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FreeHEP GraphicsIO Base Library
There is a newer version: 2.4
// Copyright 2001-2004 FreeHEP
package org.freehep.graphicsio;

import java.awt.geom.Point2D;
import java.io.IOException;

/**
 * Implements the Cubic Bezier Curve PathConstructor functionality in terms of
 * Quadratic Bezier Curves
 * 
 * Uses the same algorithm published as ActionScript (SWF) by Robert Penner:
 * 
 * ========================== Cubic Bezier Drawing v1.1
 * ========================== recursive quadratic approximation with adjustable
 * tolerance
 * 
 * March 4, 2004
 * 
 * Robert Penner www.robertpenner.com/tools/bezier_cubic.zip file:
 * bezier_draw_cubic.as ==========================
 * 
 * @author Mark Donszelmann
 * @version $Id: freehep-graphicsio/src/main/java/org/freehep/graphicsio/CubicToQuadPathConstructor.java efe5341792e9 2006/11/13 22:08:58 duns $
 */
public abstract class CubicToQuadPathConstructor extends
        AbstractPathConstructor {

    private double resolutionSq;

    protected CubicToQuadPathConstructor(double resolution) {
        super();
        resolutionSq = resolution * resolution;
    }

    public void move(double x, double y) throws IOException {
        currentX = x;
        currentY = y;
    }

    public void line(double x, double y) throws IOException {
        currentX = x;
        currentY = y;
    }

    public void cubic(double x1, double y1, double x2, double y2, double x3,
            double y3) throws IOException {
        quadratify(new Point2D.Double(currentX, currentY), new Point2D.Double(
                x1, y1), new Point2D.Double(x2, y2), new Point2D.Double(x3, y3));

        currentX = x3;
        currentY = y3;
    }

    public void closePath(double x0, double y0) throws IOException {
        currentX = 0;
        currentY = 0;
    }

    public static Point2D intersect(Point2D p1, Point2D p2, Point2D p3,
            Point2D p4) {

        double dx1 = p2.getX() - p1.getX();
        double dx2 = p3.getX() - p4.getX();
        
        // line are vertical
        if ((dx1 == 0) && (dx2 == 0)) return null;

        double dy1 = p2.getY() - p1.getY();
        double dy2 = p3.getY() - p4.getY();
        
        // line are horizontal
        if ((dy1 == 0) && (dy2 == 0)) return null;
        
        double m1 = (p2.getY() - p1.getY()) / dx1;
        double m2 = (p3.getY() - p4.getY()) / dx2;

        if (dx1 == 0) {
            // infinity
            return new Point2D.Double(p1.getX(), m2 * (p1.getX() - p4.getX())
                    + p4.getY());
        } else if (dx2 == 0) {
            // infinity
            return new Point2D.Double(p4.getX(), m1 * (p4.getX() - p1.getX())
                    + p1.getY());
        }
        
        // lines are parallel
        if (m1 == m2) return null;
        
        double x = (-m2 * p4.getX() + p4.getY() + m1 * p1.getX() - p1.getY())
                / (m1 - m2);
        double y = m1 * (x - p1.getX()) + p1.getY();
        return new Point2D.Double(x, y);
    }

    public static Point2D midPoint(Point2D a, Point2D b) {
        return new Point2D.Double((a.getX() + b.getX()) / 2.0, (a.getY() + b
                .getY()) / 2.0);
    }

    public void quadratify(Point2D a, Point2D b, Point2D c, Point2D d)
            throws IOException {
        // find intersection between bezier arms
        Point2D s = intersect(a, b, c, d);
        if (s == null) return;
        
        // find distance between the midpoints
        double dx = (a.getX() + d.getX() + s.getX() * 4 - (b.getX() + c.getX()) * 3) * .125;
        double dy = (a.getY() + d.getY() + s.getY() * 4 - (b.getY() + c.getY()) * 3) * .125;
        // split curve if the quadratic isn't close enough
        if (dx * dx + dy * dy > resolutionSq) {
            Point2D p01 = midPoint(a, b);
            Point2D p12 = midPoint(b, c);
            Point2D p23 = midPoint(c, d);
            Point2D p02 = midPoint(p01, p12);
            Point2D p13 = midPoint(p12, p23);
            Point2D p03 = midPoint(p02, p13);
            // recursive call to subdivide curve
            quadratify(a, p01, p02, p03);
            quadratify(p03, p13, p23, d);
        } else {
            // end recursion by drawing quadratic bezier
            quad(s.getX(), s.getY(), d.getX(), d.getY());
        }
    }

    static class Test extends CubicToQuadPathConstructor {
        public Test(double resolution) {
            super(resolution);
        }

        public void quad(double x1, double y1, double x2, double y2) {
            System.out.println("Quad: (" + currentX + ", " + currentY + ") ("
                    + x1 + ", " + y1 + ") (" + x2 + ", " + y2 + ")");
            currentX = x2;
            currentY = y2;
        }

    }

    public static void main(String[] args) throws Exception {
        PathConstructor pc = new Test(0.5);
        // A, B, C, D
        pc.move(20, 20);
        pc.cubic(20, 40, 40, 60, 60, 60);

        // A, B, D, C
        pc.move(20, 20);
        pc.cubic(20, 40, 60, 60, 40, 60);

        // Intersecting Curve
        pc.move(183, 149);
        pc.cubic(189, 291, 256, 347, 295, 244);
        pc.cubic(334, 141, 286, 216, 214, 228);
        pc.cubic(142, 240, 142, 256, 176, 284);
    }
}