path: root/src/main/java/com/kitfox/svg/pathcmd/Arc.java

/*
 * SVG Salamander
 * Copyright (c) 2004, Mark McKay
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or 
 * without modification, are permitted provided that the following
 * conditions are met:
 *
 *   - Redistributions of source code must retain the above 
 *     copyright notice, this list of conditions and the following
 *     disclaimer.
 *   - Redistributions in binary form must reproduce the above
 *     copyright notice, this list of conditions and the following
 *     disclaimer in the documentation and/or other materials 
 *     provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
 * COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
 * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 * OF THE POSSIBILITY OF SUCH DAMAGE. 
 * 
 * Mark McKay can be contacted at mark@kitfox.com.  Salamander and other
 * projects can be found at http://www.kitfox.com
 *
 * Created on January 26, 2004, 8:40 PM
 */

package com.kitfox.svg.pathcmd;

//import org.apache.batik.ext.awt.geom.ExtendedGeneralPath;
import java.awt.*;
import java.awt.geom.*;

/**
 * This is a little used SVG function, as most editors will save curves as 
 * Beziers.  To reduce the need to rely on the Batik library, this functionallity
 * is being bypassed for the time being.  In the future, it would be nice to
 * extend the GeneralPath command to include the arcTo ability provided by Batik.
 *
 * @author Mark McKay
 * @author <a href="mailto:mark@kitfox.com">Mark McKay</a>
 */
public class Arc extends PathCommand 
{

    public float rx = 0f;
    public float ry = 0f;
    public float xAxisRot = 0f;
    public boolean largeArc = false;
    public boolean sweep = false;
    public float x = 0f;
    public float y = 0f;

    /** Creates a new instance of MoveTo */
    public Arc() {
    }

    public Arc(boolean isRelative, float rx, float ry, float xAxisRot, boolean largeArc, boolean sweep, float x, float y) {
        super(isRelative);
        this.rx = rx;
        this.ry = ry;
        this.xAxisRot = xAxisRot;
        this.largeArc = largeArc;
        this.sweep = sweep;
        this.x = x;
        this.y = y;
    }

//    public void appendPath(ExtendedGeneralPath path, BuildHistory hist)
    public void appendPath(GeneralPath path, BuildHistory hist)
    {
        float offx = isRelative ? hist.lastPoint.x : 0f;
        float offy = isRelative ? hist.lastPoint.y : 0f;

        arcTo(path, rx, ry, xAxisRot, largeArc, sweep,
            x + offx, y + offy,
            hist.lastPoint.x, hist.lastPoint.y);
//        path.lineTo(x + offx, y + offy);
//        hist.setPoint(x + offx, y + offy);
        hist.setLastPoint(x + offx, y + offy);
        hist.setLastKnot(x + offx, y + offy);
    }

    public int getNumKnotsAdded()
    {
        return 6;
    }

    /**
     * Adds an elliptical arc, defined by two radii, an angle from the
     * x-axis, a flag to choose the large arc or not, a flag to
     * indicate if we increase or decrease the angles and the final
     * point of the arc.
     *
     * @param rx the x radius of the ellipse
     * @param ry the y radius of the ellipse
     *
     * @param angle the angle from the x-axis of the current
     * coordinate system to the x-axis of the ellipse in degrees.
     *
     * @param largeArcFlag the large arc flag. If true the arc
     * spanning less than or equal to 180 degrees is chosen, otherwise
     * the arc spanning greater than 180 degrees is chosen
     *
     * @param sweepFlag the sweep flag. If true the line joining
     * center to arc sweeps through decreasing angles otherwise it
     * sweeps through increasing angles
     *
     * @param x the absolute x coordinate of the final point of the arc.
     * @param y the absolute y coordinate of the final point of the arc.
     * @param x0 - The absolute x coordinate of the initial point of the arc.
     * @param y0 - The absolute y coordinate of the initial point of the arc.
     */
    public void arcTo(GeneralPath path, float rx, float ry,
                                   float angle,
                                   boolean largeArcFlag,
                                   boolean sweepFlag,
                                   float x, float y, float x0, float y0) 
    {

        // Ensure radii are valid
        if (rx == 0 || ry == 0) {
            path.lineTo((float) x, (float) y);
            return;
        }

        if (x0 == x && y0 == y) {
            // If the endpoints (x, y) and (x0, y0) are identical, then this
            // is equivalent to omitting the elliptical arc segment entirely.
            return;
        }

        Arc2D arc = computeArc(x0, y0, rx, ry, angle, 
                               largeArcFlag, sweepFlag, x, y);
        if (arc == null) return;

        AffineTransform t = AffineTransform.getRotateInstance
            (Math.toRadians(angle), arc.getCenterX(), arc.getCenterY());
        Shape s = t.createTransformedShape(arc);
        path.append(s, true);
    }


    /** 
     * This constructs an unrotated Arc2D from the SVG specification of an 
     * Elliptical arc.  To get the final arc you need to apply a rotation
     * transform such as:
     * 
     * AffineTransform.getRotateInstance
     *     (angle, arc.getX()+arc.getWidth()/2, arc.getY()+arc.getHeight()/2);
     */
    public static Arc2D computeArc(double x0, double y0,
                                   double rx, double ry,
                                   double angle,
                                   boolean largeArcFlag,
                                   boolean sweepFlag,
                                   double x, double y) {
        //
        // Elliptical arc implementation based on the SVG specification notes
        //

        // Compute the half distance between the current and the final point
        double dx2 = (x0 - x) / 2.0;
        double dy2 = (y0 - y) / 2.0;
        // Convert angle from degrees to radians
        angle = Math.toRadians(angle % 360.0);
        double cosAngle = Math.cos(angle);
        double sinAngle = Math.sin(angle);

        //
        // Step 1 : Compute (x1, y1)
        //
        double x1 = (cosAngle * dx2 + sinAngle * dy2);
        double y1 = (-sinAngle * dx2 + cosAngle * dy2);
        // Ensure radii are large enough
        rx = Math.abs(rx);
        ry = Math.abs(ry);
        double Prx = rx * rx;
        double Pry = ry * ry;
        double Px1 = x1 * x1;
        double Py1 = y1 * y1;
        // check that radii are large enough
        double radiiCheck = Px1/Prx + Py1/Pry;
        if (radiiCheck > 1) {
            rx = Math.sqrt(radiiCheck) * rx;
            ry = Math.sqrt(radiiCheck) * ry;
            Prx = rx * rx;
            Pry = ry * ry;
        }

        //
        // Step 2 : Compute (cx1, cy1)
        //
        double sign = (largeArcFlag == sweepFlag) ? -1 : 1;
        double sq = ((Prx*Pry)-(Prx*Py1)-(Pry*Px1)) / ((Prx*Py1)+(Pry*Px1));
        sq = (sq < 0) ? 0 : sq;
        double coef = (sign * Math.sqrt(sq));
        double cx1 = coef * ((rx * y1) / ry);
        double cy1 = coef * -((ry * x1) / rx);

        //
        // Step 3 : Compute (cx, cy) from (cx1, cy1)
        //
        double sx2 = (x0 + x) / 2.0;
        double sy2 = (y0 + y) / 2.0;
        double cx = sx2 + (cosAngle * cx1 - sinAngle * cy1);
        double cy = sy2 + (sinAngle * cx1 + cosAngle * cy1);

        //
        // Step 4 : Compute the angleStart (angle1) and the angleExtent (dangle)
        //
        double ux = (x1 - cx1) / rx;
        double uy = (y1 - cy1) / ry;
        double vx = (-x1 - cx1) / rx;
        double vy = (-y1 - cy1) / ry;
        double p, n;
        // Compute the angle start
        n = Math.sqrt((ux * ux) + (uy * uy));
        p = ux; // (1 * ux) + (0 * uy)
        sign = (uy < 0) ? -1d : 1d;
        double angleStart = Math.toDegrees(sign * Math.acos(p / n));

        // Compute the angle extent
        n = Math.sqrt((ux * ux + uy * uy) * (vx * vx + vy * vy));
        p = ux * vx + uy * vy;
        sign = (ux * vy - uy * vx < 0) ? -1d : 1d;
        double angleExtent = Math.toDegrees(sign * Math.acos(p / n));
        if(!sweepFlag && angleExtent > 0) {
            angleExtent -= 360f;
        } else if (sweepFlag && angleExtent < 0) {
            angleExtent += 360f;
        }
        angleExtent %= 360f;
        angleStart %= 360f;

        //
        // We can now build the resulting Arc2D in double precision
        //
        Arc2D.Double arc = new Arc2D.Double();
        arc.x = cx - rx;
        arc.y = cy - ry;
        arc.width = rx * 2.0;
        arc.height = ry * 2.0;
        arc.start = -angleStart;
        arc.extent = -angleExtent;

        return arc;
    }

    public String toString()
    {
        return "A " + rx + " " + ry
             + " " + xAxisRot + " " + largeArc
             + " " + sweep
             + " " + x + " " + y;
    }
}