / 2;
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double xmc1 = (xmid + xc1) / 2;
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double ymc1 = (ymid + yc1) / 2;
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xmid = (xc0m + xmc1) / 2;
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ymid = (yc0m + ymc1) / 2;
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if (Double.isNaN(xmid) || Double.isNaN(ymid)) {
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// [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN
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// [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN
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// These values are also NaN if opposing infinities are added
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return 0;
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}
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return (pointCrossingsForCubic(px, py,
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x0, y0, xc0, yc0,
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xc0m, yc0m, xmid, ymid, level+1) +
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pointCrossingsForCubic(px, py,
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xmid, ymid, xmc1, ymc1,
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xc1, yc1, x1, y1, level+1));
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}
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/**
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* The rectangle intersection test counts the number of times
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* that the path crosses through the shadow that the rectangle
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* projects to the right towards (x => +INFINITY).
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*
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* During processing of the path it actually counts every time
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* the path crosses either or both of the top and bottom edges
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* of that shadow. If the path enters from the top, the count
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* is incremented. If it then exits back through the top, the
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* same way it came in, the count is decremented and there is
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* no impact on the winding count. If, instead, the path exits
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* out the bottom, then the count is incremented again and a
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* full pass through the shadow is indicated by the winding count
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* having been incremented by 2.
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*
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* Thus, the winding count that it accumulates is actually double
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* the real winding count. Since the path is continuous, the
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* final answer should be a multiple of 2, otherwise there is a
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* logic error somewhere.
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*
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* If the path ever has a direct hit on the rectangle, then a
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* special value is returned. This special value terminates
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* all ongoing accumulation on up through the call chain and
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* ends up getting returned to the calling function which can
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* then produce an answer directly. For intersection tests,
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* the answer is always "true" if the path intersects the
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* rectangle. For containment tests, the answer is always
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* "false" if the path intersects the rectangle. Thus, no
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* further processing is ever needed if an intersection occurs.
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*/
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public static final int RECT_INTERSECTS = 0x80000000;
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/**
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* Accumulate the number of times the path crosses the shadow
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* extending to the right of the rectangle. See the comment
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* for the RECT_INTERSECTS constant for more complete details.
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* The return value is the sum of all crossings for both the
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* top and bottom of the shadow for every segment in the path,
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* or the special value RECT_INTERSECTS if the path ever enters
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* the interior of the rectangle.
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* The path must start with a SEG_MOVETO, otherwise an exception is
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* thrown.
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* The caller must check r[xy]{min,max} for NaN values.
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*/
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public static int rectCrossingsForPath(PathIterator pi,
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double rxmin, double rymin,
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double rxmax, double rymax)
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{
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if (rxmax <= rxmin || rymax <= rymin) {
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return 0;
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}
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if (pi.isDone()) {
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return 0;
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}
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double coords[] = new double[6];
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if (pi.currentSegment(coords) != PathIterator.SEG_MOVETO) {
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throw new IllegalPathStateException("missing initial moveto "+
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"in path definition");
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}
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pi.next();
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double curx, cury, movx, movy, endx, endy;
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curx = movx = coords[0];
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cury = movy = coords[1];
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int crossings = 0;
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while (crossings != RECT_INTERSECTS && !pi.isDone()) {
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switch (pi.currentSegment(coords)) {
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case PathIterator.SEG_MOVETO:
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if (curx != movx || cury != movy) {
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crossings = rectCrossingsForLine(crossings,
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rxmin, rymin,
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rxmax, rymax,
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curx, cury,
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movx, movy);
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}
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// Count should always be a multiple of 2 here.
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// assert((crossings & 1) != 0);
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movx = curx = coords[0];
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movy = cury = coords[1];
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break;
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case PathIterator.SEG_LINETO:
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endx = coords[0];
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endy = coords[1];
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crossings = rectCrossingsForLine(crossings,
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rxmin, rymin,
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rxmax, rymax,
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curx, cury,
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endx, endy);
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curx = endx;
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cury = endy;
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break;
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case PathIterator.SEG_QUADTO:
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endx = coords[2];
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endy = coords[3];
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crossings = rectCrossingsForQuad(crossings,
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rxmin, rymin,
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rxmax, rymax,
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curx, cury,
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coords[0], coords[1],
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endx, endy, 0);
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curx = endx;
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cury = endy;
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break;
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case PathIterator.SEG_CUBICTO:
|
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endx = coords[4];
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endy = coords[5];
|
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crossings = rectCrossingsForCubic(crossings,
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rxmin, rymin,
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rxmax, rymax,
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curx, cury,
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coords[0], coords[1],
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coords[2], coords[3],
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endx, endy, 0);
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curx = endx;
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cury = endy;
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break;
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case PathIterator.SEG_CLOSE:
|
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if (curx != movx || cury != movy) {
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crossings = rectCrossingsForLine(crossings,
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rxmin, rymin,
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rxmax, rymax,
|
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curx, cury,
|
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movx, movy);
|
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}
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curx = movx;
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cury = movy;
|
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// Count should always be a multiple of 2 here.
|
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// assert((crossings & 1) != 0);
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break;
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}
|
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pi.next();
|
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}
|
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if (crossings != RECT_INTERSECTS && (curx != movx || cury != movy)) {
|
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crossings = rectCrossingsForLine(crossings,
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rxmin, rymin,
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rxmax, rymax,
|
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curx, cury,
|
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movx, movy);
|
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}
|
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// Count should always be a multiple of 2 here.
|
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// assert((crossings & 1) != 0);
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return crossings;
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}
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|
/**
|
|
* Accumulate the number of times the line crosses the shadow
|
|
* extending to the right of the rectangle. See the comment
|
|
* for the RECT_INTERSECTS constant for more complete details.
|
|
*/
|
|
public static int rectCrossingsForLine(int crossings,
|
|
double rxmin, double rymin,
|
|
double rxmax, double rymax,
|
|
double x0, double y0,
|
|
double x1, double y1)
|
|
{
|
|
if (y0 >= rymax && y1 >= rymax) return crossings;
|
|
if (y0 <= rymin && y1 <= rymin) return crossings;
|
|
if (x0 <= rxmin && x1 <= rxmin) return crossings;
|
|
if (x0 >= rxmax && x1 >= rxmax) {
|
|
// Line is entirely to the right of the rect
|
|
// and the vertical ranges of the two overlap by a non-empty amount
|
|
// Thus, this line segment is partially in the "right-shadow"
|
|
// Path may have done a complete crossing
|
|
// Or path may have entered or exited the right-shadow
|
|
if (y0 < y1) {
|
|
// y-increasing line segment...
|
|
// We know that y0 < rymax and y1 > rymin
|
|
if (y0 <= rymin) crossings++;
|
|
if (y1 >= rymax) crossings++;
|
|
} else if (y1 < y0) {
|
|
// y-decreasing line segment...
|
|
// We know that y1 < rymax and y0 > rymin
|
|
if (y1 <= rymin) crossings--;
|
|
if (y0 >= rymax) crossings--;
|
|
}
|
|
return crossings;
|
|
}
|
|
// Remaining case:
|
|
// Both x and y ranges overlap by a non-empty amount
|
|
// First do trivial INTERSECTS rejection of the cases
|
|
// where one of the endpoints is inside the rectangle.
|
|
if ((x0 > rxmin && x0 < rxmax && y0 > rymin && y0 < rymax) ||
|
|
(x1 > rxmin && x1 < rxmax && y1 > rymin && y1 < rymax))
|
|
{
|
|
return RECT_INTERSECTS;
|
|
}
|
|
// Otherwise calculate the y intercepts and see where
|
|
// they fall with respect to the rectangle
|
|
double xi0 = x0;
|
|
if (y0 < rymin) {
|
|
xi0 += ((rymin - y0) * (x1 - x0) / (y1 - y0));
|
|
} else if (y0 > rymax) {
|
|
xi0 += ((rymax - y0) * (x1 - x0) / (y1 - y0));
|
|
}
|
|
double xi1 = x1;
|
|
if (y1 < rymin) {
|
|
xi1 += ((rymin - y1) * (x0 - x1) / (y0 - y1));
|
|
} else if (y1 > rymax) {
|
|
xi1 += ((rymax - y1) * (x0 - x1) / (y0 - y1));
|
|
}
|
|
if (xi0 <= rxmin && xi1 <= rxmin) return crossings;
|
|
if (xi0 >= rxmax && xi1 >= rxmax) {
|
|
if (y0 < y1) {
|
|
// y-increasing line segment...
|
|
// We know that y0 < rymax and y1 > rymin
|
|
if (y0 <= rymin) crossings++;
|
|
if (y1 >= rymax) crossings++;
|
|
} else if (y1 < y0) {
|
|
// y-decreasing line segment...
|
|
// We know that y1 < rymax and y0 > rymin
|
|
if (y1 <= rymin) crossings--;
|
|
if (y0 >= rymax) crossings--;
|
|
}
|
|
return crossings;
|
|
}
|
|
return RECT_INTERSECTS;
|
|
}
|
|
|
|
/**
|
|
* Accumulate the number of times the quad crosses the shadow
|
|
* extending to the right of the rectangle. See the comment
|
|
* for the RECT_INTERSECTS constant for more complete details.
|
|
*/
|
|
public static int rectCrossingsForQuad(int crossings,
|
|
double rxmin, double rymin,
|
|
double rxmax, double rymax,
|
|
double x0, double y0,
|
|
double xc, double yc,
|
|
double x1, double y1,
|
|
int level)
|
|
{
|
|
if (y0 >= rymax && yc >= rymax && y1 >= rymax) return crossings;
|
|
if (y0 <= rymin && yc <= rymin && y1 <= rymin) return crossings;
|
|
if (x0 <= rxmin && xc <= rxmin && x1 <= rxmin) return crossings;
|
|
if (x0 >= rxmax && xc >= rxmax && x1 >= rxmax) {
|
|
// Quad is entirely to the right of the rect
|
|
// and the vertical range of the 3 Y coordinates of the quad
|
|
// overlaps the vertical range of the rect by a non-empty amount
|
|
// We now judge the crossings solely based on the line segment
|
|
// connecting the endpoints of the quad.
|
|
// Note that we may have 0, 1, or 2 crossings as the control
|
|
// point may be causing the Y range intersection while the
|
|
// two endpoints are entirely above or below.
|
|
if (y0 < y1) {
|
|
// y-increasing line segment...
|
|
if (y0 <= rymin && y1 > rymin) crossings++;
|
|
if (y0 < rymax && y1 >= rymax) crossings++;
|
|
} else if (y1 < y0) {
|
|
// y-decreasing line segment...
|
|
if (y1 <= rymin && y0 > rymin) crossings--;
|
|
if (y1 < rymax && y0 >= rymax) crossings--;
|
|
}
|
|
return crossings;
|
|
}
|
|
// The intersection of ranges is more complicated
|
|
// First do trivial INTERSECTS rejection of the cases
|
|
// where one of the endpoints is inside the rectangle.
|
|
if ((x0 < rxmax && x0 > rxmin && y0 < rymax && y0 > rymin) ||
|
|
(x1 < rxmax && x1 > rxmin && y1 < rymax && y1 > rymin))
|
|
{
|
|
return RECT_INTERSECTS;
|
|
}
|
|
// Otherwise, subdivide and look for one of the cases above.
|
|
// double precision only has 52 bits of mantissa
|
|
if (level > 52) {
|
|
return rectCrossingsForLine(crossings,
|
|
rxmin, rymin, rxmax, rymax,
|
|
x0, y0, x1, y1);
|
|
}
|
|
double x0c = (x0 + xc) / 2;
|
|
double y0c = (y0 + yc) / 2;
|
|
double xc1 = (xc + x1) / 2;
|
|
double yc1 = (yc + y1) / 2;
|
|
xc = (x0c + xc1) / 2;
|
|
yc = (y0c + yc1) / 2;
|
|
if (Double.isNaN(xc) || Double.isNaN(yc)) {
|
|
// [xy]c are NaN if any of [xy]0c or [xy]c1 are NaN
|
|
// [xy]0c or [xy]c1 are NaN if any of [xy][0c1] are NaN
|
|
// These values are also NaN if opposing infinities are added
|
|
return 0;
|
|
}
|
|
crossings = rectCrossingsForQuad(crossings,
|
|
rxmin, rymin, rxmax, rymax,
|
|
x0, y0, x0c, y0c, xc, yc,
|
|
level+1);
|
|
if (crossings != RECT_INTERSECTS) {
|
|
crossings = rectCrossingsForQuad(crossings,
|
|
rxmin, rymin, rxmax, rymax,
|
|
xc, yc, xc1, yc1, x1, y1,
|
|
level+1);
|
|
}
|
|
return crossings;
|
|
}
|
|
|
|
/**
|
|
* Accumulate the number of times the cubic crosses the shadow
|
|
* extending to the right of the rectangle. See the comment
|
|
* for the RECT_INTERSECTS constant for more complete details.
|
|
*/
|
|
public static int rectCrossingsForCubic(int crossings,
|
|
double rxmin, double rymin,
|
|
double rxmax, double rymax,
|
|
double x0, double y0,
|
|
double xc0, double yc0,
|
|
double xc1, double yc1,
|
|
double x1, double y1,
|
|
int level)
|
|
{
|
|
if (y0 >= rymax && yc0 >= rymax && yc1 >= rymax && y1 >= rymax) {
|
|
return crossings;
|
|
}
|
|
if (y0 <= rymin && yc0 <= rymin && yc1 <= rymin && y1 <= rymin) {
|
|
return crossings;
|
|
}
|
|
if (x0 <= rxmin && xc0 <= rxmin && xc1 <= rxmin && x1 <= rxmin) {
|
|
return crossings;
|
|
}
|
|
if (x0 >= rxmax && xc0 >= rxmax && xc1 >= rxmax && x1 >= rxmax) {
|
|
// Cubic is entirely to the right of the rect
|
|
// and the vertical range of the 4 Y coordinates of the cubic
|
|
// overlaps the vertical range of the rect by a non-empty amount
|
|
// We now judge the crossings solely based on the line segment
|
|
// connecting the endpoints of the cubic.
|
|
// Note that we may have 0, 1, or 2 crossings as the control
|
|
// points may be causing the Y range intersection while the
|
|
// two endpoints are entirely above or below.
|
|
if (y0 < y1) {
|
|
// y-increasing line segment...
|
|
if (y0 <= rymin && y1 > rymin) crossings++;
|
|
if (y0 < rymax && y1 >= rymax) crossings++;
|
|
} else if (y1 < y0) {
|
|
// y-decreasing line segment...
|
|
if (y1 <= rymin && y0 > rymin) crossings--;
|
|
if (y1 < rymax && y0 >= rymax) crossings--;
|
|
}
|
|
return crossings;
|
|
}
|
|
// The intersection of ranges is more complicated
|
|
// First do trivial INTERSECTS rejection of the cases
|
|
// where one of the endpoints is inside the rectangle.
|
|
if ((x0 > rxmin && x0 < rxmax && y0 > rymin && y0 < rymax) ||
|
|
(x1 > rxmin && x1 < rxmax && y1 > rymin && y1 < rymax))
|
|
{
|
|
return RECT_INTERSECTS;
|
|
}
|
|
// Otherwise, subdivide and look for one of the cases above.
|
|
// double precision only has 52 bits of mantissa
|
|
if (level > 52) {
|
|
return rectCrossingsForLine(crossings,
|
|
rxmin, rymin, rxmax, rymax,
|
|
x0, y0, x1, y1);
|
|
}
|
|
double xmid = (xc0 + xc1) / 2;
|
|
double ymid = (yc0 + yc1) / 2;
|
|
xc0 = (x0 + xc0) / 2;
|
|
yc0 = (y0 + yc0) / 2;
|
|
xc1 = (xc1 + x1) / 2;
|
|
yc1 = (yc1 + y1) / 2;
|
|
double xc0m = (xc0 + xmid) / 2;
|
|
double yc0m = (yc0 + ymid) / 2;
|
|
double xmc1 = (xmid + xc1) / 2;
|
|
double ymc1 = (ymid + yc1) / 2;
|
|
xmid = (xc0m + xmc1) / 2;
|
|
ymid = (yc0m + ymc1) / 2;
|
|
if (Double.isNaN(xmid) || Double.isNaN(ymid)) {
|
|
// [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN
|
|
// [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN
|
|
// These values are also NaN if opposing infinities are added
|
|
return 0;
|
|
}
|
|
crossings = rectCrossingsForCubic(crossings,
|
|
rxmin, rymin, rxmax, rymax,
|
|
x0, y0, xc0, yc0,
|
|
xc0m, yc0m, xmid, ymid, level+1);
|
|
if (crossings != RECT_INTERSECTS) {
|
|
crossings = rectCrossingsForCubic(crossings,
|
|
rxmin, rymin, rxmax, rymax,
|
|
xmid, ymid, xmc1, ymc1,
|
|
xc1, yc1, x1, y1, level+1);
|
|
}
|
|
return crossings;
|
|
}
|
|
|
|
public Curve(int direction) {
|
|
this.direction = direction;
|
|
}
|
|
|
|
public final int getDirection() {
|
|
return direction;
|
|
}
|
|
|
|
public final Curve getWithDirection(int direction) {
|
|
return (this.direction == direction ? this : getReversedCurve());
|
|
}
|
|
|
|
public static double round(double v) {
|
|
//return Math.rint(v*10)/10;
|
|
return v;
|
|
}
|
|
|
|
public static int orderof(double x1, double x2) {
|
|
if (x1 < x2) {
|
|
return -1;
|
|
}
|
|
if (x1 > x2) {
|
|
return 1;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
public static long signeddiffbits(double y1, double y2) {
|
|
return (Double.doubleToLongBits(y1) - Double.doubleToLongBits(y2));
|
|
}
|
|
public static long diffbits(double y1, double y2) {
|
|
return Math.abs(Double.doubleToLongBits(y1) -
|
|
Double.doubleToLongBits(y2));
|
|
}
|
|
public static double prev(double v) {
|
|
return Double.longBitsToDouble(Double.doubleToLongBits(v)-1);
|
|
}
|
|
public static double next(double v) {
|
|
return Double.longBitsToDouble(Double.doubleToLongBits(v)+1);
|
|
}
|
|
|
|
public String toString() {
|
|
return ("Curve["+
|
|
getOrder()+", "+
|
|
("("+round(getX0())+", "+round(getY0())+"), ")+
|
|
controlPointString()+
|
|
("("+round(getX1())+", "+round(getY1())+"), ")+
|
|
(direction == INCREASING ? "D" : "U")+
|
|
"]");
|
|
}
|
|
|
|
public String controlPointString() {
|
|
return "";
|
|
}
|
|
|
|
public abstract int getOrder();
|
|
|
|
public abstract double getXTop();
|
|
public abstract double getYTop();
|
|
public abstract double getXBot();
|
|
public abstract double getYBot();
|
|
|
|
public abstract double getXMin();
|
|
public abstract double getXMax();
|
|
|
|
public abstract double getX0();
|
|
public abstract double getY0();
|
|
public abstract double getX1();
|
|
public abstract double getY1();
|
|
|
|
public abstract double XforY(double y);
|
|
public abstract double TforY(double y);
|
|
public abstract double XforT(double t);
|
|
public abstract double YforT(double t);
|
|
public abstract double dXforT(double t, int deriv);
|
|
public abstract double dYforT(double t, int deriv);
|
|
|
|
public abstract double nextVertical(double t0, double t1);
|
|
|
|
public int crossingsFor(double x, double y) {
|
|
if (y >= getYTop() && y < getYBot()) {
|
|
if (x < getXMax() && (x < getXMin() || x < XforY(y))) {
|
|
return 1;
|
|
}
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
public boolean accumulateCrossings(Crossings c) {
|
|
double xhi = c.getXHi();
|
|
if (getXMin() >= xhi) {
|
|
return false;
|
|
}
|
|
double xlo = c.getXLo();
|
|
double ylo = c.getYLo();
|
|
double yhi = c.getYHi();
|
|
double y0 = getYTop();
|
|
double y1 = getYBot();
|
|
double tstart, ystart, tend, yend;
|
|
if (y0 < ylo) {
|
|
if (y1 <= ylo) {
|
|
return false;
|
|
}
|
|
ystart = ylo;
|
|
tstart = TforY(ylo);
|
|
} else {
|
|
if (y0 >= yhi) {
|
|
return false;
|
|
}
|
|
ystart = y0;
|
|
tstart = 0;
|
|
}
|
|
if (y1 > yhi) {
|
|
yend = yhi;
|
|
tend = TforY(yhi);
|
|
} else {
|
|
yend = y1;
|
|
tend = 1;
|
|
}
|
|
boolean hitLo = false;
|
|
boolean hitHi = false;
|
|
while (true) {
|
|
double x = XforT(tstart);
|
|
if (x < xhi) {
|
|
if (hitHi || x > xlo) {
|
|
return true;
|
|
}
|
|
hitLo = true;
|
|
} else {
|
|
if (hitLo) {
|
|
return true;
|
|
}
|
|
hitHi = true;
|
|
}
|
|
if (tstart >= tend) {
|
|
break;
|
|
}
|
|
tstart = nextVertical(tstart, tend);
|
|
}
|
|
if (hitLo) {
|
|
c.record(ystart, yend, direction);
|
|
}
|
|
return false;
|
|
}
|
|
|
|
public abstract void enlarge(Rectangle2D r);
|
|
|
|
public Curve getSubCurve(double ystart, double yend) {
|
|
return getSubCurve(ystart, yend, direction);
|
|
}
|
|
|
|
public abstract Curve getReversedCurve();
|
|
public abstract Curve getSubCurve(double ystart, double yend, int dir);
|
|
|
|
public int compareTo(Curve that, double yrange[]) {
|
|
/*
|
|
System.out.println(this+".compareTo("+that+")");
|
|
System.out.println("target range = "+yrange[0]+"=>"+yrange[1]);
|
|
*/
|
|
double y0 = yrange[0];
|
|
double y1 = yrange[1];
|
|
y1 = Math.min(Math.min(y1, this.getYBot()), that.getYBot());
|
|
if (y1 <= yrange[0]) {
|
|
System.err.println("this == "+this);
|
|
System.err.println("that == "+that);
|
|
System.out.println("target range = "+yrange[0]+"=>"+yrange[1]);
|
|
throw new InternalError("backstepping from "+yrange[0]+" to "+y1);
|
|
}
|
|
yrange[1] = y1;
|
|
if (this.getXMax() <= that.getXMin()) {
|
|
if (this.getXMin() == that.getXMax()) {
|
|
return 0;
|
|
}
|
|
return -1;
|
|
}
|
|
if (this.getXMin() >= that.getXMax()) {
|
|
return 1;
|
|
}
|
|
// Parameter s for thi(s) curve and t for tha(t) curve
|
|
// [st]0 = parameters for top of current section of interest
|
|
// [st]1 = parameters for bottom of valid range
|
|
// [st]h = parameters for hypothesis point
|
|
// [d][xy]s = valuations of thi(s) curve at sh
|
|
// [d][xy]t = valuations of tha(t) curve at th
|
|
double s0 = this.TforY(y0);
|
|
double ys0 = this.YforT(s0);
|
|
if (ys0 < y0) {
|
|
s0 = refineTforY(s0, ys0, y0);
|
|
ys0 = this.YforT(s0);
|
|
}
|
|
double s1 = this.TforY(y1);
|
|
if (this.YforT(s1) < y0) {
|
|
s1 = refineTforY(s1, this.YforT(s1), y0);
|
|
//System.out.println("s1 problem!");
|
|
}
|
|
double t0 = that.TforY(y0);
|
|
double yt0 = that.YforT(t0);
|
|
if (yt0 < y0) {
|
|
t0 = that.refineTforY(t0, yt0, y0);
|
|
yt0 = that.YforT(t0);
|
|
}
|
|
double t1 = that.TforY(y1);
|
|
if (that.YforT(t1) < y0) {
|
|
t1 = that.refineTforY(t1, that.YforT(t1), y0);
|
|
//System.out.println("t1 problem!");
|
|
}
|
|
double xs0 = this.XforT(s0);
|
|
double xt0 = that.XforT(t0);
|
|
double scale = Math.max(Math.abs(y0), Math.abs(y1));
|
|
double ymin = Math.max(scale * 1E-14, 1E-300);
|
|
if (fairlyClose(xs0, xt0)) {
|
|
double bump = ymin;
|
|
double maxbump = Math.min(ymin * 1E13, (y1 - y0) * .1);
|
|
double y = y0 + bump;
|
|
while (y <= y1) {
|
|
if (fairlyClose(this.XforY(y), that.XforY(y))) {
|
|
if ((bump *= 2) > maxbump) {
|
|
bump = maxbump;
|
|
}
|
|
} else {
|
|
y -= bump;
|
|
while (true) {
|
|
bump /= 2;
|
|
double newy = y + bump;
|
|
if (newy <= y) {
|
|
break;
|
|
}
|
|
if (fairlyClose(this.XforY(newy), that.XforY(newy))) {
|
|
y = newy;
|
|
}
|
|
}
|
|
break;
|
|
}
|
|
y += bump;
|
|
}
|
|
if (y > y0) {
|
|
if (y < y1) {
|
|
yrange[1] = y;
|
|
}
|
|
return 0;
|
|
}
|
|
}
|
|
//double ymin = y1 * 1E-14;
|
|
if (ymin <= 0) {
|
|
System.out.println("ymin = "+ymin);
|
|
}
|
|
/*
|
|
System.out.println("s range = "+s0+" to "+s1);
|
|
System.out.println("t range = "+t0+" to "+t1);
|
|
*/
|
|
while (s0 < s1 && t0 < t1) {
|
|
double sh = this.nextVertical(s0, s1);
|
|
double xsh = this.XforT(sh);
|
|
double ysh = this.YforT(sh);
|
|
double th = that.nextVertical(t0, t1);
|
|
double xth = that.XforT(th);
|
|
double yth = that.YforT(th);
|
|
/*
|
|
System.out.println("sh = "+sh);
|
|
System.out.println("th = "+th);
|
|
*/
|
|
try {
|
|
if (findIntersect(that, yrange, ymin, 0, 0,
|
|
s0, xs0, ys0, sh, xsh, ysh,
|
|
t0, xt0, yt0, th, xth, yth)) {
|
|
break;
|
|
}
|
|
} catch (Throwable t) {
|
|
System.err.println("Error: "+t);
|
|
System.err.println("y range was "+yrange[0]+"=>"+yrange[1]);
|
|
System.err.println("s y range is "+ys0+"=>"+ysh);
|
|
System.err.println("t y range is "+yt0+"=>"+yth);
|
|
System.err.println("ymin is "+ymin);
|
|
return 0;
|
|
}
|
|
if (ysh < yth) {
|
|
if (ysh > yrange[0]) {
|
|
if (ysh < yrange[1]) {
|
|
yrange[1] = ysh;
|
|
}
|
|
break;
|
|
}
|
|
s0 = sh;
|
|
xs0 = xsh;
|
|
ys0 = ysh;
|
|
} else {
|
|
if (yth > yrange[0]) {
|
|
if (yth < yrange[1]) {
|
|
yrange[1] = yth;
|
|
}
|
|
break;
|
|
}
|
|
t0 = th;
|
|
xt0 = xth;
|
|
yt0 = yth;
|
|
}
|
|
}
|
|
double ymid = (yrange[0] + yrange[1]) / 2;
|
|
/*
|
|
System.out.println("final this["+s0+", "+sh+", "+s1+"]");
|
|
System.out.println("final y["+ys0+", "+ysh+"]");
|
|
System.out.println("final that["+t0+", "+th+", "+t1+"]");
|
|
System.out.println("final y["+yt0+", "+yth+"]");
|
|
System.out.println("final order = "+orderof(this.XforY(ymid),
|
|
that.XforY(ymid)));
|
|
System.out.println("final range = "+yrange[0]+"=>"+yrange[1]);
|
|
*/
|
|
/*
|
|
System.out.println("final sx = "+this.XforY(ymid));
|
|
System.out.println("final tx = "+that.XforY(ymid));
|
|
System.out.println("final order = "+orderof(this.XforY(ymid),
|
|
that.XforY(ymid)));
|
|
*/
|
|
return orderof(this.XforY(ymid), that.XforY(ymid));
|
|
}
|
|
|
|
public static final double TMIN = 1E-3;
|
|
|
|
public boolean findIntersect(Curve that, double yrange[], double ymin,
|
|
int slevel, int tlevel,
|
|
double s0, double xs0, double ys0,
|
|
double s1, double xs1, double ys1,
|
|
double t0, double xt0, double yt0,
|
|
double t1, double xt1, double yt1)
|
|
{
|
|
/*
|
|
String pad = " ";
|
|
pad = pad+pad+pad+pad+pad;
|
|
pad = pad+pad;
|
|
System.out.println("----------------------------------------------");
|
|
System.out.println(pad.substring(0, slevel)+ys0);
|
|
System.out.println(pad.substring(0, slevel)+ys1);
|
|
System.out.println(pad.substring(0, slevel)+(s1-s0));
|
|
System.out.println("-------");
|
|
System.out.println(pad.substring(0, tlevel)+yt0);
|
|
System.out.println(pad.substring(0, tlevel)+yt1);
|
|
System.out.println(pad.substring(0, tlevel)+(t1-t0));
|
|
*/
|
|
if (ys0 > yt1 || yt0 > ys1) {
|
|
return false;
|
|
}
|
|
if (Math.min(xs0, xs1) > Math.max(xt0, xt1) ||
|
|
Math.max(xs0, xs1) < Math.min(xt0, xt1))
|
|
{
|
|
return false;
|
|
}
|
|
// Bounding boxes intersect - back off the larger of
|
|
// the two subcurves by half until they stop intersecting
|
|
// (or until they get small enough to switch to a more
|
|
// intensive algorithm).
|
|
if (s1 - s0 > TMIN) {
|
|
double s = (s0 + s1) / 2;
|
|
double xs = this.XforT(s);
|
|
double ys = this.YforT(s);
|
|
if (s == s0 || s == s1) {
|
|
System.out.println("s0 = "+s0);
|
|
System.out.println("s1 = "+s1);
|
|
throw new InternalError("no s progress!");
|
|
}
|
|
if (t1 - t0 > TMIN) {
|
|
double t = (t0 + t1) / 2;
|
|
double xt = that.XforT(t);
|
|
double yt = that.YforT(t);
|
|
if (t == t0 || t == t1) {
|
|
System.out.println("t0 = "+t0);
|
|
System.out.println("t1 = "+t1);
|
|
throw new InternalError("no t progress!");
|
|
}
|
|
if (ys >= yt0 && yt >= ys0) {
|
|
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
|
|
s0, xs0, ys0, s, xs, ys,
|
|
t0, xt0, yt0, t, xt, yt)) {
|
|
return true;
|
|
}
|
|
}
|
|
if (ys >= yt) {
|
|
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
|
|
s0, xs0, ys0, s, xs, ys,
|
|
t, xt, yt, t1, xt1, yt1)) {
|
|
return true;
|
|
}
|
|
}
|
|
if (yt >= ys) {
|
|
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
|
|
s, xs, ys, s1, xs1, ys1,
|
|
t0, xt0, yt0, t, xt, yt)) {
|
|
return true;
|
|
}
|
|
}
|
|
if (ys1 >= yt && yt1 >= ys) {
|
|
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
|
|
s, xs, ys, s1, xs1, ys1,
|
|
t, xt, yt, t1, xt1, yt1)) {
|
|
return true;
|
|
}
|
|
}
|
|
} else {
|
|
if (ys >= yt0) {
|
|
if (findIntersect(that, yrange, ymin, slevel+1, tlevel,
|
|
s0, xs0, ys0, s, xs, ys,
|
|
t0, xt0, yt0, t1, xt1, yt1)) {
|
|
return true;
|
|
}
|
|
}
|
|
if (yt1 >= ys) {
|
|
if (findIntersect(that, yrange, ymin, slevel+1, tlevel,
|
|
s, xs, ys, s1, xs1, ys1,
|
|
t0, xt0, yt0, t1, xt1, yt1)) {
|
|
return true;
|
|
}
|
|
}
|
|
}
|
|
} else if (t1 - t0 > TMIN) {
|
|
double t = (t0 + t1) / 2;
|
|
double xt = that.XforT(t);
|
|
double yt = that.YforT(t);
|
|
if (t == t0 || t == t1) {
|
|
System.out.println("t0 = "+t0);
|
|
System.out.println("t1 = "+t1);
|
|
throw new InternalError("no t progress!");
|
|
}
|
|
if (yt >= ys0) {
|
|
if (findIntersect(that, yrange, ymin, slevel, tlevel+1,
|
|
s0, xs0, ys0, s1, xs1, ys1,
|
|
t0, xt0, yt0, t, xt, yt)) {
|
|
return true;
|
|
}
|
|
}
|
|
if (ys1 >= yt) {
|
|
if (findIntersect(that, yrange, ymin, slevel, tlevel+1,
|
|
s0, xs0, ys0, s1, xs1, ys1,
|
|
t, xt, yt, t1, xt1, yt1)) {
|
|
return true;
|
|
}
|
|
}
|
|
} else {
|
|
// No more subdivisions
|
|
double xlk = xs1 - xs0;
|
|
double ylk = ys1 - ys0;
|
|
double xnm = xt1 - xt0;
|
|
double ynm = yt1 - yt0;
|
|
double xmk = xt0 - xs0;
|
|
double ymk = yt0 - ys0;
|
|
double det = xnm * ylk - ynm * xlk;
|
|
if (det != 0) {
|
|
double detinv = 1 / det;
|
|
double s = (xnm * ymk - ynm * xmk) * detinv;
|
|
double t = (xlk * ymk - ylk * xmk) * detinv;
|
|
if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
|
|
s = s0 + s * (s1 - s0);
|
|
t = t0 + t * (t1 - t0);
|
|
if (s < 0 || s > 1 || t < 0 || t > 1) {
|
|
System.out.println("Uh oh!");
|
|
}
|
|
double y = (this.YforT(s) + that.YforT(t)) / 2;
|
|
if (y <= yrange[1] && y > yrange[0]) {
|
|
yrange[1] = y;
|
|
return true;
|
|
}
|
|
}
|
|
}
|
|
//System.out.println("Testing lines!");
|
|
}
|
|
return false;
|
|
}
|
|
|
|
public double refineTforY(double t0, double yt0, double y0) {
|
|
double t1 = 1;
|
|
while (true) {
|
|
double th = (t0 + t1) / 2;
|
|
if (th == t0 || th == t1) {
|
|
return t1;
|
|
}
|
|
double y = YforT(th);
|
|
if (y < y0) {
|
|
t0 = th;
|
|
yt0 = y;
|
|
} else if (y > y0) {
|
|
t1 = th;
|
|
} else {
|
|
return t1;
|
|
}
|
|
}
|
|
}
|
|
|
|
public boolean fairlyClose(double v1, double v2) {
|
|
return (Math.abs(v1 - v2) <
|
|
Math.max(Math.abs(v1), Math.abs(v2)) * 1E-10);
|
|
}
|
|
|
|
public abstract int getSegment(double coords[]);
|
|
}
|