001/*
002 * SVG Salamander
003 * Copyright (c) 2004, Mark McKay
004 * All rights reserved.
005 *
006 * Redistribution and use in source and binary forms, with or 
007 * without modification, are permitted provided that the following
008 * conditions are met:
009 *
010 *   - Redistributions of source code must retain the above 
011 *     copyright notice, this list of conditions and the following
012 *     disclaimer.
013 *   - Redistributions in binary form must reproduce the above
014 *     copyright notice, this list of conditions and the following
015 *     disclaimer in the documentation and/or other materials 
016 *     provided with the distribution.
017 *
018 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
019 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
020 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
021 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
022 * COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
023 * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
024 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
025 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
026 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
027 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
028 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
029 * OF THE POSSIBILITY OF SUCH DAMAGE. 
030 * 
031 * Mark McKay can be contacted at mark@kitfox.com.  Salamander and other
032 * projects can be found at http://www.kitfox.com
033 *
034 * Created on January 26, 2004, 8:40 PM
035 */
036
037package com.kitfox.svg.pathcmd;
038
039//import org.apache.batik.ext.awt.geom.ExtendedGeneralPath;
040import java.awt.*;
041import java.awt.geom.*;
042
043/**
044 * This is a little used SVG function, as most editors will save curves as 
045 * Beziers.  To reduce the need to rely on the Batik library, this functionallity
046 * is being bypassed for the time being.  In the future, it would be nice to
047 * extend the GeneralPath command to include the arcTo ability provided by Batik.
048 *
049 * @author Mark McKay
050 * @author <a href="mailto:mark@kitfox.com">Mark McKay</a>
051 */
052public class Arc extends PathCommand 
053{
054
055    public float rx = 0f;
056    public float ry = 0f;
057    public float xAxisRot = 0f;
058    public boolean largeArc = false;
059    public boolean sweep = false;
060    public float x = 0f;
061    public float y = 0f;
062
063    /** Creates a new instance of MoveTo */
064    public Arc() {
065    }
066
067    public Arc(boolean isRelative, float rx, float ry, float xAxisRot, boolean largeArc, boolean sweep, float x, float y) {
068        super(isRelative);
069        this.rx = rx;
070        this.ry = ry;
071        this.xAxisRot = xAxisRot;
072        this.largeArc = largeArc;
073        this.sweep = sweep;
074        this.x = x;
075        this.y = y;
076    }
077
078//    public void appendPath(ExtendedGeneralPath path, BuildHistory hist)
079    public void appendPath(GeneralPath path, BuildHistory hist)
080    {
081        float offx = isRelative ? hist.lastPoint.x : 0f;
082        float offy = isRelative ? hist.lastPoint.y : 0f;
083
084        arcTo(path, rx, ry, xAxisRot, largeArc, sweep,
085            x + offx, y + offy,
086            hist.lastPoint.x, hist.lastPoint.y);
087//        path.lineTo(x + offx, y + offy);
088//        hist.setPoint(x + offx, y + offy);
089        hist.setLastPoint(x + offx, y + offy);
090        hist.setLastKnot(x + offx, y + offy);
091    }
092
093    public int getNumKnotsAdded()
094    {
095        return 6;
096    }
097
098    /**
099     * Adds an elliptical arc, defined by two radii, an angle from the
100     * x-axis, a flag to choose the large arc or not, a flag to
101     * indicate if we increase or decrease the angles and the final
102     * point of the arc.
103     *
104     * @param rx the x radius of the ellipse
105     * @param ry the y radius of the ellipse
106     *
107     * @param angle the angle from the x-axis of the current
108     * coordinate system to the x-axis of the ellipse in degrees.
109     *
110     * @param largeArcFlag the large arc flag. If true the arc
111     * spanning less than or equal to 180 degrees is chosen, otherwise
112     * the arc spanning greater than 180 degrees is chosen
113     *
114     * @param sweepFlag the sweep flag. If true the line joining
115     * center to arc sweeps through decreasing angles otherwise it
116     * sweeps through increasing angles
117     *
118     * @param x the absolute x coordinate of the final point of the arc.
119     * @param y the absolute y coordinate of the final point of the arc.
120     * @param x0 - The absolute x coordinate of the initial point of the arc.
121     * @param y0 - The absolute y coordinate of the initial point of the arc.
122     */
123    public void arcTo(GeneralPath path, float rx, float ry,
124                                   float angle,
125                                   boolean largeArcFlag,
126                                   boolean sweepFlag,
127                                   float x, float y, float x0, float y0) 
128    {
129
130        // Ensure radii are valid
131        if (rx == 0 || ry == 0) {
132            path.lineTo((float) x, (float) y);
133            return;
134        }
135
136        if (x0 == x && y0 == y) {
137            // If the endpoints (x, y) and (x0, y0) are identical, then this
138            // is equivalent to omitting the elliptical arc segment entirely.
139            return;
140        }
141
142        Arc2D arc = computeArc(x0, y0, rx, ry, angle, 
143                               largeArcFlag, sweepFlag, x, y);
144        if (arc == null) return;
145
146        AffineTransform t = AffineTransform.getRotateInstance
147            (Math.toRadians(angle), arc.getCenterX(), arc.getCenterY());
148        Shape s = t.createTransformedShape(arc);
149        path.append(s, true);
150    }
151
152
153    /** 
154     * This constructs an unrotated Arc2D from the SVG specification of an 
155     * Elliptical arc.  To get the final arc you need to apply a rotation
156     * transform such as:
157     * 
158     * AffineTransform.getRotateInstance
159     *     (angle, arc.getX()+arc.getWidth()/2, arc.getY()+arc.getHeight()/2);
160     */
161    public static Arc2D computeArc(double x0, double y0,
162                                   double rx, double ry,
163                                   double angle,
164                                   boolean largeArcFlag,
165                                   boolean sweepFlag,
166                                   double x, double y) {
167        //
168        // Elliptical arc implementation based on the SVG specification notes
169        //
170
171        // Compute the half distance between the current and the final point
172        double dx2 = (x0 - x) / 2.0;
173        double dy2 = (y0 - y) / 2.0;
174        // Convert angle from degrees to radians
175        angle = Math.toRadians(angle % 360.0);
176        double cosAngle = Math.cos(angle);
177        double sinAngle = Math.sin(angle);
178
179        //
180        // Step 1 : Compute (x1, y1)
181        //
182        double x1 = (cosAngle * dx2 + sinAngle * dy2);
183        double y1 = (-sinAngle * dx2 + cosAngle * dy2);
184        // Ensure radii are large enough
185        rx = Math.abs(rx);
186        ry = Math.abs(ry);
187        double Prx = rx * rx;
188        double Pry = ry * ry;
189        double Px1 = x1 * x1;
190        double Py1 = y1 * y1;
191        // check that radii are large enough
192        double radiiCheck = Px1/Prx + Py1/Pry;
193        if (radiiCheck > 1) {
194            rx = Math.sqrt(radiiCheck) * rx;
195            ry = Math.sqrt(radiiCheck) * ry;
196            Prx = rx * rx;
197            Pry = ry * ry;
198        }
199
200        //
201        // Step 2 : Compute (cx1, cy1)
202        //
203        double sign = (largeArcFlag == sweepFlag) ? -1 : 1;
204        double sq = ((Prx*Pry)-(Prx*Py1)-(Pry*Px1)) / ((Prx*Py1)+(Pry*Px1));
205        sq = (sq < 0) ? 0 : sq;
206        double coef = (sign * Math.sqrt(sq));
207        double cx1 = coef * ((rx * y1) / ry);
208        double cy1 = coef * -((ry * x1) / rx);
209
210        //
211        // Step 3 : Compute (cx, cy) from (cx1, cy1)
212        //
213        double sx2 = (x0 + x) / 2.0;
214        double sy2 = (y0 + y) / 2.0;
215        double cx = sx2 + (cosAngle * cx1 - sinAngle * cy1);
216        double cy = sy2 + (sinAngle * cx1 + cosAngle * cy1);
217
218        //
219        // Step 4 : Compute the angleStart (angle1) and the angleExtent (dangle)
220        //
221        double ux = (x1 - cx1) / rx;
222        double uy = (y1 - cy1) / ry;
223        double vx = (-x1 - cx1) / rx;
224        double vy = (-y1 - cy1) / ry;
225        double p, n;
226        // Compute the angle start
227        n = Math.sqrt((ux * ux) + (uy * uy));
228        p = ux; // (1 * ux) + (0 * uy)
229        sign = (uy < 0) ? -1d : 1d;
230        double angleStart = Math.toDegrees(sign * Math.acos(p / n));
231
232        // Compute the angle extent
233        n = Math.sqrt((ux * ux + uy * uy) * (vx * vx + vy * vy));
234        p = ux * vx + uy * vy;
235        sign = (ux * vy - uy * vx < 0) ? -1d : 1d;
236        double angleExtent = Math.toDegrees(sign * Math.acos(p / n));
237        if(!sweepFlag && angleExtent > 0) {
238            angleExtent -= 360f;
239        } else if (sweepFlag && angleExtent < 0) {
240            angleExtent += 360f;
241        }
242        angleExtent %= 360f;
243        angleStart %= 360f;
244
245        //
246        // We can now build the resulting Arc2D in double precision
247        //
248        Arc2D.Double arc = new Arc2D.Double();
249        arc.x = cx - rx;
250        arc.y = cy - ry;
251        arc.width = rx * 2.0;
252        arc.height = ry * 2.0;
253        arc.start = -angleStart;
254        arc.extent = -angleExtent;
255
256        return arc;
257    }
258
259    public String toString()
260    {
261        return "A " + rx + " " + ry
262             + " " + xAxisRot + " " + largeArc
263             + " " + sweep
264             + " " + x + " " + y;
265    }
266}