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/*
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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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2
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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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331 |
}
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332 |
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333 |
/**
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334 |
* The rectangle intersection test counts the number of times
|
|
|
335 |
* that the path crosses through the shadow that the rectangle
|
|
|
336 |
* projects to the right towards (x => +INFINITY).
|
|
|
337 |
*
|
|
|
338 |
* During processing of the path it actually counts every time
|
|
|
339 |
* the path crosses either or both of the top and bottom edges
|
|
|
340 |
* of that shadow. If the path enters from the top, the count
|
|
|
341 |
* is incremented. If it then exits back through the top, the
|
|
|
342 |
* same way it came in, the count is decremented and there is
|
|
|
343 |
* no impact on the winding count. If, instead, the path exits
|
|
|
344 |
* out the bottom, then the count is incremented again and a
|
|
|
345 |
* full pass through the shadow is indicated by the winding count
|
|
|
346 |
* having been incremented by 2.
|
|
|
347 |
*
|
|
|
348 |
* Thus, the winding count that it accumulates is actually double
|
|
|
349 |
* the real winding count. Since the path is continuous, the
|
|
|
350 |
* final answer should be a multiple of 2, otherwise there is a
|
|
|
351 |
* logic error somewhere.
|
|
|
352 |
*
|
|
|
353 |
* If the path ever has a direct hit on the rectangle, then a
|
|
|
354 |
* special value is returned. This special value terminates
|
|
|
355 |
* all ongoing accumulation on up through the call chain and
|
|
|
356 |
* ends up getting returned to the calling function which can
|
|
|
357 |
* then produce an answer directly. For intersection tests,
|
|
|
358 |
* the answer is always "true" if the path intersects the
|
|
|
359 |
* rectangle. For containment tests, the answer is always
|
|
|
360 |
* "false" if the path intersects the rectangle. Thus, no
|
|
|
361 |
* further processing is ever needed if an intersection occurs.
|
|
|
362 |
*/
|
|
|
363 |
public static final int RECT_INTERSECTS = 0x80000000;
|
|
|
364 |
|
|
|
365 |
/**
|
|
|
366 |
* Accumulate the number of times the path crosses the shadow
|
|
|
367 |
* extending to the right of the rectangle. See the comment
|
|
|
368 |
* for the RECT_INTERSECTS constant for more complete details.
|
|
|
369 |
* The return value is the sum of all crossings for both the
|
|
|
370 |
* top and bottom of the shadow for every segment in the path,
|
|
|
371 |
* or the special value RECT_INTERSECTS if the path ever enters
|
|
|
372 |
* the interior of the rectangle.
|
|
|
373 |
* The path must start with a SEG_MOVETO, otherwise an exception is
|
|
|
374 |
* thrown.
|
|
|
375 |
* The caller must check r[xy]{min,max} for NaN values.
|
|
|
376 |
*/
|
|
|
377 |
public static int rectCrossingsForPath(PathIterator pi,
|
|
|
378 |
double rxmin, double rymin,
|
|
|
379 |
double rxmax, double rymax)
|
|
|
380 |
{
|
|
|
381 |
if (rxmax <= rxmin || rymax <= rymin) {
|
|
|
382 |
return 0;
|
|
|
383 |
}
|
|
|
384 |
if (pi.isDone()) {
|
|
|
385 |
return 0;
|
|
|
386 |
}
|
|
|
387 |
double coords[] = new double[6];
|
|
|
388 |
if (pi.currentSegment(coords) != PathIterator.SEG_MOVETO) {
|
|
|
389 |
throw new IllegalPathStateException("missing initial moveto "+
|
|
|
390 |
"in path definition");
|
|
|
391 |
}
|
|
|
392 |
pi.next();
|
|
|
393 |
double curx, cury, movx, movy, endx, endy;
|
|
|
394 |
curx = movx = coords[0];
|
|
|
395 |
cury = movy = coords[1];
|
|
|
396 |
int crossings = 0;
|
|
|
397 |
while (crossings != RECT_INTERSECTS && !pi.isDone()) {
|
|
|
398 |
switch (pi.currentSegment(coords)) {
|
|
|
399 |
case PathIterator.SEG_MOVETO:
|
|
|
400 |
if (curx != movx || cury != movy) {
|
|
|
401 |
crossings = rectCrossingsForLine(crossings,
|
|
|
402 |
rxmin, rymin,
|
|
|
403 |
rxmax, rymax,
|
|
|
404 |
curx, cury,
|
|
|
405 |
movx, movy);
|
|
|
406 |
}
|
|
|
407 |
// Count should always be a multiple of 2 here.
|
|
|
408 |
// assert((crossings & 1) != 0);
|
|
|
409 |
movx = curx = coords[0];
|
|
|
410 |
movy = cury = coords[1];
|
|
|
411 |
break;
|
|
|
412 |
case PathIterator.SEG_LINETO:
|
|
|
413 |
endx = coords[0];
|
|
|
414 |
endy = coords[1];
|
|
|
415 |
crossings = rectCrossingsForLine(crossings,
|
|
|
416 |
rxmin, rymin,
|
|
|
417 |
rxmax, rymax,
|
|
|
418 |
curx, cury,
|
|
|
419 |
endx, endy);
|
|
|
420 |
curx = endx;
|
|
|
421 |
cury = endy;
|
|
|
422 |
break;
|
|
|
423 |
case PathIterator.SEG_QUADTO:
|
|
|
424 |
endx = coords[2];
|
|
|
425 |
endy = coords[3];
|
|
|
426 |
crossings = rectCrossingsForQuad(crossings,
|
|
|
427 |
rxmin, rymin,
|
|
|
428 |
rxmax, rymax,
|
|
|
429 |
curx, cury,
|
|
|
430 |
coords[0], coords[1],
|
|
|
431 |
endx, endy, 0);
|
|
|
432 |
curx = endx;
|
|
|
433 |
cury = endy;
|
|
|
434 |
break;
|
|
|
435 |
case PathIterator.SEG_CUBICTO:
|
|
|
436 |
endx = coords[4];
|
|
|
437 |
endy = coords[5];
|
|
|
438 |
crossings = rectCrossingsForCubic(crossings,
|
|
|
439 |
rxmin, rymin,
|
|
|
440 |
rxmax, rymax,
|
|
|
441 |
curx, cury,
|
|
|
442 |
coords[0], coords[1],
|
|
|
443 |
coords[2], coords[3],
|
|
|
444 |
endx, endy, 0);
|
|
|
445 |
curx = endx;
|
|
|
446 |
cury = endy;
|
|
|
447 |
break;
|
|
|
448 |
case PathIterator.SEG_CLOSE:
|
|
|
449 |
if (curx != movx || cury != movy) {
|
|
|
450 |
crossings = rectCrossingsForLine(crossings,
|
|
|
451 |
rxmin, rymin,
|
|
|
452 |
rxmax, rymax,
|
|
|
453 |
curx, cury,
|
|
|
454 |
movx, movy);
|
|
|
455 |
}
|
|
|
456 |
curx = movx;
|
|
|
457 |
cury = movy;
|
|
|
458 |
// Count should always be a multiple of 2 here.
|
|
|
459 |
// assert((crossings & 1) != 0);
|
|
|
460 |
break;
|
|
|
461 |
}
|
|
|
462 |
pi.next();
|
|
|
463 |
}
|
|
|
464 |
if (crossings != RECT_INTERSECTS && (curx != movx || cury != movy)) {
|
|
|
465 |
crossings = rectCrossingsForLine(crossings,
|
|
|
466 |
rxmin, rymin,
|
|
|
467 |
rxmax, rymax,
|
|
|
468 |
curx, cury,
|
|
|
469 |
movx, movy);
|
|
|
470 |
}
|
|
|
471 |
// Count should always be a multiple of 2 here.
|
|
|
472 |
// assert((crossings & 1) != 0);
|
|
|
473 |
return crossings;
|
|
|
474 |
}
|
|
|
475 |
|
|
|
476 |
/**
|
|
|
477 |
* Accumulate the number of times the line crosses the shadow
|
|
|
478 |
* extending to the right of the rectangle. See the comment
|
|
|
479 |
* for the RECT_INTERSECTS constant for more complete details.
|
|
|
480 |
*/
|
|
|
481 |
public static int rectCrossingsForLine(int crossings,
|
|
|
482 |
double rxmin, double rymin,
|
|
|
483 |
double rxmax, double rymax,
|
|
|
484 |
double x0, double y0,
|
|
|
485 |
double x1, double y1)
|
|
|
486 |
{
|
|
|
487 |
if (y0 >= rymax && y1 >= rymax) return crossings;
|
|
|
488 |
if (y0 <= rymin && y1 <= rymin) return crossings;
|
|
|
489 |
if (x0 <= rxmin && x1 <= rxmin) return crossings;
|
|
|
490 |
if (x0 >= rxmax && x1 >= rxmax) {
|
|
|
491 |
// Line is entirely to the right of the rect
|
|
|
492 |
// and the vertical ranges of the two overlap by a non-empty amount
|
|
|
493 |
// Thus, this line segment is partially in the "right-shadow"
|
|
|
494 |
// Path may have done a complete crossing
|
|
|
495 |
// Or path may have entered or exited the right-shadow
|
|
|
496 |
if (y0 < y1) {
|
|
|
497 |
// y-increasing line segment...
|
|
|
498 |
// We know that y0 < rymax and y1 > rymin
|
|
|
499 |
if (y0 <= rymin) crossings++;
|
|
|
500 |
if (y1 >= rymax) crossings++;
|
|
|
501 |
} else if (y1 < y0) {
|
|
|
502 |
// y-decreasing line segment...
|
|
|
503 |
// We know that y1 < rymax and y0 > rymin
|
|
|
504 |
if (y1 <= rymin) crossings--;
|
|
|
505 |
if (y0 >= rymax) crossings--;
|
|
|
506 |
}
|
|
|
507 |
return crossings;
|
|
|
508 |
}
|
|
|
509 |
// Remaining case:
|
|
|
510 |
// Both x and y ranges overlap by a non-empty amount
|
|
|
511 |
// First do trivial INTERSECTS rejection of the cases
|
|
|
512 |
// where one of the endpoints is inside the rectangle.
|
|
|
513 |
if ((x0 > rxmin && x0 < rxmax && y0 > rymin && y0 < rymax) ||
|
|
|
514 |
(x1 > rxmin && x1 < rxmax && y1 > rymin && y1 < rymax))
|
|
|
515 |
{
|
|
|
516 |
return RECT_INTERSECTS;
|
|
|
517 |
}
|
|
|
518 |
// Otherwise calculate the y intercepts and see where
|
|
|
519 |
// they fall with respect to the rectangle
|
|
|
520 |
double xi0 = x0;
|
|
|
521 |
if (y0 < rymin) {
|
|
|
522 |
xi0 += ((rymin - y0) * (x1 - x0) / (y1 - y0));
|
|
|
523 |
} else if (y0 > rymax) {
|
|
|
524 |
xi0 += ((rymax - y0) * (x1 - x0) / (y1 - y0));
|
|
|
525 |
}
|
|
|
526 |
double xi1 = x1;
|
|
|
527 |
if (y1 < rymin) {
|
|
|
528 |
xi1 += ((rymin - y1) * (x0 - x1) / (y0 - y1));
|
|
|
529 |
} else if (y1 > rymax) {
|
|
|
530 |
xi1 += ((rymax - y1) * (x0 - x1) / (y0 - y1));
|
|
|
531 |
}
|
|
|
532 |
if (xi0 <= rxmin && xi1 <= rxmin) return crossings;
|
|
|
533 |
if (xi0 >= rxmax && xi1 >= rxmax) {
|
|
|
534 |
if (y0 < y1) {
|
|
|
535 |
// y-increasing line segment...
|
|
|
536 |
// We know that y0 < rymax and y1 > rymin
|
|
|
537 |
if (y0 <= rymin) crossings++;
|
|
|
538 |
if (y1 >= rymax) crossings++;
|
|
|
539 |
} else if (y1 < y0) {
|
|
|
540 |
// y-decreasing line segment...
|
|
|
541 |
// We know that y1 < rymax and y0 > rymin
|
|
|
542 |
if (y1 <= rymin) crossings--;
|
|
|
543 |
if (y0 >= rymax) crossings--;
|
|
|
544 |
}
|
|
|
545 |
return crossings;
|
|
|
546 |
}
|
|
|
547 |
return RECT_INTERSECTS;
|
|
|
548 |
}
|
|
|
549 |
|
|
|
550 |
/**
|
|
|
551 |
* Accumulate the number of times the quad crosses the shadow
|
|
|
552 |
* extending to the right of the rectangle. See the comment
|
|
|
553 |
* for the RECT_INTERSECTS constant for more complete details.
|
|
|
554 |
*/
|
|
|
555 |
public static int rectCrossingsForQuad(int crossings,
|
|
|
556 |
double rxmin, double rymin,
|
|
|
557 |
double rxmax, double rymax,
|
|
|
558 |
double x0, double y0,
|
|
|
559 |
double xc, double yc,
|
|
|
560 |
double x1, double y1,
|
|
|
561 |
int level)
|
|
|
562 |
{
|
|
|
563 |
if (y0 >= rymax && yc >= rymax && y1 >= rymax) return crossings;
|
|
|
564 |
if (y0 <= rymin && yc <= rymin && y1 <= rymin) return crossings;
|
|
|
565 |
if (x0 <= rxmin && xc <= rxmin && x1 <= rxmin) return crossings;
|
|
|
566 |
if (x0 >= rxmax && xc >= rxmax && x1 >= rxmax) {
|
|
|
567 |
// Quad is entirely to the right of the rect
|
|
|
568 |
// and the vertical range of the 3 Y coordinates of the quad
|
|
|
569 |
// overlaps the vertical range of the rect by a non-empty amount
|
|
|
570 |
// We now judge the crossings solely based on the line segment
|
|
|
571 |
// connecting the endpoints of the quad.
|
|
|
572 |
// Note that we may have 0, 1, or 2 crossings as the control
|
|
|
573 |
// point may be causing the Y range intersection while the
|
|
|
574 |
// two endpoints are entirely above or below.
|
|
|
575 |
if (y0 < y1) {
|
|
|
576 |
// y-increasing line segment...
|
|
|
577 |
if (y0 <= rymin && y1 > rymin) crossings++;
|
|
|
578 |
if (y0 < rymax && y1 >= rymax) crossings++;
|
|
|
579 |
} else if (y1 < y0) {
|
|
|
580 |
// y-decreasing line segment...
|
|
|
581 |
if (y1 <= rymin && y0 > rymin) crossings--;
|
|
|
582 |
if (y1 < rymax && y0 >= rymax) crossings--;
|
|
|
583 |
}
|
|
|
584 |
return crossings;
|
|
|
585 |
}
|
|
|
586 |
// The intersection of ranges is more complicated
|
|
|
587 |
// First do trivial INTERSECTS rejection of the cases
|
|
|
588 |
// where one of the endpoints is inside the rectangle.
|
|
|
589 |
if ((x0 < rxmax && x0 > rxmin && y0 < rymax && y0 > rymin) ||
|
|
|
590 |
(x1 < rxmax && x1 > rxmin && y1 < rymax && y1 > rymin))
|
|
|
591 |
{
|
|
|
592 |
return RECT_INTERSECTS;
|
|
|
593 |
}
|
|
|
594 |
// Otherwise, subdivide and look for one of the cases above.
|
|
|
595 |
// double precision only has 52 bits of mantissa
|
|
|
596 |
if (level > 52) {
|
|
|
597 |
return rectCrossingsForLine(crossings,
|
|
|
598 |
rxmin, rymin, rxmax, rymax,
|
|
|
599 |
x0, y0, x1, y1);
|
|
|
600 |
}
|
|
|
601 |
double x0c = (x0 + xc) / 2;
|
|
|
602 |
double y0c = (y0 + yc) / 2;
|
|
|
603 |
double xc1 = (xc + x1) / 2;
|
|
|
604 |
double yc1 = (yc + y1) / 2;
|
|
|
605 |
xc = (x0c + xc1) / 2;
|
|
|
606 |
yc = (y0c + yc1) / 2;
|
|
|
607 |
if (Double.isNaN(xc) || Double.isNaN(yc)) {
|
|
|
608 |
// [xy]c are NaN if any of [xy]0c or [xy]c1 are NaN
|
|
|
609 |
// [xy]0c or [xy]c1 are NaN if any of [xy][0c1] are NaN
|
|
|
610 |
// These values are also NaN if opposing infinities are added
|
|
|
611 |
return 0;
|
|
|
612 |
}
|
|
|
613 |
crossings = rectCrossingsForQuad(crossings,
|
|
|
614 |
rxmin, rymin, rxmax, rymax,
|
|
|
615 |
x0, y0, x0c, y0c, xc, yc,
|
|
|
616 |
level+1);
|
|
|
617 |
if (crossings != RECT_INTERSECTS) {
|
|
|
618 |
crossings = rectCrossingsForQuad(crossings,
|
|
|
619 |
rxmin, rymin, rxmax, rymax,
|
|
|
620 |
xc, yc, xc1, yc1, x1, y1,
|
|
|
621 |
level+1);
|
|
|
622 |
}
|
|
|
623 |
return crossings;
|
|
|
624 |
}
|
|
|
625 |
|
|
|
626 |
/**
|
|
|
627 |
* Accumulate the number of times the cubic crosses the shadow
|
|
|
628 |
* extending to the right of the rectangle. See the comment
|
|
|
629 |
* for the RECT_INTERSECTS constant for more complete details.
|
|
|
630 |
*/
|
|
|
631 |
public static int rectCrossingsForCubic(int crossings,
|
|
|
632 |
double rxmin, double rymin,
|
|
|
633 |
double rxmax, double rymax,
|
|
|
634 |
double x0, double y0,
|
|
|
635 |
double xc0, double yc0,
|
|
|
636 |
double xc1, double yc1,
|
|
|
637 |
double x1, double y1,
|
|
|
638 |
int level)
|
|
|
639 |
{
|
|
|
640 |
if (y0 >= rymax && yc0 >= rymax && yc1 >= rymax && y1 >= rymax) {
|
|
|
641 |
return crossings;
|
|
|
642 |
}
|
|
|
643 |
if (y0 <= rymin && yc0 <= rymin && yc1 <= rymin && y1 <= rymin) {
|
|
|
644 |
return crossings;
|
|
|
645 |
}
|
|
|
646 |
if (x0 <= rxmin && xc0 <= rxmin && xc1 <= rxmin && x1 <= rxmin) {
|
|
|
647 |
return crossings;
|
|
|
648 |
}
|
|
|
649 |
if (x0 >= rxmax && xc0 >= rxmax && xc1 >= rxmax && x1 >= rxmax) {
|
|
|
650 |
// Cubic is entirely to the right of the rect
|
|
|
651 |
// and the vertical range of the 4 Y coordinates of the cubic
|
|
|
652 |
// overlaps the vertical range of the rect by a non-empty amount
|
|
|
653 |
// We now judge the crossings solely based on the line segment
|
|
|
654 |
// connecting the endpoints of the cubic.
|
|
|
655 |
// Note that we may have 0, 1, or 2 crossings as the control
|
|
|
656 |
// points may be causing the Y range intersection while the
|
|
|
657 |
// two endpoints are entirely above or below.
|
|
|
658 |
if (y0 < y1) {
|
|
|
659 |
// y-increasing line segment...
|
|
|
660 |
if (y0 <= rymin && y1 > rymin) crossings++;
|
|
|
661 |
if (y0 < rymax && y1 >= rymax) crossings++;
|
|
|
662 |
} else if (y1 < y0) {
|
|
|
663 |
// y-decreasing line segment...
|
|
|
664 |
if (y1 <= rymin && y0 > rymin) crossings--;
|
|
|
665 |
if (y1 < rymax && y0 >= rymax) crossings--;
|
|
|
666 |
}
|
|
|
667 |
return crossings;
|
|
|
668 |
}
|
|
|
669 |
// The intersection of ranges is more complicated
|
|
|
670 |
// First do trivial INTERSECTS rejection of the cases
|
|
|
671 |
// where one of the endpoints is inside the rectangle.
|
|
|
672 |
if ((x0 > rxmin && x0 < rxmax && y0 > rymin && y0 < rymax) ||
|
|
|
673 |
(x1 > rxmin && x1 < rxmax && y1 > rymin && y1 < rymax))
|
|
|
674 |
{
|
|
|
675 |
return RECT_INTERSECTS;
|
|
|
676 |
}
|
|
|
677 |
// Otherwise, subdivide and look for one of the cases above.
|
|
|
678 |
// double precision only has 52 bits of mantissa
|
|
|
679 |
if (level > 52) {
|
|
|
680 |
return rectCrossingsForLine(crossings,
|
|
|
681 |
rxmin, rymin, rxmax, rymax,
|
|
|
682 |
x0, y0, x1, y1);
|
|
|
683 |
}
|
|
|
684 |
double xmid = (xc0 + xc1) / 2;
|
|
|
685 |
double ymid = (yc0 + yc1) / 2;
|
|
|
686 |
xc0 = (x0 + xc0) / 2;
|
|
|
687 |
yc0 = (y0 + yc0) / 2;
|
|
|
688 |
xc1 = (xc1 + x1) / 2;
|
|
|
689 |
yc1 = (yc1 + y1) / 2;
|
|
|
690 |
double xc0m = (xc0 + xmid) / 2;
|
|
|
691 |
double yc0m = (yc0 + ymid) / 2;
|
|
|
692 |
double xmc1 = (xmid + xc1) / 2;
|
|
|
693 |
double ymc1 = (ymid + yc1) / 2;
|
|
|
694 |
xmid = (xc0m + xmc1) / 2;
|
|
|
695 |
ymid = (yc0m + ymc1) / 2;
|
|
|
696 |
if (Double.isNaN(xmid) || Double.isNaN(ymid)) {
|
|
|
697 |
// [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN
|
|
|
698 |
// [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN
|
|
|
699 |
// These values are also NaN if opposing infinities are added
|
|
|
700 |
return 0;
|
|
|
701 |
}
|
|
|
702 |
crossings = rectCrossingsForCubic(crossings,
|
|
|
703 |
rxmin, rymin, rxmax, rymax,
|
|
|
704 |
x0, y0, xc0, yc0,
|
|
|
705 |
xc0m, yc0m, xmid, ymid, level+1);
|
|
|
706 |
if (crossings != RECT_INTERSECTS) {
|
|
|
707 |
crossings = rectCrossingsForCubic(crossings,
|
|
|
708 |
rxmin, rymin, rxmax, rymax,
|
|
|
709 |
xmid, ymid, xmc1, ymc1,
|
|
|
710 |
xc1, yc1, x1, y1, level+1);
|
|
|
711 |
}
|
|
|
712 |
return crossings;
|
|
|
713 |
}
|
|
|
714 |
|
|
|
715 |
public Curve(int direction) {
|
|
|
716 |
this.direction = direction;
|
|
|
717 |
}
|
|
|
718 |
|
|
|
719 |
public final int getDirection() {
|
|
|
720 |
return direction;
|
|
|
721 |
}
|
|
|
722 |
|
|
|
723 |
public final Curve getWithDirection(int direction) {
|
|
|
724 |
return (this.direction == direction ? this : getReversedCurve());
|
|
|
725 |
}
|
|
|
726 |
|
|
|
727 |
public static double round(double v) {
|
|
|
728 |
//return Math.rint(v*10)/10;
|
|
|
729 |
return v;
|
|
|
730 |
}
|
|
|
731 |
|
|
|
732 |
public static int orderof(double x1, double x2) {
|
|
|
733 |
if (x1 < x2) {
|
|
|
734 |
return -1;
|
|
|
735 |
}
|
|
|
736 |
if (x1 > x2) {
|
|
|
737 |
return 1;
|
|
|
738 |
}
|
|
|
739 |
return 0;
|
|
|
740 |
}
|
|
|
741 |
|
|
|
742 |
public static long signeddiffbits(double y1, double y2) {
|
|
|
743 |
return (Double.doubleToLongBits(y1) - Double.doubleToLongBits(y2));
|
|
|
744 |
}
|
|
|
745 |
public static long diffbits(double y1, double y2) {
|
|
|
746 |
return Math.abs(Double.doubleToLongBits(y1) -
|
|
|
747 |
Double.doubleToLongBits(y2));
|
|
|
748 |
}
|
|
|
749 |
public static double prev(double v) {
|
|
|
750 |
return Double.longBitsToDouble(Double.doubleToLongBits(v)-1);
|
|
|
751 |
}
|
|
|
752 |
public static double next(double v) {
|
|
|
753 |
return Double.longBitsToDouble(Double.doubleToLongBits(v)+1);
|
|
|
754 |
}
|
|
|
755 |
|
|
|
756 |
public String toString() {
|
|
|
757 |
return ("Curve["+
|
|
|
758 |
getOrder()+", "+
|
|
|
759 |
("("+round(getX0())+", "+round(getY0())+"), ")+
|
|
|
760 |
controlPointString()+
|
|
|
761 |
("("+round(getX1())+", "+round(getY1())+"), ")+
|
|
|
762 |
(direction == INCREASING ? "D" : "U")+
|
|
|
763 |
"]");
|
|
|
764 |
}
|
|
|
765 |
|
|
|
766 |
public String controlPointString() {
|
|
|
767 |
return "";
|
|
|
768 |
}
|
|
|
769 |
|
|
|
770 |
public abstract int getOrder();
|
|
|
771 |
|
|
|
772 |
public abstract double getXTop();
|
|
|
773 |
public abstract double getYTop();
|
|
|
774 |
public abstract double getXBot();
|
|
|
775 |
public abstract double getYBot();
|
|
|
776 |
|
|
|
777 |
public abstract double getXMin();
|
|
|
778 |
public abstract double getXMax();
|
|
|
779 |
|
|
|
780 |
public abstract double getX0();
|
|
|
781 |
public abstract double getY0();
|
|
|
782 |
public abstract double getX1();
|
|
|
783 |
public abstract double getY1();
|
|
|
784 |
|
|
|
785 |
public abstract double XforY(double y);
|
|
|
786 |
public abstract double TforY(double y);
|
|
|
787 |
public abstract double XforT(double t);
|
|
|
788 |
public abstract double YforT(double t);
|
|
|
789 |
public abstract double dXforT(double t, int deriv);
|
|
|
790 |
public abstract double dYforT(double t, int deriv);
|
|
|
791 |
|
|
|
792 |
public abstract double nextVertical(double t0, double t1);
|
|
|
793 |
|
|
|
794 |
public int crossingsFor(double x, double y) {
|
|
|
795 |
if (y >= getYTop() && y < getYBot()) {
|
|
|
796 |
if (x < getXMax() && (x < getXMin() || x < XforY(y))) {
|
|
|
797 |
return 1;
|
|
|
798 |
}
|
|
|
799 |
}
|
|
|
800 |
return 0;
|
|
|
801 |
}
|
|
|
802 |
|
|
|
803 |
public boolean accumulateCrossings(Crossings c) {
|
|
|
804 |
double xhi = c.getXHi();
|
|
|
805 |
if (getXMin() >= xhi) {
|
|
|
806 |
return false;
|
|
|
807 |
}
|
|
|
808 |
double xlo = c.getXLo();
|
|
|
809 |
double ylo = c.getYLo();
|
|
|
810 |
double yhi = c.getYHi();
|
|
|
811 |
double y0 = getYTop();
|
|
|
812 |
double y1 = getYBot();
|
|
|
813 |
double tstart, ystart, tend, yend;
|
|
|
814 |
if (y0 < ylo) {
|
|
|
815 |
if (y1 <= ylo) {
|
|
|
816 |
return false;
|
|
|
817 |
}
|
|
|
818 |
ystart = ylo;
|
|
|
819 |
tstart = TforY(ylo);
|
|
|
820 |
} else {
|
|
|
821 |
if (y0 >= yhi) {
|
|
|
822 |
return false;
|
|
|
823 |
}
|
|
|
824 |
ystart = y0;
|
|
|
825 |
tstart = 0;
|
|
|
826 |
}
|
|
|
827 |
if (y1 > yhi) {
|
|
|
828 |
yend = yhi;
|
|
|
829 |
tend = TforY(yhi);
|
|
|
830 |
} else {
|
|
|
831 |
yend = y1;
|
|
|
832 |
tend = 1;
|
|
|
833 |
}
|
|
|
834 |
boolean hitLo = false;
|
|
|
835 |
boolean hitHi = false;
|
|
|
836 |
while (true) {
|
|
|
837 |
double x = XforT(tstart);
|
|
|
838 |
if (x < xhi) {
|
|
|
839 |
if (hitHi || x > xlo) {
|
|
|
840 |
return true;
|
|
|
841 |
}
|
|
|
842 |
hitLo = true;
|
|
|
843 |
} else {
|
|
|
844 |
if (hitLo) {
|
|
|
845 |
return true;
|
|
|
846 |
}
|
|
|
847 |
hitHi = true;
|
|
|
848 |
}
|
|
|
849 |
if (tstart >= tend) {
|
|
|
850 |
break;
|
|
|
851 |
}
|
|
|
852 |
tstart = nextVertical(tstart, tend);
|
|
|
853 |
}
|
|
|
854 |
if (hitLo) {
|
|
|
855 |
c.record(ystart, yend, direction);
|
|
|
856 |
}
|
|
|
857 |
return false;
|
|
|
858 |
}
|
|
|
859 |
|
|
|
860 |
public abstract void enlarge(Rectangle2D r);
|
|
|
861 |
|
|
|
862 |
public Curve getSubCurve(double ystart, double yend) {
|
|
|
863 |
return getSubCurve(ystart, yend, direction);
|
|
|
864 |
}
|
|
|
865 |
|
|
|
866 |
public abstract Curve getReversedCurve();
|
|
|
867 |
public abstract Curve getSubCurve(double ystart, double yend, int dir);
|
|
|
868 |
|
|
|
869 |
public int compareTo(Curve that, double yrange[]) {
|
|
|
870 |
/*
|
|
|
871 |
System.out.println(this+".compareTo("+that+")");
|
|
|
872 |
System.out.println("target range = "+yrange[0]+"=>"+yrange[1]);
|
|
|
873 |
*/
|
|
|
874 |
double y0 = yrange[0];
|
|
|
875 |
double y1 = yrange[1];
|
|
|
876 |
y1 = Math.min(Math.min(y1, this.getYBot()), that.getYBot());
|
|
|
877 |
if (y1 <= yrange[0]) {
|
|
|
878 |
System.err.println("this == "+this);
|
|
|
879 |
System.err.println("that == "+that);
|
|
|
880 |
System.out.println("target range = "+yrange[0]+"=>"+yrange[1]);
|
|
|
881 |
throw new InternalError("backstepping from "+yrange[0]+" to "+y1);
|
|
|
882 |
}
|
|
|
883 |
yrange[1] = y1;
|
|
|
884 |
if (this.getXMax() <= that.getXMin()) {
|
|
|
885 |
if (this.getXMin() == that.getXMax()) {
|
|
|
886 |
return 0;
|
|
|
887 |
}
|
|
|
888 |
return -1;
|
|
|
889 |
}
|
|
|
890 |
if (this.getXMin() >= that.getXMax()) {
|
|
|
891 |
return 1;
|
|
|
892 |
}
|
|
|
893 |
// Parameter s for thi(s) curve and t for tha(t) curve
|
|
|
894 |
// [st]0 = parameters for top of current section of interest
|
|
|
895 |
// [st]1 = parameters for bottom of valid range
|
|
|
896 |
// [st]h = parameters for hypothesis point
|
|
|
897 |
// [d][xy]s = valuations of thi(s) curve at sh
|
|
|
898 |
// [d][xy]t = valuations of tha(t) curve at th
|
|
|
899 |
double s0 = this.TforY(y0);
|
|
|
900 |
double ys0 = this.YforT(s0);
|
|
|
901 |
if (ys0 < y0) {
|
|
|
902 |
s0 = refineTforY(s0, ys0, y0);
|
|
|
903 |
ys0 = this.YforT(s0);
|
|
|
904 |
}
|
|
|
905 |
double s1 = this.TforY(y1);
|
|
|
906 |
if (this.YforT(s1) < y0) {
|
|
|
907 |
s1 = refineTforY(s1, this.YforT(s1), y0);
|
|
|
908 |
//System.out.println("s1 problem!");
|
|
|
909 |
}
|
|
|
910 |
double t0 = that.TforY(y0);
|
|
|
911 |
double yt0 = that.YforT(t0);
|
|
|
912 |
if (yt0 < y0) {
|
|
|
913 |
t0 = that.refineTforY(t0, yt0, y0);
|
|
|
914 |
yt0 = that.YforT(t0);
|
|
|
915 |
}
|
|
|
916 |
double t1 = that.TforY(y1);
|
|
|
917 |
if (that.YforT(t1) < y0) {
|
|
|
918 |
t1 = that.refineTforY(t1, that.YforT(t1), y0);
|
|
|
919 |
//System.out.println("t1 problem!");
|
|
|
920 |
}
|
|
|
921 |
double xs0 = this.XforT(s0);
|
|
|
922 |
double xt0 = that.XforT(t0);
|
|
|
923 |
double scale = Math.max(Math.abs(y0), Math.abs(y1));
|
|
|
924 |
double ymin = Math.max(scale * 1E-14, 1E-300);
|
|
|
925 |
if (fairlyClose(xs0, xt0)) {
|
|
|
926 |
double bump = ymin;
|
|
|
927 |
double maxbump = Math.min(ymin * 1E13, (y1 - y0) * .1);
|
|
|
928 |
double y = y0 + bump;
|
|
|
929 |
while (y <= y1) {
|
|
|
930 |
if (fairlyClose(this.XforY(y), that.XforY(y))) {
|
|
|
931 |
if ((bump *= 2) > maxbump) {
|
|
|
932 |
bump = maxbump;
|
|
|
933 |
}
|
|
|
934 |
} else {
|
|
|
935 |
y -= bump;
|
|
|
936 |
while (true) {
|
|
|
937 |
bump /= 2;
|
|
|
938 |
double newy = y + bump;
|
|
|
939 |
if (newy <= y) {
|
|
|
940 |
break;
|
|
|
941 |
}
|
|
|
942 |
if (fairlyClose(this.XforY(newy), that.XforY(newy))) {
|
|
|
943 |
y = newy;
|
|
|
944 |
}
|
|
|
945 |
}
|
|
|
946 |
break;
|
|
|
947 |
}
|
|
|
948 |
y += bump;
|
|
|
949 |
}
|
|
|
950 |
if (y > y0) {
|
|
|
951 |
if (y < y1) {
|
|
|
952 |
yrange[1] = y;
|
|
|
953 |
}
|
|
|
954 |
return 0;
|
|
|
955 |
}
|
|
|
956 |
}
|
|
|
957 |
//double ymin = y1 * 1E-14;
|
|
|
958 |
if (ymin <= 0) {
|
|
|
959 |
System.out.println("ymin = "+ymin);
|
|
|
960 |
}
|
|
|
961 |
/*
|
|
|
962 |
System.out.println("s range = "+s0+" to "+s1);
|
|
|
963 |
System.out.println("t range = "+t0+" to "+t1);
|
|
|
964 |
*/
|
|
|
965 |
while (s0 < s1 && t0 < t1) {
|
|
|
966 |
double sh = this.nextVertical(s0, s1);
|
|
|
967 |
double xsh = this.XforT(sh);
|
|
|
968 |
double ysh = this.YforT(sh);
|
|
|
969 |
double th = that.nextVertical(t0, t1);
|
|
|
970 |
double xth = that.XforT(th);
|
|
|
971 |
double yth = that.YforT(th);
|
|
|
972 |
/*
|
|
|
973 |
System.out.println("sh = "+sh);
|
|
|
974 |
System.out.println("th = "+th);
|
|
|
975 |
*/
|
|
|
976 |
try {
|
|
|
977 |
if (findIntersect(that, yrange, ymin, 0, 0,
|
|
|
978 |
s0, xs0, ys0, sh, xsh, ysh,
|
|
|
979 |
t0, xt0, yt0, th, xth, yth)) {
|
|
|
980 |
break;
|
|
|
981 |
}
|
|
|
982 |
} catch (Throwable t) {
|
|
|
983 |
System.err.println("Error: "+t);
|
|
|
984 |
System.err.println("y range was "+yrange[0]+"=>"+yrange[1]);
|
|
|
985 |
System.err.println("s y range is "+ys0+"=>"+ysh);
|
|
|
986 |
System.err.println("t y range is "+yt0+"=>"+yth);
|
|
|
987 |
System.err.println("ymin is "+ymin);
|
|
|
988 |
return 0;
|
|
|
989 |
}
|
|
|
990 |
if (ysh < yth) {
|
|
|
991 |
if (ysh > yrange[0]) {
|
|
|
992 |
if (ysh < yrange[1]) {
|
|
|
993 |
yrange[1] = ysh;
|
|
|
994 |
}
|
|
|
995 |
break;
|
|
|
996 |
}
|
|
|
997 |
s0 = sh;
|
|
|
998 |
xs0 = xsh;
|
|
|
999 |
ys0 = ysh;
|
|
|
1000 |
} else {
|
|
|
1001 |
if (yth > yrange[0]) {
|
|
|
1002 |
if (yth < yrange[1]) {
|
|
|
1003 |
yrange[1] = yth;
|
|
|
1004 |
}
|
|
|
1005 |
break;
|
|
|
1006 |
}
|
|
|
1007 |
t0 = th;
|
|
|
1008 |
xt0 = xth;
|
|
|
1009 |
yt0 = yth;
|
|
|
1010 |
}
|
|
|
1011 |
}
|
|
|
1012 |
double ymid = (yrange[0] + yrange[1]) / 2;
|
|
|
1013 |
/*
|
|
|
1014 |
System.out.println("final this["+s0+", "+sh+", "+s1+"]");
|
|
|
1015 |
System.out.println("final y["+ys0+", "+ysh+"]");
|
|
|
1016 |
System.out.println("final that["+t0+", "+th+", "+t1+"]");
|
|
|
1017 |
System.out.println("final y["+yt0+", "+yth+"]");
|
|
|
1018 |
System.out.println("final order = "+orderof(this.XforY(ymid),
|
|
|
1019 |
that.XforY(ymid)));
|
|
|
1020 |
System.out.println("final range = "+yrange[0]+"=>"+yrange[1]);
|
|
|
1021 |
*/
|
|
|
1022 |
/*
|
|
|
1023 |
System.out.println("final sx = "+this.XforY(ymid));
|
|
|
1024 |
System.out.println("final tx = "+that.XforY(ymid));
|
|
|
1025 |
System.out.println("final order = "+orderof(this.XforY(ymid),
|
|
|
1026 |
that.XforY(ymid)));
|
|
|
1027 |
*/
|
|
|
1028 |
return orderof(this.XforY(ymid), that.XforY(ymid));
|
|
|
1029 |
}
|
|
|
1030 |
|
|
|
1031 |
public static final double TMIN = 1E-3;
|
|
|
1032 |
|
|
|
1033 |
public boolean findIntersect(Curve that, double yrange[], double ymin,
|
|
|
1034 |
int slevel, int tlevel,
|
|
|
1035 |
double s0, double xs0, double ys0,
|
|
|
1036 |
double s1, double xs1, double ys1,
|
|
|
1037 |
double t0, double xt0, double yt0,
|
|
|
1038 |
double t1, double xt1, double yt1)
|
|
|
1039 |
{
|
|
|
1040 |
/*
|
|
|
1041 |
String pad = " ";
|
|
|
1042 |
pad = pad+pad+pad+pad+pad;
|
|
|
1043 |
pad = pad+pad;
|
|
|
1044 |
System.out.println("----------------------------------------------");
|
|
|
1045 |
System.out.println(pad.substring(0, slevel)+ys0);
|
|
|
1046 |
System.out.println(pad.substring(0, slevel)+ys1);
|
|
|
1047 |
System.out.println(pad.substring(0, slevel)+(s1-s0));
|
|
|
1048 |
System.out.println("-------");
|
|
|
1049 |
System.out.println(pad.substring(0, tlevel)+yt0);
|
|
|
1050 |
System.out.println(pad.substring(0, tlevel)+yt1);
|
|
|
1051 |
System.out.println(pad.substring(0, tlevel)+(t1-t0));
|
|
|
1052 |
*/
|
|
|
1053 |
if (ys0 > yt1 || yt0 > ys1) {
|
|
|
1054 |
return false;
|
|
|
1055 |
}
|
|
|
1056 |
if (Math.min(xs0, xs1) > Math.max(xt0, xt1) ||
|
|
|
1057 |
Math.max(xs0, xs1) < Math.min(xt0, xt1))
|
|
|
1058 |
{
|
|
|
1059 |
return false;
|
|
|
1060 |
}
|
|
|
1061 |
// Bounding boxes intersect - back off the larger of
|
|
|
1062 |
// the two subcurves by half until they stop intersecting
|
|
|
1063 |
// (or until they get small enough to switch to a more
|
|
|
1064 |
// intensive algorithm).
|
|
|
1065 |
if (s1 - s0 > TMIN) {
|
|
|
1066 |
double s = (s0 + s1) / 2;
|
|
|
1067 |
double xs = this.XforT(s);
|
|
|
1068 |
double ys = this.YforT(s);
|
|
|
1069 |
if (s == s0 || s == s1) {
|
|
|
1070 |
System.out.println("s0 = "+s0);
|
|
|
1071 |
System.out.println("s1 = "+s1);
|
|
|
1072 |
throw new InternalError("no s progress!");
|
|
|
1073 |
}
|
|
|
1074 |
if (t1 - t0 > TMIN) {
|
|
|
1075 |
double t = (t0 + t1) / 2;
|
|
|
1076 |
double xt = that.XforT(t);
|
|
|
1077 |
double yt = that.YforT(t);
|
|
|
1078 |
if (t == t0 || t == t1) {
|
|
|
1079 |
System.out.println("t0 = "+t0);
|
|
|
1080 |
System.out.println("t1 = "+t1);
|
|
|
1081 |
throw new InternalError("no t progress!");
|
|
|
1082 |
}
|
|
|
1083 |
if (ys >= yt0 && yt >= ys0) {
|
|
|
1084 |
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
|
|
|
1085 |
s0, xs0, ys0, s, xs, ys,
|
|
|
1086 |
t0, xt0, yt0, t, xt, yt)) {
|
|
|
1087 |
return true;
|
|
|
1088 |
}
|
|
|
1089 |
}
|
|
|
1090 |
if (ys >= yt) {
|
|
|
1091 |
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
|
|
|
1092 |
s0, xs0, ys0, s, xs, ys,
|
|
|
1093 |
t, xt, yt, t1, xt1, yt1)) {
|
|
|
1094 |
return true;
|
|
|
1095 |
}
|
|
|
1096 |
}
|
|
|
1097 |
if (yt >= ys) {
|
|
|
1098 |
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
|
|
|
1099 |
s, xs, ys, s1, xs1, ys1,
|
|
|
1100 |
t0, xt0, yt0, t, xt, yt)) {
|
|
|
1101 |
return true;
|
|
|
1102 |
}
|
|
|
1103 |
}
|
|
|
1104 |
if (ys1 >= yt && yt1 >= ys) {
|
|
|
1105 |
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
|
|
|
1106 |
s, xs, ys, s1, xs1, ys1,
|
|
|
1107 |
t, xt, yt, t1, xt1, yt1)) {
|
|
|
1108 |
return true;
|
|
|
1109 |
}
|
|
|
1110 |
}
|
|
|
1111 |
} else {
|
|
|
1112 |
if (ys >= yt0) {
|
|
|
1113 |
if (findIntersect(that, yrange, ymin, slevel+1, tlevel,
|
|
|
1114 |
s0, xs0, ys0, s, xs, ys,
|
|
|
1115 |
t0, xt0, yt0, t1, xt1, yt1)) {
|
|
|
1116 |
return true;
|
|
|
1117 |
}
|
|
|
1118 |
}
|
|
|
1119 |
if (yt1 >= ys) {
|
|
|
1120 |
if (findIntersect(that, yrange, ymin, slevel+1, tlevel,
|
|
|
1121 |
s, xs, ys, s1, xs1, ys1,
|
|
|
1122 |
t0, xt0, yt0, t1, xt1, yt1)) {
|
|
|
1123 |
return true;
|
|
|
1124 |
}
|
|
|
1125 |
}
|
|
|
1126 |
}
|
|
|
1127 |
} else if (t1 - t0 > TMIN) {
|
|
|
1128 |
double t = (t0 + t1) / 2;
|
|
|
1129 |
double xt = that.XforT(t);
|
|
|
1130 |
double yt = that.YforT(t);
|
|
|
1131 |
if (t == t0 || t == t1) {
|
|
|
1132 |
System.out.println("t0 = "+t0);
|
|
|
1133 |
System.out.println("t1 = "+t1);
|
|
|
1134 |
throw new InternalError("no t progress!");
|
|
|
1135 |
}
|
|
|
1136 |
if (yt >= ys0) {
|
|
|
1137 |
if (findIntersect(that, yrange, ymin, slevel, tlevel+1,
|
|
|
1138 |
s0, xs0, ys0, s1, xs1, ys1,
|
|
|
1139 |
t0, xt0, yt0, t, xt, yt)) {
|
|
|
1140 |
return true;
|
|
|
1141 |
}
|
|
|
1142 |
}
|
|
|
1143 |
if (ys1 >= yt) {
|
|
|
1144 |
if (findIntersect(that, yrange, ymin, slevel, tlevel+1,
|
|
|
1145 |
s0, xs0, ys0, s1, xs1, ys1,
|
|
|
1146 |
t, xt, yt, t1, xt1, yt1)) {
|
|
|
1147 |
return true;
|
|
|
1148 |
}
|
|
|
1149 |
}
|
|
|
1150 |
} else {
|
|
|
1151 |
// No more subdivisions
|
|
|
1152 |
double xlk = xs1 - xs0;
|
|
|
1153 |
double ylk = ys1 - ys0;
|
|
|
1154 |
double xnm = xt1 - xt0;
|
|
|
1155 |
double ynm = yt1 - yt0;
|
|
|
1156 |
double xmk = xt0 - xs0;
|
|
|
1157 |
double ymk = yt0 - ys0;
|
|
|
1158 |
double det = xnm * ylk - ynm * xlk;
|
|
|
1159 |
if (det != 0) {
|
|
|
1160 |
double detinv = 1 / det;
|
|
|
1161 |
double s = (xnm * ymk - ynm * xmk) * detinv;
|
|
|
1162 |
double t = (xlk * ymk - ylk * xmk) * detinv;
|
|
|
1163 |
if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
|
|
|
1164 |
s = s0 + s * (s1 - s0);
|
|
|
1165 |
t = t0 + t * (t1 - t0);
|
|
|
1166 |
if (s < 0 || s > 1 || t < 0 || t > 1) {
|
|
|
1167 |
System.out.println("Uh oh!");
|
|
|
1168 |
}
|
|
|
1169 |
double y = (this.YforT(s) + that.YforT(t)) / 2;
|
|
|
1170 |
if (y <= yrange[1] && y > yrange[0]) {
|
|
|
1171 |
yrange[1] = y;
|
|
|
1172 |
return true;
|
|
|
1173 |
}
|
|
|
1174 |
}
|
|
|
1175 |
}
|
|
|
1176 |
//System.out.println("Testing lines!");
|
|
|
1177 |
}
|
|
|
1178 |
return false;
|
|
|
1179 |
}
|
|
|
1180 |
|
|
|
1181 |
public double refineTforY(double t0, double yt0, double y0) {
|
|
|
1182 |
double t1 = 1;
|
|
|
1183 |
while (true) {
|
|
|
1184 |
double th = (t0 + t1) / 2;
|
|
|
1185 |
if (th == t0 || th == t1) {
|
|
|
1186 |
return t1;
|
|
|
1187 |
}
|
|
|
1188 |
double y = YforT(th);
|
|
|
1189 |
if (y < y0) {
|
|
|
1190 |
t0 = th;
|
|
|
1191 |
yt0 = y;
|
|
|
1192 |
} else if (y > y0) {
|
|
|
1193 |
t1 = th;
|
|
|
1194 |
} else {
|
|
|
1195 |
return t1;
|
|
|
1196 |
}
|
|
|
1197 |
}
|
|
|
1198 |
}
|
|
|
1199 |
|
|
|
1200 |
public boolean fairlyClose(double v1, double v2) {
|
|
|
1201 |
return (Math.abs(v1 - v2) <
|
|
|
1202 |
Math.max(Math.abs(v1), Math.abs(v2)) * 1E-10);
|
|
|
1203 |
}
|
|
|
1204 |
|
|
|
1205 |
public abstract int getSegment(double coords[]);
|
|
|
1206 |
}
|