sources/org/apache/batik/ext/awt/geom/AbstractSegment.java - xmlgraphics-batik - Git at Google

 /*

    Copyright 2003 The Apache Software Foundation

    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

        http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.

  */
 package org.apache.batik.ext.awt.geom;

 import java.awt.geom.Point2D;
 import java.util.Arrays;

 /**
  * An abstract class for path segments.
  *
  * @version $Id$
  */
 public abstract class AbstractSegment implements Segment {

     protected abstract int findRoots(double y, double [] roots);

     public Segment.SplitResults split(double y) {
         double [] roots = { 0, 0, 0 };
         int numSol = findRoots(y, roots);
         if (numSol == 0) return null; // No split

         Arrays.sort(roots, 0, numSol);
         double [] segs = new double[numSol+2];
         int numSegments=0;
         segs[numSegments++] = 0;
         for (int i=0; i<numSol; i++) {
             double r = roots[i];
             if (r <= 0.0) continue;
             if (r >= 1.0) break;
             if (segs[numSegments-1] != r)
                 segs[numSegments++] = r;
         }
         segs[numSegments++] = 1.0;

         if (numSegments == 2) return null;
         // System.err.println("Y: " + y + "#Seg: " + numSegments +
         //                    " Seg: " + this);

         Segment [] parts = new Segment[numSegments];
         double pT = 0.0;
         int pIdx = 0;
         boolean firstAbove=false, prevAbove=false;
         for (int i=1; i<numSegments; i++) {
             // System.err.println("Segs: " + segs[i-1]+", "+segs[i]);
             parts[pIdx] = getSegment(segs[i-1], segs[i]);
             Point2D.Double pt = parts[pIdx].eval(0.5);
             // System.err.println("Pt: " + pt);
             if (pIdx == 0) {
                 pIdx++;
                 firstAbove = prevAbove = (pt.y < y);
                 continue;
             }
             boolean above = (pt.y < y);
             if (prevAbove == above) {
                 // Merge segments
                 parts[pIdx-1] = getSegment(pT, segs[i]);
             } else {
                 pIdx++;
                 pT=segs[i-1];
                 prevAbove = above;
             }
         }
         if (pIdx == 1) return null;
         Segment [] below, above;
         if (firstAbove) {
             above = new Segment[(pIdx+1)/2];
             below = new Segment[pIdx/2];
         } else {
             above = new Segment[pIdx/2];
             below = new Segment[(pIdx+1)/2];
         }
         int ai=0, bi=0;
         for (int i=0; i<pIdx; i++) {
             if (firstAbove) above[ai++] = parts[i];
             else            below[bi++] = parts[i];
             firstAbove = !firstAbove;
         }
         return new SplitResults(below, above);
     }

     public Segment splitBefore(double t) {
         return getSegment(0.0, t);
     }

     public Segment splitAfter(double t) {
         return getSegment(t, 1.0);
     }

     // Doubles have 48bit precision
     static final double eps = 1/(double)(1l<<48);
     static final double tol = 4.0*eps;

     public static int solveLine(double a, double b,
                                  double [] roots) {
         if (a == 0) {
             if (b != 0)
                 // No intersection.
                 return 0;
             // All pts intersect just return 0.
             roots[0] = 0;
             return 1;
         }

         roots[0] = -b/a;
         return 1;
     }

     public static int solveQuad(double a, double b, double c,
                                  double [] roots) {
         // System.err.println("Quad: " + a +"t^2 + " + b +"t + " + c);
         if (a == 0) {
             // no square term.
             return solveLine(b, c, roots);
         }

         double det = b*b-4*a*c;
         // System.err.println("Det: " + det);

         if (Math.abs(det) <= tol*b*b) {
             // one real root (det doesn't contain any useful info)
             roots[0] =  -b/(2*a);
             return 1;
         }

         if (det < 0)
             return 0; // No real roots

         // Two real roots
         det = Math.sqrt(det);
         double w = -(b + matchSign(det, b));
         roots[0] = (2*c)/w;
         roots[1] = w/(2*a);
         return 2;
     }

     public static double matchSign(double a, double b) {
         if (b < 0) return (a < 0)?a:-a;
         return (a > 0)?a:-a;
     }

     public static int solveCubic(double a3, double a2,
                                   double a1, double a0,
                                   double [] roots) {

         // System.err.println("Cubic: " + a3 + "t^3 + " +
         //                    a2 +"t^2 + " +
         //                    a1 +"t + " + a0);

         double [] dRoots = { 0, 0};
         int dCnt = solveQuad(3*a3, 2*a2, a1, dRoots);
         double [] yVals = {0, 0, 0, 0};
         double [] tVals = {0, 0, 0, 0};
         int yCnt=0;
         yVals[yCnt]   = a0;
         tVals[yCnt++] = 0;
         double r;
         switch (dCnt) {
         case 1:
             r = dRoots[0];
             if ((r > 0) && (r < 1)) {
                 yVals[yCnt]   = ((a3*r+a2)*r+a1)*r+a0;
                 tVals[yCnt++] = r;
             }
             break;
         case 2:
             if (dRoots[0] > dRoots[1]) {
                 double t  = dRoots[0];
                 dRoots[0] = dRoots[1];
                 dRoots[1] = t;
             }
             r = dRoots[0];
             if ((r > 0) && (r < 1)) {
                 yVals[yCnt]   = ((a3*r+a2)*r+a1)*r+a0;
                 tVals[yCnt++] = r;
             }
             r = dRoots[1];
             if ((r > 0) && (r < 1)) {
                 yVals[yCnt]   = ((a3*r+a2)*r+a1)*r+a0;
                 tVals[yCnt++] = r;
             }
             break;
         default: break;
         }
         yVals[yCnt]   = a3+a2+a1+a0;
         tVals[yCnt++] = 1.0;

         int ret=0;
         for (int i=0; i<yCnt-1; i++) {
             double y0 = yVals[i],   t0 = tVals[i];
             double y1 = yVals[i+1], t1 = tVals[i+1];
             if ((y0 < 0) && (y1 < 0)) continue;
             if ((y0 > 0) && (y1 > 0)) continue;

             if (y0 > y1) { // swap so y0 < 0 and y1 > 0
                 double t;
                 t = y0; y0=y1; y1=t;
                 t = t0; t0=t1; t1=t;
             }

             if (-y0 < tol*y1) { roots[ret++] = t0;      continue; }
             if (y1 < -tol*y0) { roots[ret++] = t1; i++; continue; }

             double epsZero = tol*(y1-y0);
             int cnt;
             for (cnt=0; cnt<20; cnt++) {
                 double dt = t1-t0;
                 double dy = y1-y0;
                 // double t = (t0+t1)/2;
                 // double t= t0+Math.abs(y0/dy)*dt;
                 // This tends to make sure that we come up
                 // a little short each time this generaly allows
                 // you to eliminate as much of the range as possible
                 // without overshooting (in which case you may eliminate
                 // almost nothing).
                 double t= t0+(Math.abs(y0/dy)*99+.5)*dt/100;
                 double v = ((a3*t+a2)*t+a1)*t+a0;
                 if (Math.abs(v) < epsZero) {
                     roots[ret++] = t; break;
                 }
                 if (v < 0) { t0 = t; y0=v;}
                 else       { t1 = t; y1=v;}
             }
             if (cnt == 20)
                 roots[ret++] = (t0+t1)/2;
         }
         return ret;
     }

     /*
     public static void check(Segment seg, float y, PrintStream ps) {
         ps.println("<path fill=\"none\" stroke=\"black\" " +
                    " stroke-width=\"3\" d=\"" + seg + "\"/>");

         ps.println("<line x1=\"-1000\" y1=\""+y+
                    "\" x2=\"1000\" y2=\""+y+"\" fill=\"none\" stroke=\"orange\"/>\n");

         SplitResults sr = seg.split(y);
         if (sr == null) return;
         Segment [] above = sr.getAbove();
         Segment [] below = sr.getBelow();
         for (int i=0; i<above.length; i++) {
             ps.println("<path fill=\"none\" stroke=\"blue\" " +
                        " stroke-width=\"2.5\" " +
                        " d=\"" + above[i] + "\"/>");
         }
         for (int i=0; i<below.length; i++) {
             ps.println("<path fill=\"none\" stroke=\"red\" " +
                        " stroke-width=\"2\" " +
                        "d=\"" + below[i] + "\"/>");
         }
     }
     public static void main(String [] args) {
         PrintStream ps;
         double [] roots = { 0, 0, 0 };
         int n = solveCubic (-0.10000991821289062, 9.600013732910156,
                             -35.70000457763672, 58.0, roots);
         for (int i=0; i<n; i++)
             System.err.println("Root: " + roots[i]);
         Cubic c;
         c = new Cubic(new Point2D.Double(153.6999969482422,5.099999904632568),
                       new Point2D.Double(156.6999969482422,4.099999904632568),
                       new Point2D.Double(160.39999389648438,2.3999998569488525),
                       new Point2D.Double(164.6999969482422,0.0));
         c.split(0);

         c = new Cubic(new Point2D.Double(24.899999618530273,23.10000228881836),
                       new Point2D.Double(41.5,8.399999618530273),
                       new Point2D.Double(64.69999694824219,1.0),
                       new Point2D.Double(94.5999984741211,1.0));
         c.split(0);

         try {
             ps = new PrintStream(new FileOutputStream(args[0]));
         } catch(java.io.IOException ioe) {
             ioe.printStackTrace();
             return;
         }

         ps.println("<?xml version=\"1.0\" standalone=\"no\"?>\n" +
                    "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.0//EN\"\n" +
                    "\"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd\">\n" +
                    "<svg width=\"450\" height=\"500\"\n" +
                    "     viewBox=\"-100 -100 450 500\"\n" +
                    "     xmlns=\"http://www.w3.org/2000/svg\"\n" +
                    "     xmlns:xlink=\"http://www.w3.org/1999/xlink\">");

         check(new Cubic(new Point2D.Double(0, 0),
                         new Point2D.Double(100, 100),
                         new Point2D.Double(-50, 100),
                         new Point2D.Double(50, 0)), 40, ps);

         check(new Cubic(new Point2D.Double(100, 0),
                         new Point2D.Double(200, 100),
                         new Point2D.Double(50, -50),
                         new Point2D.Double(150, 30)), 20, ps);

         check(new Cubic(new Point2D.Double(200, 0),
                         new Point2D.Double(300, 100),
                         new Point2D.Double(150, 100),
                         new Point2D.Double(250, 0)), 75, ps);

         check(new Quadradic(new Point2D.Double(0, 100),
                             new Point2D.Double(50,150),
                             new Point2D.Double(10,100)), 115, ps);

         check(new Linear(new Point2D.Double(100, 100),
                          new Point2D.Double(150,150)), 115, ps);
         ps.println("</svg>");
     }
     */
 }
	/*

	Copyright 2003 The Apache Software Foundation

	Licensed under the Apache License, Version 2.0 (the "License");
	you may not use this file except in compliance with the License.
	You may obtain a copy of the License at

	http://www.apache.org/licenses/LICENSE-2.0

	Unless required by applicable law or agreed to in writing, software
	distributed under the License is distributed on an "AS IS" BASIS,
	WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	See the License for the specific language governing permissions and
	limitations under the License.

	*/
	package org.apache.batik.ext.awt.geom;

	import java.awt.geom.Point2D;
	import java.util.Arrays;

	/**
	* An abstract class for path segments.
	*
	* @version $Id$
	*/
	public abstract class AbstractSegment implements Segment {

	protected abstract int findRoots(double y, double [] roots);

	public Segment.SplitResults split(double y) {
	double [] roots = { 0, 0, 0 };
	int numSol = findRoots(y, roots);
	if (numSol == 0) return null; // No split

	Arrays.sort(roots, 0, numSol);
	double [] segs = new double[numSol+2];
	int numSegments=0;
	segs[numSegments++] = 0;
	for (int i=0; i<numSol; i++) {
	double r = roots[i];
	if (r <= 0.0) continue;
	if (r >= 1.0) break;
	if (segs[numSegments-1] != r)
	segs[numSegments++] = r;
	}
	segs[numSegments++] = 1.0;

	if (numSegments == 2) return null;
	// System.err.println("Y: " + y + "#Seg: " + numSegments +
	// " Seg: " + this);

	Segment [] parts = new Segment[numSegments];
	double pT = 0.0;
	int pIdx = 0;
	boolean firstAbove=false, prevAbove=false;
	for (int i=1; i<numSegments; i++) {
	// System.err.println("Segs: " + segs[i-1]+", "+segs[i]);
	parts[pIdx] = getSegment(segs[i-1], segs[i]);
	Point2D.Double pt = parts[pIdx].eval(0.5);
	// System.err.println("Pt: " + pt);
	if (pIdx == 0) {
	pIdx++;
	firstAbove = prevAbove = (pt.y < y);
	continue;
	}
	boolean above = (pt.y < y);
	if (prevAbove == above) {
	// Merge segments
	parts[pIdx-1] = getSegment(pT, segs[i]);
	} else {
	pIdx++;
	pT=segs[i-1];
	prevAbove = above;
	}
	}
	if (pIdx == 1) return null;
	Segment [] below, above;
	if (firstAbove) {
	above = new Segment[(pIdx+1)/2];
	below = new Segment[pIdx/2];
	} else {
	above = new Segment[pIdx/2];
	below = new Segment[(pIdx+1)/2];
	}
	int ai=0, bi=0;
	for (int i=0; i<pIdx; i++) {
	if (firstAbove) above[ai++] = parts[i];
	else below[bi++] = parts[i];
	firstAbove = !firstAbove;
	}
	return new SplitResults(below, above);
	}

	public Segment splitBefore(double t) {
	return getSegment(0.0, t);
	}

	public Segment splitAfter(double t) {
	return getSegment(t, 1.0);
	}

	// Doubles have 48bit precision
	static final double eps = 1/(double)(1l<<48);
	static final double tol = 4.0*eps;

	public static int solveLine(double a, double b,
	double [] roots) {
	if (a == 0) {
	if (b != 0)
	// No intersection.
	return 0;
	// All pts intersect just return 0.
	roots[0] = 0;
	return 1;
	}

	roots[0] = -b/a;
	return 1;
	}

	public static int solveQuad(double a, double b, double c,
	double [] roots) {
	// System.err.println("Quad: " + a +"t^2 + " + b +"t + " + c);
	if (a == 0) {
	// no square term.
	return solveLine(b, c, roots);
	}

	double det = bb-4a*c;
	// System.err.println("Det: " + det);

	if (Math.abs(det) <= tolbb) {
	// one real root (det doesn't contain any useful info)
	roots[0] = -b/(2*a);
	return 1;
	}

	if (det < 0)
	return 0; // No real roots

	// Two real roots
	det = Math.sqrt(det);
	double w = -(b + matchSign(det, b));
	roots[0] = (2*c)/w;
	roots[1] = w/(2*a);
	return 2;
	}

	public static double matchSign(double a, double b) {
	if (b < 0) return (a < 0)?a:-a;
	return (a > 0)?a:-a;
	}

	public static int solveCubic(double a3, double a2,
	double a1, double a0,
	double [] roots) {

	// System.err.println("Cubic: " + a3 + "t^3 + " +
	// a2 +"t^2 + " +
	// a1 +"t + " + a0);

	double [] dRoots = { 0, 0};
	int dCnt = solveQuad(3a3, 2a2, a1, dRoots);
	double [] yVals = {0, 0, 0, 0};
	double [] tVals = {0, 0, 0, 0};
	int yCnt=0;
	yVals[yCnt] = a0;
	tVals[yCnt++] = 0;
	double r;
	switch (dCnt) {
	case 1:
	r = dRoots[0];
	if ((r > 0) && (r < 1)) {
	yVals[yCnt] = ((a3r+a2)r+a1)*r+a0;
	tVals[yCnt++] = r;
	}
	break;
	case 2:
	if (dRoots[0] > dRoots[1]) {
	double t = dRoots[0];
	dRoots[0] = dRoots[1];
	dRoots[1] = t;
	}
	r = dRoots[0];
	if ((r > 0) && (r < 1)) {
	yVals[yCnt] = ((a3r+a2)r+a1)*r+a0;
	tVals[yCnt++] = r;
	}
	r = dRoots[1];
	if ((r > 0) && (r < 1)) {
	yVals[yCnt] = ((a3r+a2)r+a1)*r+a0;
	tVals[yCnt++] = r;
	}
	break;
	default: break;
	}
	yVals[yCnt] = a3+a2+a1+a0;
	tVals[yCnt++] = 1.0;

	int ret=0;
	for (int i=0; i<yCnt-1; i++) {
	double y0 = yVals[i], t0 = tVals[i];
	double y1 = yVals[i+1], t1 = tVals[i+1];
	if ((y0 < 0) && (y1 < 0)) continue;
	if ((y0 > 0) && (y1 > 0)) continue;

	if (y0 > y1) { // swap so y0 < 0 and y1 > 0
	double t;
	t = y0; y0=y1; y1=t;
	t = t0; t0=t1; t1=t;
	}

	if (-y0 < tol*y1) { roots[ret++] = t0; continue; }
	if (y1 < -tol*y0) { roots[ret++] = t1; i++; continue; }

	double epsZero = tol*(y1-y0);
	int cnt;
	for (cnt=0; cnt<20; cnt++) {
	double dt = t1-t0;
	double dy = y1-y0;
	// double t = (t0+t1)/2;
	// double t= t0+Math.abs(y0/dy)*dt;
	// This tends to make sure that we come up
	// a little short each time this generaly allows
	// you to eliminate as much of the range as possible
	// without overshooting (in which case you may eliminate
	// almost nothing).
	double t= t0+(Math.abs(y0/dy)99+.5)dt/100;
	double v = ((a3t+a2)t+a1)*t+a0;
	if (Math.abs(v) < epsZero) {
	roots[ret++] = t; break;
	}
	if (v < 0) { t0 = t; y0=v;}
	else { t1 = t; y1=v;}
	}
	if (cnt == 20)
	roots[ret++] = (t0+t1)/2;
	}
	return ret;
	}

	/*
	public static void check(Segment seg, float y, PrintStream ps) {
	ps.println("<path fill=\"none\" stroke=\"black\" " +
	" stroke-width=\"3\" d=\"" + seg + "\"/>");

	ps.println("<line x1=\"-1000\" y1=\""+y+
	"\" x2=\"1000\" y2=\""+y+"\" fill=\"none\" stroke=\"orange\"/>\n");

	SplitResults sr = seg.split(y);
	if (sr == null) return;
	Segment [] above = sr.getAbove();
	Segment [] below = sr.getBelow();
	for (int i=0; i<above.length; i++) {
	ps.println("<path fill=\"none\" stroke=\"blue\" " +
	" stroke-width=\"2.5\" " +
	" d=\"" + above[i] + "\"/>");
	}
	for (int i=0; i<below.length; i++) {
	ps.println("<path fill=\"none\" stroke=\"red\" " +
	" stroke-width=\"2\" " +
	"d=\"" + below[i] + "\"/>");
	}
	}
	public static void main(String [] args) {
	PrintStream ps;
	double [] roots = { 0, 0, 0 };
	int n = solveCubic (-0.10000991821289062, 9.600013732910156,
	-35.70000457763672, 58.0, roots);
	for (int i=0; i<n; i++)
	System.err.println("Root: " + roots[i]);
	Cubic c;
	c = new Cubic(new Point2D.Double(153.6999969482422,5.099999904632568),
	new Point2D.Double(156.6999969482422,4.099999904632568),
	new Point2D.Double(160.39999389648438,2.3999998569488525),
	new Point2D.Double(164.6999969482422,0.0));
	c.split(0);

	c = new Cubic(new Point2D.Double(24.899999618530273,23.10000228881836),
	new Point2D.Double(41.5,8.399999618530273),
	new Point2D.Double(64.69999694824219,1.0),
	new Point2D.Double(94.5999984741211,1.0));
	c.split(0);

	try {
	ps = new PrintStream(new FileOutputStream(args[0]));
	} catch(java.io.IOException ioe) {
	ioe.printStackTrace();
	return;
	}

	ps.println("<?xml version=\"1.0\" standalone=\"no\"?>\n" +
	"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.0//EN\"\n" +
	"\"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd\">\n" +
	"<svg width=\"450\" height=\"500\"\n" +
	" viewBox=\"-100 -100 450 500\"\n" +
	" xmlns=\"http://www.w3.org/2000/svg\"\n" +
	" xmlns:xlink=\"http://www.w3.org/1999/xlink\">");

	check(new Cubic(new Point2D.Double(0, 0),
	new Point2D.Double(100, 100),
	new Point2D.Double(-50, 100),
	new Point2D.Double(50, 0)), 40, ps);

	check(new Cubic(new Point2D.Double(100, 0),
	new Point2D.Double(200, 100),
	new Point2D.Double(50, -50),
	new Point2D.Double(150, 30)), 20, ps);

	check(new Cubic(new Point2D.Double(200, 0),
	new Point2D.Double(300, 100),
	new Point2D.Double(150, 100),
	new Point2D.Double(250, 0)), 75, ps);

	check(new Quadradic(new Point2D.Double(0, 100),
	new Point2D.Double(50,150),
	new Point2D.Double(10,100)), 115, ps);

	check(new Linear(new Point2D.Double(100, 100),
	new Point2D.Double(150,150)), 115, ps);
	ps.println("</svg>");
	}
	*/
	}