001    /*
002     * MoveTo.java
003     *
004     *
005     *  The Salamander Project - 2D and 3D graphics libraries in Java
006     *  Copyright (C) 2004 Mark McKay
007     *
008     *  This library is free software; you can redistribute it and/or
009     *  modify it under the terms of the GNU Lesser General Public
010     *  License as published by the Free Software Foundation; either
011     *  version 2.1 of the License, or (at your option) any later version.
012     *
013     *  This library is distributed in the hope that it will be useful,
014     *  but WITHOUT ANY WARRANTY; without even the implied warranty of
015     *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
016     *  Lesser General Public License for more details.
017     *
018     *  You should have received a copy of the GNU Lesser General Public
019     *  License along with this library; if not, write to the Free Software
020     *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
021     *
022     *  Mark McKay can be contacted at mark@kitfox.com.  Salamander and other
023     *  projects can be found at http://www.kitfox.com
024     *
025     * Created on January 26, 2004, 8:40 PM
026     */
027    
028    package com.kitfox.svg.pathcmd;
029    
030    //import org.apache.batik.ext.awt.geom.ExtendedGeneralPath;
031    import java.awt.*;
032    import java.awt.geom.*;
033    
034    /**
035     * This is a little used SVG function, as most editors will save curves as 
036     * Beziers.  To reduce the need to rely on the Batik library, this functionallity
037     * is being bypassed for the time being.  In the future, it would be nice to
038     * extend the GeneralPath command to include the arcTo ability provided by Batik.
039     *
040     * @author Mark McKay
041     * @author <a href="mailto:mark@kitfox.com">Mark McKay</a>
042     */
043    public class Arc extends PathCommand 
044    {
045    
046        public float rx = 0f;
047        public float ry = 0f;
048        public float xAxisRot = 0f;
049        public boolean largeArc = false;
050        public boolean sweep = false;
051        public float x = 0f;
052        public float y = 0f;
053    
054        /** Creates a new instance of MoveTo */
055        public Arc() {
056        }
057    
058        public Arc(boolean isRelative, float rx, float ry, float xAxisRot, boolean largeArc, boolean sweep, float x, float y) {
059            super(isRelative);
060            this.rx = rx;
061            this.ry = ry;
062            this.xAxisRot = xAxisRot;
063            this.largeArc = largeArc;
064            this.sweep = sweep;
065            this.x = x;
066            this.y = y;
067        }
068    
069    //    public void appendPath(ExtendedGeneralPath path, BuildHistory hist)
070        public void appendPath(GeneralPath path, BuildHistory hist)
071        {
072            float offx = isRelative ? hist.history[0].x : 0f;
073            float offy = isRelative ? hist.history[0].y : 0f;
074    
075            arcTo(path, rx, ry, xAxisRot, largeArc, sweep, x + offx, y + offy, hist.history[0].x, hist.history[0].y);
076    //        path.lineTo(x + offx, y + offy);
077            hist.setPoint(x + offx, y + offy);
078        }
079    
080        public int getNumKnotsAdded()
081        {
082            return 6;
083        }
084    
085        /**
086         * Adds an elliptical arc, defined by two radii, an angle from the
087         * x-axis, a flag to choose the large arc or not, a flag to
088         * indicate if we increase or decrease the angles and the final
089         * point of the arc.
090         *
091         * @param rx the x radius of the ellipse
092         * @param ry the y radius of the ellipse
093         *
094         * @param angle the angle from the x-axis of the current
095         * coordinate system to the x-axis of the ellipse in degrees.
096         *
097         * @param largeArcFlag the large arc flag. If true the arc
098         * spanning less than or equal to 180 degrees is chosen, otherwise
099         * the arc spanning greater than 180 degrees is chosen
100         *
101         * @param sweepFlag the sweep flag. If true the line joining
102         * center to arc sweeps through decreasing angles otherwise it
103         * sweeps through increasing angles
104         *
105         * @param x the absolute x coordinate of the final point of the arc.
106         * @param y the absolute y coordinate of the final point of the arc.
107         * @param x0 - The absolute x coordinate of the initial point of the arc.
108         * @param y0 - The absolute y coordinate of the initial point of the arc.
109         */
110        public void arcTo(GeneralPath path, float rx, float ry,
111                                       float angle,
112                                       boolean largeArcFlag,
113                                       boolean sweepFlag,
114                                       float x, float y, float x0, float y0) 
115        {
116    
117            // Ensure radii are valid
118            if (rx == 0 || ry == 0) {
119                path.lineTo((float) x, (float) y);
120                return;
121            }
122    
123            if (x0 == x && y0 == y) {
124                // If the endpoints (x, y) and (x0, y0) are identical, then this
125                // is equivalent to omitting the elliptical arc segment entirely.
126                return;
127            }
128    
129            Arc2D arc = computeArc(x0, y0, rx, ry, angle, 
130                                   largeArcFlag, sweepFlag, x, y);
131            if (arc == null) return;
132    
133            AffineTransform t = AffineTransform.getRotateInstance
134                (Math.toRadians(angle), arc.getCenterX(), arc.getCenterY());
135            Shape s = t.createTransformedShape(arc);
136            path.append(s, true);
137        }
138    
139    
140        /** 
141         * This constructs an unrotated Arc2D from the SVG specification of an 
142         * Elliptical arc.  To get the final arc you need to apply a rotation
143         * transform such as:
144         * 
145         * AffineTransform.getRotateInstance
146         *     (angle, arc.getX()+arc.getWidth()/2, arc.getY()+arc.getHeight()/2);
147         */
148        public static Arc2D computeArc(double x0, double y0,
149                                       double rx, double ry,
150                                       double angle,
151                                       boolean largeArcFlag,
152                                       boolean sweepFlag,
153                                       double x, double y) {
154            //
155            // Elliptical arc implementation based on the SVG specification notes
156            //
157    
158            // Compute the half distance between the current and the final point
159            double dx2 = (x0 - x) / 2.0;
160            double dy2 = (y0 - y) / 2.0;
161            // Convert angle from degrees to radians
162            angle = Math.toRadians(angle % 360.0);
163            double cosAngle = Math.cos(angle);
164            double sinAngle = Math.sin(angle);
165    
166            //
167            // Step 1 : Compute (x1, y1)
168            //
169            double x1 = (cosAngle * dx2 + sinAngle * dy2);
170            double y1 = (-sinAngle * dx2 + cosAngle * dy2);
171            // Ensure radii are large enough
172            rx = Math.abs(rx);
173            ry = Math.abs(ry);
174            double Prx = rx * rx;
175            double Pry = ry * ry;
176            double Px1 = x1 * x1;
177            double Py1 = y1 * y1;
178            // check that radii are large enough
179            double radiiCheck = Px1/Prx + Py1/Pry;
180            if (radiiCheck > 1) {
181                rx = Math.sqrt(radiiCheck) * rx;
182                ry = Math.sqrt(radiiCheck) * ry;
183                Prx = rx * rx;
184                Pry = ry * ry;
185            }
186    
187            //
188            // Step 2 : Compute (cx1, cy1)
189            //
190            double sign = (largeArcFlag == sweepFlag) ? -1 : 1;
191            double sq = ((Prx*Pry)-(Prx*Py1)-(Pry*Px1)) / ((Prx*Py1)+(Pry*Px1));
192            sq = (sq < 0) ? 0 : sq;
193            double coef = (sign * Math.sqrt(sq));
194            double cx1 = coef * ((rx * y1) / ry);
195            double cy1 = coef * -((ry * x1) / rx);
196    
197            //
198            // Step 3 : Compute (cx, cy) from (cx1, cy1)
199            //
200            double sx2 = (x0 + x) / 2.0;
201            double sy2 = (y0 + y) / 2.0;
202            double cx = sx2 + (cosAngle * cx1 - sinAngle * cy1);
203            double cy = sy2 + (sinAngle * cx1 + cosAngle * cy1);
204    
205            //
206            // Step 4 : Compute the angleStart (angle1) and the angleExtent (dangle)
207            //
208            double ux = (x1 - cx1) / rx;
209            double uy = (y1 - cy1) / ry;
210            double vx = (-x1 - cx1) / rx;
211            double vy = (-y1 - cy1) / ry;
212            double p, n;
213            // Compute the angle start
214            n = Math.sqrt((ux * ux) + (uy * uy));
215            p = ux; // (1 * ux) + (0 * uy)
216            sign = (uy < 0) ? -1d : 1d;
217            double angleStart = Math.toDegrees(sign * Math.acos(p / n));
218    
219            // Compute the angle extent
220            n = Math.sqrt((ux * ux + uy * uy) * (vx * vx + vy * vy));
221            p = ux * vx + uy * vy;
222            sign = (ux * vy - uy * vx < 0) ? -1d : 1d;
223            double angleExtent = Math.toDegrees(sign * Math.acos(p / n));
224            if(!sweepFlag && angleExtent > 0) {
225                angleExtent -= 360f;
226            } else if (sweepFlag && angleExtent < 0) {
227                angleExtent += 360f;
228            }
229            angleExtent %= 360f;
230            angleStart %= 360f;
231    
232            //
233            // We can now build the resulting Arc2D in double precision
234            //
235            Arc2D.Double arc = new Arc2D.Double();
236            arc.x = cx - rx;
237            arc.y = cy - ry;
238            arc.width = rx * 2.0;
239            arc.height = ry * 2.0;
240            arc.start = -angleStart;
241            arc.extent = -angleExtent;
242    
243            return arc;
244        }
245    }