diff options
Diffstat (limited to 'libjava/classpath/java/awt/geom/Area.java')
| -rw-r--r-- | libjava/classpath/java/awt/geom/Area.java | 3312 |
1 files changed, 3312 insertions, 0 deletions
diff --git a/libjava/classpath/java/awt/geom/Area.java b/libjava/classpath/java/awt/geom/Area.java new file mode 100644 index 0000000..7a0fac4 --- /dev/null +++ b/libjava/classpath/java/awt/geom/Area.java @@ -0,0 +1,3312 @@ +/* Area.java -- represents a shape built by constructive area geometry + Copyright (C) 2002, 2004 Free Software Foundation + +This file is part of GNU Classpath. + +GNU Classpath is free software; you can redistribute it and/or modify +it under the terms of the GNU General Public License as published by +the Free Software Foundation; either version 2, or (at your option) +any later version. + +GNU Classpath is distributed in the hope that it will be useful, but +WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +General Public License for more details. + +You should have received a copy of the GNU General Public License +along with GNU Classpath; see the file COPYING. If not, write to the +Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA +02110-1301 USA. + +Linking this library statically or dynamically with other modules is +making a combined work based on this library. Thus, the terms and +conditions of the GNU General Public License cover the whole +combination. + +As a special exception, the copyright holders of this library give you +permission to link this library with independent modules to produce an +executable, regardless of the license terms of these independent +modules, and to copy and distribute the resulting executable under +terms of your choice, provided that you also meet, for each linked +independent module, the terms and conditions of the license of that +module. An independent module is a module which is not derived from +or based on this library. If you modify this library, you may extend +this exception to your version of the library, but you are not +obligated to do so. If you do not wish to do so, delete this +exception statement from your version. */ + +package java.awt.geom; + +import java.awt.Rectangle; +import java.awt.Shape; +import java.util.Vector; + + +/** + * The Area class represents any area for the purpose of + * Constructive Area Geometry (CAG) manipulations. CAG manipulations + * work as an area-wise form of boolean logic, where the basic operations are: + * <P><li>Add (in boolean algebra: A <B>or</B> B)<BR> + * <li>Subtract (in boolean algebra: A <B>and</B> (<B>not</B> B) )<BR> + * <li>Intersect (in boolean algebra: A <B>and</B> B)<BR> + * <li>Exclusive Or <BR> + * <img src="doc-files/Area-1.png" width="342" height="302" + * alt="Illustration of CAG operations" /><BR> + * Above is an illustration of the CAG operations on two ring shapes.<P> + * + * The contains and intersects() methods are also more accurate than the + * specification of #Shape requires.<P> + * + * Please note that constructing an Area can be slow + * (Self-intersection resolving is proportional to the square of + * the number of segments).<P> + * @see #add(Area) + * @see #subtract(Area) + * @see #intersect(Area) + * @see #exclusiveOr(Area) + * + * @author Sven de Marothy (sven@physto.se) + * + * @since 1.2 + * @status Works, but could be faster and more reliable. + */ +public class Area implements Shape, Cloneable +{ + /** + * General numerical precision + */ + private static final double EPSILON = 1E-11; + + /** + * recursive subdivision epsilon - (see getRecursionDepth) + */ + private static final double RS_EPSILON = 1E-13; + + /** + * Snap distance - points within this distance are considered equal + */ + private static final double PE_EPSILON = 1E-11; + + /** + * Segment vectors containing solid areas and holes + * This is package-private to avoid an accessor method. + */ + Vector solids; + + /** + * Segment vectors containing solid areas and holes + * This is package-private to avoid an accessor method. + */ + Vector holes; + + /** + * Vector (temporary) storing curve-curve intersections + */ + private Vector cc_intersections; + + /** + * Winding rule WIND_NON_ZERO used, after construction, + * this is irrelevant. + */ + private int windingRule; + + /** + * Constructs an empty Area + */ + public Area() + { + solids = new Vector(); + holes = new Vector(); + } + + /** + * Constructs an Area from any given Shape. <P> + * + * If the Shape is self-intersecting, the created Area will consist + * of non-self-intersecting subpaths, and any inner paths which + * are found redundant in accordance with the Shape's winding rule + * will not be included. + * + * @param s the shape (<code>null</code> not permitted). + * + * @throws NullPointerException if <code>s</code> is <code>null</code>. + */ + public Area(Shape s) + { + this(); + + Vector p = makeSegment(s); + + // empty path + if (p == null) + return; + + // delete empty paths + for (int i = 0; i < p.size(); i++) + if (((Segment) p.elementAt(i)).getSignedArea() == 0.0) + p.remove(i--); + + /* + * Resolve self intersecting paths into non-intersecting + * solids and holes. + * Algorithm is as follows: + * 1: Create nodes at all self intersections + * 2: Put all segments into a list + * 3: Grab a segment, follow it, change direction at each node, + * removing segments from the list in the process + * 4: Repeat (3) until no segments remain in the list + * 5: Remove redundant paths and sort into solids and holes + */ + Vector paths = new Vector(); + Segment v; + + for (int i = 0; i < p.size(); i++) + { + Segment path = (Segment) p.elementAt(i); + createNodesSelf(path); + } + + if (p.size() > 1) + { + for (int i = 0; i < p.size() - 1; i++) + for (int j = i + 1; j < p.size(); j++) + { + Segment path1 = (Segment) p.elementAt(i); + Segment path2 = (Segment) p.elementAt(j); + createNodes(path1, path2); + } + } + + // we have intersecting points. + Vector segments = new Vector(); + + for (int i = 0; i < p.size(); i++) + { + Segment path = v = (Segment) p.elementAt(i); + do + { + segments.add(v); + v = v.next; + } + while (v != path); + } + + paths = weilerAtherton(segments); + deleteRedundantPaths(paths); + } + + /** + * Performs an add (union) operation on this area with another Area.<BR> + * @param area - the area to be unioned with this one + */ + public void add(Area area) + { + if (equals(area)) + return; + if (area.isEmpty()) + return; + + Area B = (Area) area.clone(); + + Vector pathA = new Vector(); + Vector pathB = new Vector(); + pathA.addAll(solids); + pathA.addAll(holes); + pathB.addAll(B.solids); + pathB.addAll(B.holes); + + int nNodes = 0; + + for (int i = 0; i < pathA.size(); i++) + { + Segment a = (Segment) pathA.elementAt(i); + for (int j = 0; j < pathB.size(); j++) + { + Segment b = (Segment) pathB.elementAt(j); + nNodes += createNodes(a, b); + } + } + + Vector paths = new Vector(); + Segment v; + + // we have intersecting points. + Vector segments = new Vector(); + + // In a union operation, we keep all + // segments of A oustide B and all B outside A + for (int i = 0; i < pathA.size(); i++) + { + v = (Segment) pathA.elementAt(i); + Segment path = v; + do + { + if (v.isSegmentOutside(area)) + segments.add(v); + v = v.next; + } + while (v != path); + } + + for (int i = 0; i < pathB.size(); i++) + { + v = (Segment) pathB.elementAt(i); + Segment path = v; + do + { + if (v.isSegmentOutside(this)) + segments.add(v); + v = v.next; + } + while (v != path); + } + + paths = weilerAtherton(segments); + deleteRedundantPaths(paths); + } + + /** + * Performs a subtraction operation on this Area.<BR> + * @param area the area to be subtracted from this area. + * @throws NullPointerException if <code>area</code> is <code>null</code>. + */ + public void subtract(Area area) + { + if (isEmpty() || area.isEmpty()) + return; + + if (equals(area)) + { + reset(); + return; + } + + Vector pathA = new Vector(); + Area B = (Area) area.clone(); + pathA.addAll(solids); + pathA.addAll(holes); + + // reverse the directions of B paths. + setDirection(B.holes, true); + setDirection(B.solids, false); + + Vector pathB = new Vector(); + pathB.addAll(B.solids); + pathB.addAll(B.holes); + + int nNodes = 0; + + // create nodes + for (int i = 0; i < pathA.size(); i++) + { + Segment a = (Segment) pathA.elementAt(i); + for (int j = 0; j < pathB.size(); j++) + { + Segment b = (Segment) pathB.elementAt(j); + nNodes += createNodes(a, b); + } + } + + Vector paths = new Vector(); + + // we have intersecting points. + Vector segments = new Vector(); + + // In a subtraction operation, we keep all + // segments of A oustide B and all B within A + // We outsideness-test only one segment in each path + // and the segments before and after any node + for (int i = 0; i < pathA.size(); i++) + { + Segment v = (Segment) pathA.elementAt(i); + Segment path = v; + if (v.isSegmentOutside(area) && v.node == null) + segments.add(v); + boolean node = false; + do + { + if ((v.node != null || node)) + { + node = (v.node != null); + if (v.isSegmentOutside(area)) + segments.add(v); + } + v = v.next; + } + while (v != path); + } + + for (int i = 0; i < pathB.size(); i++) + { + Segment v = (Segment) pathB.elementAt(i); + Segment path = v; + if (! v.isSegmentOutside(this) && v.node == null) + segments.add(v); + v = v.next; + boolean node = false; + do + { + if ((v.node != null || node)) + { + node = (v.node != null); + if (! v.isSegmentOutside(this)) + segments.add(v); + } + v = v.next; + } + while (v != path); + } + + paths = weilerAtherton(segments); + deleteRedundantPaths(paths); + } + + /** + * Performs an intersection operation on this Area.<BR> + * @param area - the area to be intersected with this area. + * @throws NullPointerException if <code>area</code> is <code>null</code>. + */ + public void intersect(Area area) + { + if (isEmpty() || area.isEmpty()) + { + reset(); + return; + } + if (equals(area)) + return; + + Vector pathA = new Vector(); + Area B = (Area) area.clone(); + pathA.addAll(solids); + pathA.addAll(holes); + + Vector pathB = new Vector(); + pathB.addAll(B.solids); + pathB.addAll(B.holes); + + int nNodes = 0; + + // create nodes + for (int i = 0; i < pathA.size(); i++) + { + Segment a = (Segment) pathA.elementAt(i); + for (int j = 0; j < pathB.size(); j++) + { + Segment b = (Segment) pathB.elementAt(j); + nNodes += createNodes(a, b); + } + } + + Vector paths = new Vector(); + + // we have intersecting points. + Vector segments = new Vector(); + + // In an intersection operation, we keep all + // segments of A within B and all B within A + // (The rest must be redundant) + // We outsideness-test only one segment in each path + // and the segments before and after any node + for (int i = 0; i < pathA.size(); i++) + { + Segment v = (Segment) pathA.elementAt(i); + Segment path = v; + if (! v.isSegmentOutside(area) && v.node == null) + segments.add(v); + boolean node = false; + do + { + if ((v.node != null || node)) + { + node = (v.node != null); + if (! v.isSegmentOutside(area)) + segments.add(v); + } + v = v.next; + } + while (v != path); + } + + for (int i = 0; i < pathB.size(); i++) + { + Segment v = (Segment) pathB.elementAt(i); + Segment path = v; + if (! v.isSegmentOutside(this) && v.node == null) + segments.add(v); + v = v.next; + boolean node = false; + do + { + if ((v.node != null || node)) + { + node = (v.node != null); + if (! v.isSegmentOutside(this)) + segments.add(v); + } + v = v.next; + } + while (v != path); + } + + paths = weilerAtherton(segments); + deleteRedundantPaths(paths); + } + + /** + * Performs an exclusive-or operation on this Area.<BR> + * @param area - the area to be XORed with this area. + * @throws NullPointerException if <code>area</code> is <code>null</code>. + */ + public void exclusiveOr(Area area) + { + if (area.isEmpty()) + return; + + if (isEmpty()) + { + Area B = (Area) area.clone(); + solids = B.solids; + holes = B.holes; + return; + } + if (equals(area)) + { + reset(); + return; + } + + Vector pathA = new Vector(); + + Area B = (Area) area.clone(); + Vector pathB = new Vector(); + pathA.addAll(solids); + pathA.addAll(holes); + + // reverse the directions of B paths. + setDirection(B.holes, true); + setDirection(B.solids, false); + pathB.addAll(B.solids); + pathB.addAll(B.holes); + + int nNodes = 0; + + for (int i = 0; i < pathA.size(); i++) + { + Segment a = (Segment) pathA.elementAt(i); + for (int j = 0; j < pathB.size(); j++) + { + Segment b = (Segment) pathB.elementAt(j); + nNodes += createNodes(a, b); + } + } + + Vector paths = new Vector(); + Segment v; + + // we have intersecting points. + Vector segments = new Vector(); + + // In an XOR operation, we operate on all segments + for (int i = 0; i < pathA.size(); i++) + { + v = (Segment) pathA.elementAt(i); + Segment path = v; + do + { + segments.add(v); + v = v.next; + } + while (v != path); + } + + for (int i = 0; i < pathB.size(); i++) + { + v = (Segment) pathB.elementAt(i); + Segment path = v; + do + { + segments.add(v); + v = v.next; + } + while (v != path); + } + + paths = weilerAtherton(segments); + deleteRedundantPaths(paths); + } + + /** + * Clears the Area object, creating an empty area. + */ + public void reset() + { + solids = new Vector(); + holes = new Vector(); + } + + /** + * Returns whether this area encloses any area. + * @return true if the object encloses any area. + */ + public boolean isEmpty() + { + if (solids.size() == 0) + return true; + + double totalArea = 0; + for (int i = 0; i < solids.size(); i++) + totalArea += Math.abs(((Segment) solids.elementAt(i)).getSignedArea()); + for (int i = 0; i < holes.size(); i++) + totalArea -= Math.abs(((Segment) holes.elementAt(i)).getSignedArea()); + if (totalArea <= EPSILON) + return true; + + return false; + } + + /** + * Determines whether the Area consists entirely of line segments + * @return true if the Area lines-only, false otherwise + */ + public boolean isPolygonal() + { + for (int i = 0; i < holes.size(); i++) + if (! ((Segment) holes.elementAt(i)).isPolygonal()) + return false; + for (int i = 0; i < solids.size(); i++) + if (! ((Segment) solids.elementAt(i)).isPolygonal()) + return false; + return true; + } + + /** + * Determines if the Area is rectangular.<P> + * + * This is strictly qualified. An area is considered rectangular if:<BR> + * <li>It consists of a single polygonal path.<BR> + * <li>It is oriented parallel/perpendicular to the xy axis<BR> + * <li>It must be exactly rectangular, i.e. small errors induced by + * transformations may cause a false result, although the area is + * visibly rectangular.<P> + * @return true if the above criteria are met, false otherwise + */ + public boolean isRectangular() + { + if (isEmpty()) + return true; + + if (holes.size() != 0 || solids.size() != 1) + return false; + + Segment path = (Segment) solids.elementAt(0); + if (! path.isPolygonal()) + return false; + + int nCorners = 0; + Segment s = path; + do + { + Segment s2 = s.next; + double d1 = (s.P2.getX() - s.P1.getX())*(s2.P2.getX() - s2.P1.getX())/ + ((s.P1.distance(s.P2)) * (s2.P1.distance(s2.P2))); + double d2 = (s.P2.getY() - s.P1.getY())*(s2.P2.getY() - s2.P1.getY())/ + ((s.P1.distance(s.P2)) * (s2.P1.distance(s2.P2))); + double dotproduct = d1 + d2; + + // For some reason, only rectangles on the XY axis count. + if (d1 != 0 && d2 != 0) + return false; + + if (Math.abs(dotproduct) == 0) // 90 degree angle + nCorners++; + else if ((Math.abs(1.0 - dotproduct) > 0)) // 0 degree angle? + return false; // if not, return false + + s = s.next; + } + while (s != path); + + return nCorners == 4; + } + + /** + * Returns whether the Area consists of more than one simple + * (non self-intersecting) subpath. + * + * @return true if the Area consists of none or one simple subpath, + * false otherwise. + */ + public boolean isSingular() + { + return (holes.size() == 0 && solids.size() <= 1); + } + + /** + * Returns the bounding box of the Area.<P> Unlike the CubicCurve2D and + * QuadraticCurve2D classes, this method will return the tightest possible + * bounding box, evaluating the extreme points of each curved segment.<P> + * @return the bounding box + */ + public Rectangle2D getBounds2D() + { + if (solids.size() == 0) + return new Rectangle2D.Double(0.0, 0.0, 0.0, 0.0); + + double xmin; + double xmax; + double ymin; + double ymax; + xmin = xmax = ((Segment) solids.elementAt(0)).P1.getX(); + ymin = ymax = ((Segment) solids.elementAt(0)).P1.getY(); + + for (int path = 0; path < solids.size(); path++) + { + Rectangle2D r = ((Segment) solids.elementAt(path)).getPathBounds(); + xmin = Math.min(r.getMinX(), xmin); + ymin = Math.min(r.getMinY(), ymin); + xmax = Math.max(r.getMaxX(), xmax); + ymax = Math.max(r.getMaxY(), ymax); + } + + return (new Rectangle2D.Double(xmin, ymin, (xmax - xmin), (ymax - ymin))); + } + + /** + * Returns the bounds of this object in Rectangle format. + * Please note that this may lead to loss of precision. + * + * @return The bounds. + * @see #getBounds2D() + */ + public Rectangle getBounds() + { + return getBounds2D().getBounds(); + } + + /** + * Create a new area of the same run-time type with the same contents as + * this one. + * + * @return the clone + */ + public Object clone() + { + try + { + Area clone = new Area(); + for (int i = 0; i < solids.size(); i++) + clone.solids.add(((Segment) solids.elementAt(i)).cloneSegmentList()); + for (int i = 0; i < holes.size(); i++) + clone.holes.add(((Segment) holes.elementAt(i)).cloneSegmentList()); + return clone; + } + catch (CloneNotSupportedException e) + { + throw (Error) new InternalError().initCause(e); // Impossible + } + } + + /** + * Compares two Areas. + * + * @param area the area to compare against this area (<code>null</code> + * permitted). + * @return <code>true</code> if the areas are equal, and <code>false</code> + * otherwise. + */ + public boolean equals(Area area) + { + if (area == null) + return false; + + if (! getBounds2D().equals(area.getBounds2D())) + return false; + + if (solids.size() != area.solids.size() + || holes.size() != area.holes.size()) + return false; + + Vector pathA = new Vector(); + pathA.addAll(solids); + pathA.addAll(holes); + Vector pathB = new Vector(); + pathB.addAll(area.solids); + pathB.addAll(area.holes); + + int nPaths = pathA.size(); + boolean[][] match = new boolean[2][nPaths]; + + for (int i = 0; i < nPaths; i++) + { + for (int j = 0; j < nPaths; j++) + { + Segment p1 = (Segment) pathA.elementAt(i); + Segment p2 = (Segment) pathB.elementAt(j); + if (! match[0][i] && ! match[1][j]) + if (p1.pathEquals(p2)) + match[0][i] = match[1][j] = true; + } + } + + boolean result = true; + for (int i = 0; i < nPaths; i++) + result = result && match[0][i] && match[1][i]; + return result; + } + + /** + * Transforms this area by the AffineTransform at. + * + * @param at the transform. + */ + public void transform(AffineTransform at) + { + for (int i = 0; i < solids.size(); i++) + ((Segment) solids.elementAt(i)).transformSegmentList(at); + for (int i = 0; i < holes.size(); i++) + ((Segment) holes.elementAt(i)).transformSegmentList(at); + + // Note that the orientation is not invariant under inversion + if ((at.getType() & AffineTransform.TYPE_FLIP) != 0) + { + setDirection(holes, false); + setDirection(solids, true); + } + } + + /** + * Returns a new Area equal to this one, transformed + * by the AffineTransform at. + * @param at the transform. + * @return the transformed area + * @throws NullPointerException if <code>at</code> is <code>null</code>. + */ + public Area createTransformedArea(AffineTransform at) + { + Area a = (Area) clone(); + a.transform(at); + return a; + } + + /** + * Determines if the point (x,y) is contained within this Area. + * + * @param x the x-coordinate of the point. + * @param y the y-coordinate of the point. + * @return true if the point is contained, false otherwise. + */ + public boolean contains(double x, double y) + { + int n = 0; + for (int i = 0; i < solids.size(); i++) + if (((Segment) solids.elementAt(i)).contains(x, y)) + n++; + + for (int i = 0; i < holes.size(); i++) + if (((Segment) holes.elementAt(i)).contains(x, y)) + n--; + + return (n != 0); + } + + /** + * Determines if the Point2D p is contained within this Area. + * + * @param p the point. + * @return <code>true</code> if the point is contained, <code>false</code> + * otherwise. + * @throws NullPointerException if <code>p</code> is <code>null</code>. + */ + public boolean contains(Point2D p) + { + return contains(p.getX(), p.getY()); + } + + /** + * Determines if the rectangle specified by (x,y) as the upper-left + * and with width w and height h is completely contained within this Area, + * returns false otherwise.<P> + * + * This method should always produce the correct results, unlike for other + * classes in geom. + * + * @param x the x-coordinate of the rectangle. + * @param y the y-coordinate of the rectangle. + * @param w the width of the the rectangle. + * @param h the height of the rectangle. + * @return <code>true</code> if the rectangle is considered contained + */ + public boolean contains(double x, double y, double w, double h) + { + LineSegment[] l = new LineSegment[4]; + l[0] = new LineSegment(x, y, x + w, y); + l[1] = new LineSegment(x, y + h, x + w, y + h); + l[2] = new LineSegment(x, y, x, y + h); + l[3] = new LineSegment(x + w, y, x + w, y + h); + + // Since every segment in the area must a contour + // between inside/outside segments, ANY intersection + // will mean the rectangle is not entirely contained. + for (int i = 0; i < 4; i++) + { + for (int path = 0; path < solids.size(); path++) + { + Segment v; + Segment start; + start = v = (Segment) solids.elementAt(path); + do + { + if (l[i].hasIntersections(v)) + return false; + v = v.next; + } + while (v != start); + } + for (int path = 0; path < holes.size(); path++) + { + Segment v; + Segment start; + start = v = (Segment) holes.elementAt(path); + do + { + if (l[i].hasIntersections(v)) + return false; + v = v.next; + } + while (v != start); + } + } + + // Is any point inside? + if (! contains(x, y)) + return false; + + // Final hoop: Is the rectangle non-intersecting and inside, + // but encloses a hole? + Rectangle2D r = new Rectangle2D.Double(x, y, w, h); + for (int path = 0; path < holes.size(); path++) + if (! ((Segment) holes.elementAt(path)).isSegmentOutside(r)) + return false; + + return true; + } + + /** + * Determines if the Rectangle2D specified by r is completely contained + * within this Area, returns false otherwise.<P> + * + * This method should always produce the correct results, unlike for other + * classes in geom. + * + * @param r the rectangle. + * @return <code>true</code> if the rectangle is considered contained + * + * @throws NullPointerException if <code>r</code> is <code>null</code>. + */ + public boolean contains(Rectangle2D r) + { + return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight()); + } + + /** + * Determines if the rectangle specified by (x,y) as the upper-left + * and with width w and height h intersects any part of this Area. + * + * @param x the x-coordinate for the rectangle. + * @param y the y-coordinate for the rectangle. + * @param w the width of the rectangle. + * @param h the height of the rectangle. + * @return <code>true</code> if the rectangle intersects the area, + * <code>false</code> otherwise. + */ + public boolean intersects(double x, double y, double w, double h) + { + if (solids.size() == 0) + return false; + + LineSegment[] l = new LineSegment[4]; + l[0] = new LineSegment(x, y, x + w, y); + l[1] = new LineSegment(x, y + h, x + w, y + h); + l[2] = new LineSegment(x, y, x, y + h); + l[3] = new LineSegment(x + w, y, x + w, y + h); + + // Return true on any intersection + for (int i = 0; i < 4; i++) + { + for (int path = 0; path < solids.size(); path++) + { + Segment v; + Segment start; + start = v = (Segment) solids.elementAt(path); + do + { + if (l[i].hasIntersections(v)) + return true; + v = v.next; + } + while (v != start); + } + for (int path = 0; path < holes.size(); path++) + { + Segment v; + Segment start; + start = v = (Segment) holes.elementAt(path); + do + { + if (l[i].hasIntersections(v)) + return true; + v = v.next; + } + while (v != start); + } + } + + // Non-intersecting, Is any point inside? + if (contains(x + w * 0.5, y + h * 0.5)) + return true; + + // What if the rectangle encloses the whole shape? + Point2D p = ((Segment) solids.elementAt(0)).getMidPoint(); + if ((new Rectangle2D.Double(x, y, w, h)).contains(p)) + return true; + return false; + } + + /** + * Determines if the Rectangle2D specified by r intersects any + * part of this Area. + * @param r the rectangle to test intersection with (<code>null</code> + * not permitted). + * @return <code>true</code> if the rectangle intersects the area, + * <code>false</code> otherwise. + * @throws NullPointerException if <code>r</code> is <code>null</code>. + */ + public boolean intersects(Rectangle2D r) + { + return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight()); + } + + /** + * Returns a PathIterator object defining the contour of this Area, + * transformed by at. + * + * @param at the transform. + * @return A path iterator. + */ + public PathIterator getPathIterator(AffineTransform at) + { + return (new AreaIterator(at)); + } + + /** + * Returns a flattened PathIterator object defining the contour of this + * Area, transformed by at and with a defined flatness. + * + * @param at the transform. + * @param flatness the flatness. + * @return A path iterator. + */ + public PathIterator getPathIterator(AffineTransform at, double flatness) + { + return new FlatteningPathIterator(getPathIterator(at), flatness); + } + + //--------------------------------------------------------------------- + // Non-public methods and classes + + /** + * Private pathiterator object. + */ + private class AreaIterator implements PathIterator + { + private Vector segments; + private int index; + private AffineTransform at; + + // Simple compound type for segments + class IteratorSegment + { + int type; + double[] coords; + + IteratorSegment() + { + coords = new double[6]; + } + } + + /** + * The contructor here does most of the work, + * creates a vector of IteratorSegments, which can + * readily be returned + */ + public AreaIterator(AffineTransform at) + { + this.at = at; + index = 0; + segments = new Vector(); + Vector allpaths = new Vector(); + allpaths.addAll(solids); + allpaths.addAll(holes); + + for (int i = 0; i < allpaths.size(); i++) + { + Segment v = (Segment) allpaths.elementAt(i); + Segment start = v; + + IteratorSegment is = new IteratorSegment(); + is.type = SEG_MOVETO; + is.coords[0] = start.P1.getX(); + is.coords[1] = start.P1.getY(); + segments.add(is); + + do + { + is = new IteratorSegment(); + is.type = v.pathIteratorFormat(is.coords); + segments.add(is); + v = v.next; + } + while (v != start); + + is = new IteratorSegment(); + is.type = SEG_CLOSE; + segments.add(is); + } + } + + public int currentSegment(double[] coords) + { + IteratorSegment s = (IteratorSegment) segments.elementAt(index); + if (at != null) + at.transform(s.coords, 0, coords, 0, 3); + else + for (int i = 0; i < 6; i++) + coords[i] = s.coords[i]; + return (s.type); + } + + public int currentSegment(float[] coords) + { + IteratorSegment s = (IteratorSegment) segments.elementAt(index); + double[] d = new double[6]; + if (at != null) + { + at.transform(s.coords, 0, d, 0, 3); + for (int i = 0; i < 6; i++) + coords[i] = (float) d[i]; + } + else + for (int i = 0; i < 6; i++) + coords[i] = (float) s.coords[i]; + return (s.type); + } + + // Note that the winding rule should not matter here, + // EVEN_ODD is chosen because it renders faster. + public int getWindingRule() + { + return (PathIterator.WIND_EVEN_ODD); + } + + public boolean isDone() + { + return (index >= segments.size()); + } + + public void next() + { + index++; + } + } + + /** + * Performs the fundamental task of the Weiler-Atherton algorithm, + * traverse a list of segments, for each segment: + * Follow it, removing segments from the list and switching paths + * at each node. Do so until the starting segment is reached. + * + * Returns a Vector of the resulting paths. + */ + private Vector weilerAtherton(Vector segments) + { + Vector paths = new Vector(); + while (segments.size() > 0) + { + // Iterate over the path + Segment start = (Segment) segments.elementAt(0); + Segment s = start; + do + { + segments.remove(s); + if (s.node != null) + { // switch over + s.next = s.node; + s.node = null; + } + s = s.next; // continue + } + while (s != start); + + paths.add(start); + } + return paths; + } + + /** + * A small wrapper class to store intersection points + */ + private class Intersection + { + Point2D p; // the 2D point of intersection + double ta; // the parametric value on a + double tb; // the parametric value on b + Segment seg; // segment placeholder for node setting + + public Intersection(Point2D p, double ta, double tb) + { + this.p = p; + this.ta = ta; + this.tb = tb; + } + } + + /** + * Returns the recursion depth necessary to approximate the + * curve by line segments within the error RS_EPSILON. + * + * This is done with Wang's formula: + * L0 = max{0<=i<=N-2}(|xi - 2xi+1 + xi+2|,|yi - 2yi+1 + yi+2|) + * r0 = log4(sqrt(2)*N*(N-1)*L0/8e) + * Where e is the maximum distance error (RS_EPSILON) + */ + private int getRecursionDepth(CubicSegment curve) + { + double x0 = curve.P1.getX(); + double y0 = curve.P1.getY(); + + double x1 = curve.cp1.getX(); + double y1 = curve.cp1.getY(); + + double x2 = curve.cp2.getX(); + double y2 = curve.cp2.getY(); + + double x3 = curve.P2.getX(); + double y3 = curve.P2.getY(); + + double L0 = Math.max(Math.max(Math.abs(x0 - 2 * x1 + x2), + Math.abs(x1 - 2 * x2 + x3)), + Math.max(Math.abs(y0 - 2 * y1 + y2), + Math.abs(y1 - 2 * y2 + y3))); + + double f = Math.sqrt(2) * 6.0 * L0 / (8.0 * RS_EPSILON); + + int r0 = (int) Math.ceil(Math.log(f) / Math.log(4.0)); + return (r0); + } + + /** + * Performs recursive subdivision: + * @param c1 - curve 1 + * @param c2 - curve 2 + * @param depth1 - recursion depth of curve 1 + * @param depth2 - recursion depth of curve 2 + * @param t1 - global parametric value of the first curve's starting point + * @param t2 - global parametric value of the second curve's starting point + * @param w1 - global parametric length of curve 1 + * @param c1 - global parametric length of curve 2 + * + * The final four parameters are for keeping track of the parametric + * value of the curve. For a full curve t = 0, w = 1, w is halved with + * each subdivision. + */ + private void recursiveSubdivide(CubicCurve2D c1, CubicCurve2D c2, + int depth1, int depth2, double t1, + double t2, double w1, double w2) + { + boolean flat1 = depth1 <= 0; + boolean flat2 = depth2 <= 0; + + if (flat1 && flat2) + { + double xlk = c1.getP2().getX() - c1.getP1().getX(); + double ylk = c1.getP2().getY() - c1.getP1().getY(); + + double xnm = c2.getP2().getX() - c2.getP1().getX(); + double ynm = c2.getP2().getY() - c2.getP1().getY(); + + double xmk = c2.getP1().getX() - c1.getP1().getX(); + double ymk = c2.getP1().getY() - c1.getP1().getY(); + double det = xnm * ylk - ynm * xlk; + + if (det + 1.0 == 1.0) + return; + + double detinv = 1.0 / det; + double s = (xnm * ymk - ynm * xmk) * detinv; + double t = (xlk * ymk - ylk * xmk) * detinv; + if ((s < 0.0) || (s > 1.0) || (t < 0.0) || (t > 1.0)) + return; + + double[] temp = new double[2]; + temp[0] = t1 + s * w1; + temp[1] = t2 + t * w1; + cc_intersections.add(temp); + return; + } + + CubicCurve2D.Double c11 = new CubicCurve2D.Double(); + CubicCurve2D.Double c12 = new CubicCurve2D.Double(); + CubicCurve2D.Double c21 = new CubicCurve2D.Double(); + CubicCurve2D.Double c22 = new CubicCurve2D.Double(); + + if (! flat1 && ! flat2) + { + depth1--; + depth2--; + w1 = w1 * 0.5; + w2 = w2 * 0.5; + c1.subdivide(c11, c12); + c2.subdivide(c21, c22); + if (c11.getBounds2D().intersects(c21.getBounds2D())) + recursiveSubdivide(c11, c21, depth1, depth2, t1, t2, w1, w2); + if (c11.getBounds2D().intersects(c22.getBounds2D())) + recursiveSubdivide(c11, c22, depth1, depth2, t1, t2 + w2, w1, w2); + if (c12.getBounds2D().intersects(c21.getBounds2D())) + recursiveSubdivide(c12, c21, depth1, depth2, t1 + w1, t2, w1, w2); + if (c12.getBounds2D().intersects(c22.getBounds2D())) + recursiveSubdivide(c12, c22, depth1, depth2, t1 + w1, t2 + w2, w1, w2); + return; + } + + if (! flat1) + { + depth1--; + c1.subdivide(c11, c12); + w1 = w1 * 0.5; + if (c11.getBounds2D().intersects(c2.getBounds2D())) + recursiveSubdivide(c11, c2, depth1, depth2, t1, t2, w1, w2); + if (c12.getBounds2D().intersects(c2.getBounds2D())) + recursiveSubdivide(c12, c2, depth1, depth2, t1 + w1, t2, w1, w2); + return; + } + + depth2--; + c2.subdivide(c21, c22); + w2 = w2 * 0.5; + if (c1.getBounds2D().intersects(c21.getBounds2D())) + recursiveSubdivide(c1, c21, depth1, depth2, t1, t2, w1, w2); + if (c1.getBounds2D().intersects(c22.getBounds2D())) + recursiveSubdivide(c1, c22, depth1, depth2, t1, t2 + w2, w1, w2); + } + + /** + * Returns a set of interesections between two Cubic segments + * Or null if no intersections were found. + * + * The method used to find the intersection is recursive midpoint + * subdivision. Outline description: + * + * 1) Check if the bounding boxes of the curves intersect, + * 2) If so, divide the curves in the middle and test the bounding + * boxes again, + * 3) Repeat until a maximum recursion depth has been reached, where + * the intersecting curves can be approximated by line segments. + * + * This is a reasonably accurate method, although the recursion depth + * is typically around 20, the bounding-box tests allow for significant + * pruning of the subdivision tree. + * + * This is package-private to avoid an accessor method. + */ + Intersection[] cubicCubicIntersect(CubicSegment curve1, CubicSegment curve2) + { + Rectangle2D r1 = curve1.getBounds(); + Rectangle2D r2 = curve2.getBounds(); + + if (! r1.intersects(r2)) + return null; + + cc_intersections = new Vector(); + recursiveSubdivide(curve1.getCubicCurve2D(), curve2.getCubicCurve2D(), + getRecursionDepth(curve1), getRecursionDepth(curve2), + 0.0, 0.0, 1.0, 1.0); + + if (cc_intersections.size() == 0) + return null; + + Intersection[] results = new Intersection[cc_intersections.size()]; + for (int i = 0; i < cc_intersections.size(); i++) + { + double[] temp = (double[]) cc_intersections.elementAt(i); + results[i] = new Intersection(curve1.evaluatePoint(temp[0]), temp[0], + temp[1]); + } + cc_intersections = null; + return (results); + } + + /** + * Returns the intersections between a line and a quadratic bezier + * Or null if no intersections are found1 + * This is done through combining the line's equation with the + * parametric form of the Bezier and solving the resulting quadratic. + * This is package-private to avoid an accessor method. + */ + Intersection[] lineQuadIntersect(LineSegment l, QuadSegment c) + { + double[] y = new double[3]; + double[] x = new double[3]; + double[] r = new double[3]; + int nRoots; + double x0 = c.P1.getX(); + double y0 = c.P1.getY(); + double x1 = c.cp.getX(); + double y1 = c.cp.getY(); + double x2 = c.P2.getX(); + double y2 = c.P2.getY(); + + double lx0 = l.P1.getX(); + double ly0 = l.P1.getY(); + double lx1 = l.P2.getX(); + double ly1 = l.P2.getY(); + double dx = lx1 - lx0; + double dy = ly1 - ly0; + + // form r(t) = y(t) - x(t) for the bezier + y[0] = y0; + y[1] = 2 * (y1 - y0); + y[2] = (y2 - 2 * y1 + y0); + + x[0] = x0; + x[1] = 2 * (x1 - x0); + x[2] = (x2 - 2 * x1 + x0); + + // a point, not a line + if (dy == 0 && dx == 0) + return null; + + // line on y axis + if (dx == 0 || (dy / dx) > 1.0) + { + double k = dx / dy; + x[0] -= lx0; + y[0] -= ly0; + y[0] *= k; + y[1] *= k; + y[2] *= k; + } + else + { + double k = dy / dx; + x[0] -= lx0; + y[0] -= ly0; + x[0] *= k; + x[1] *= k; + x[2] *= k; + } + + for (int i = 0; i < 3; i++) + r[i] = y[i] - x[i]; + + if ((nRoots = QuadCurve2D.solveQuadratic(r)) > 0) + { + Intersection[] temp = new Intersection[nRoots]; + int intersections = 0; + for (int i = 0; i < nRoots; i++) + { + double t = r[i]; + if (t >= 0.0 && t <= 1.0) + { + Point2D p = c.evaluatePoint(t); + + // if the line is on an axis, snap the point to that axis. + if (dx == 0) + p.setLocation(lx0, p.getY()); + if (dy == 0) + p.setLocation(p.getX(), ly0); + + if (p.getX() <= Math.max(lx0, lx1) + && p.getX() >= Math.min(lx0, lx1) + && p.getY() <= Math.max(ly0, ly1) + && p.getY() >= Math.min(ly0, ly1)) + { + double lineparameter = p.distance(l.P1) / l.P2.distance(l.P1); + temp[i] = new Intersection(p, lineparameter, t); + intersections++; + } + } + else + temp[i] = null; + } + if (intersections == 0) + return null; + + Intersection[] rValues = new Intersection[intersections]; + + for (int i = 0; i < nRoots; i++) + if (temp[i] != null) + rValues[--intersections] = temp[i]; + return (rValues); + } + return null; + } + + /** + * Returns the intersections between a line and a cubic segment + * This is done through combining the line's equation with the + * parametric form of the Bezier and solving the resulting quadratic. + * This is package-private to avoid an accessor method. + */ + Intersection[] lineCubicIntersect(LineSegment l, CubicSegment c) + { + double[] y = new double[4]; + double[] x = new double[4]; + double[] r = new double[4]; + int nRoots; + double x0 = c.P1.getX(); + double y0 = c.P1.getY(); + double x1 = c.cp1.getX(); + double y1 = c.cp1.getY(); + double x2 = c.cp2.getX(); + double y2 = c.cp2.getY(); + double x3 = c.P2.getX(); + double y3 = c.P2.getY(); + + double lx0 = l.P1.getX(); + double ly0 = l.P1.getY(); + double lx1 = l.P2.getX(); + double ly1 = l.P2.getY(); + double dx = lx1 - lx0; + double dy = ly1 - ly0; + + // form r(t) = y(t) - x(t) for the bezier + y[0] = y0; + y[1] = 3 * (y1 - y0); + y[2] = 3 * (y2 + y0 - 2 * y1); + y[3] = y3 - 3 * y2 + 3 * y1 - y0; + + x[0] = x0; + x[1] = 3 * (x1 - x0); + x[2] = 3 * (x2 + x0 - 2 * x1); + x[3] = x3 - 3 * x2 + 3 * x1 - x0; + + // a point, not a line + if (dy == 0 && dx == 0) + return null; + + // line on y axis + if (dx == 0 || (dy / dx) > 1.0) + { + double k = dx / dy; + x[0] -= lx0; + y[0] -= ly0; + y[0] *= k; + y[1] *= k; + y[2] *= k; + y[3] *= k; + } + else + { + double k = dy / dx; + x[0] -= lx0; + y[0] -= ly0; + x[0] *= k; + x[1] *= k; + x[2] *= k; + x[3] *= k; + } + for (int i = 0; i < 4; i++) + r[i] = y[i] - x[i]; + + if ((nRoots = CubicCurve2D.solveCubic(r)) > 0) + { + Intersection[] temp = new Intersection[nRoots]; + int intersections = 0; + for (int i = 0; i < nRoots; i++) + { + double t = r[i]; + if (t >= 0.0 && t <= 1.0) + { + // if the line is on an axis, snap the point to that axis. + Point2D p = c.evaluatePoint(t); + if (dx == 0) + p.setLocation(lx0, p.getY()); + if (dy == 0) + p.setLocation(p.getX(), ly0); + + if (p.getX() <= Math.max(lx0, lx1) + && p.getX() >= Math.min(lx0, lx1) + && p.getY() <= Math.max(ly0, ly1) + && p.getY() >= Math.min(ly0, ly1)) + { + double lineparameter = p.distance(l.P1) / l.P2.distance(l.P1); + temp[i] = new Intersection(p, lineparameter, t); + intersections++; + } + } + else + temp[i] = null; + } + + if (intersections == 0) + return null; + + Intersection[] rValues = new Intersection[intersections]; + for (int i = 0; i < nRoots; i++) + if (temp[i] != null) + rValues[--intersections] = temp[i]; + return (rValues); + } + return null; + } + + /** + * Returns the intersection between two lines, or null if there is no + * intersection. + * This is package-private to avoid an accessor method. + */ + Intersection linesIntersect(LineSegment a, LineSegment b) + { + Point2D P1 = a.P1; + Point2D P2 = a.P2; + Point2D P3 = b.P1; + Point2D P4 = b.P2; + + if (! Line2D.linesIntersect(P1.getX(), P1.getY(), P2.getX(), P2.getY(), + P3.getX(), P3.getY(), P4.getX(), P4.getY())) + return null; + + double x1 = P1.getX(); + double y1 = P1.getY(); + double rx = P2.getX() - x1; + double ry = P2.getY() - y1; + + double x2 = P3.getX(); + double y2 = P3.getY(); + double sx = P4.getX() - x2; + double sy = P4.getY() - y2; + + double determinant = sx * ry - sy * rx; + double nom = (sx * (y2 - y1) + sy * (x1 - x2)); + + // Parallel lines don't intersect. At least we pretend they don't. + if (Math.abs(determinant) < EPSILON) + return null; + + nom = nom / determinant; + + if (nom == 0.0) + return null; + if (nom == 1.0) + return null; + + Point2D p = new Point2D.Double(x1 + nom * rx, y1 + nom * ry); + + return new Intersection(p, p.distance(P1) / P1.distance(P2), + p.distance(P3) / P3.distance(P4)); + } + + /** + * Determines if two points are equal, within an error margin + * 'snap distance' + * This is package-private to avoid an accessor method. + */ + boolean pointEquals(Point2D a, Point2D b) + { + return (a.equals(b) || a.distance(b) < PE_EPSILON); + } + + /** + * Helper method + * Turns a shape into a Vector of Segments + */ + private Vector makeSegment(Shape s) + { + Vector paths = new Vector(); + PathIterator pi = s.getPathIterator(null); + double[] coords = new double[6]; + Segment subpath = null; + Segment current = null; + double cx; + double cy; + double subpathx; + double subpathy; + cx = cy = subpathx = subpathy = 0.0; + + this.windingRule = pi.getWindingRule(); + + while (! pi.isDone()) + { + Segment v; + switch (pi.currentSegment(coords)) + { + case PathIterator.SEG_MOVETO: + if (subpath != null) + { // close existing open path + current.next = new LineSegment(cx, cy, subpathx, subpathy); + current = current.next; + current.next = subpath; + } + subpath = null; + subpathx = cx = coords[0]; + subpathy = cy = coords[1]; + break; + + // replace 'close' with a line-to. + case PathIterator.SEG_CLOSE: + if (subpath != null && (subpathx != cx || subpathy != cy)) + { + current.next = new LineSegment(cx, cy, subpathx, subpathy); + current = current.next; + current.next = subpath; + cx = subpathx; + cy = subpathy; + subpath = null; + } + else if (subpath != null) + { + current.next = subpath; + subpath = null; + } + break; + case PathIterator.SEG_LINETO: + if (cx != coords[0] || cy != coords[1]) + { + v = new LineSegment(cx, cy, coords[0], coords[1]); + if (subpath == null) + { + subpath = current = v; + paths.add(subpath); + } + else + { + current.next = v; + current = current.next; + } + cx = coords[0]; + cy = coords[1]; + } + break; + case PathIterator.SEG_QUADTO: + v = new QuadSegment(cx, cy, coords[0], coords[1], coords[2], + coords[3]); + if (subpath == null) + { + subpath = current = v; + paths.add(subpath); + } + else + { + current.next = v; + current = current.next; + } + cx = coords[2]; + cy = coords[3]; + break; + case PathIterator.SEG_CUBICTO: + v = new CubicSegment(cx, cy, coords[0], coords[1], coords[2], + coords[3], coords[4], coords[5]); + if (subpath == null) + { + subpath = current = v; + paths.add(subpath); + } + else + { + current.next = v; + current = current.next; + } + + // check if the cubic is self-intersecting + double[] lpts = ((CubicSegment) v).getLoop(); + if (lpts != null) + { + // if it is, break off the loop into its own path. + v.subdivideInsert(lpts[0]); + v.next.subdivideInsert((lpts[1] - lpts[0]) / (1.0 - lpts[0])); + + CubicSegment loop = (CubicSegment) v.next; + v.next = loop.next; + loop.next = loop; + + v.P2 = v.next.P1 = loop.P2 = loop.P1; // snap points + paths.add(loop); + current = v.next; + } + + cx = coords[4]; + cy = coords[5]; + break; + } + pi.next(); + } + + if (subpath != null) + { // close any open path + if (subpathx != cx || subpathy != cy) + { + current.next = new LineSegment(cx, cy, subpathx, subpathy); + current = current.next; + current.next = subpath; + } + else + current.next = subpath; + } + + if (paths.size() == 0) + return (null); + + return (paths); + } + + /** + * Find the intersections of two separate closed paths, + * A and B, split the segments at the intersection points, + * and create nodes pointing from one to the other + */ + private int createNodes(Segment A, Segment B) + { + int nNodes = 0; + + Segment a = A; + Segment b = B; + + do + { + do + { + nNodes += a.splitIntersections(b); + b = b.next; + } + while (b != B); + + a = a.next; // move to the next segment + } + while (a != A); // until one wrap. + + return (nNodes); + } + + /** + * Find the intersections of a path with itself. + * Splits the segments at the intersection points, + * and create nodes pointing from one to the other. + */ + private int createNodesSelf(Segment A) + { + int nNodes = 0; + Segment a = A; + + if (A.next == A) + return 0; + + do + { + Segment b = a.next; + do + { + if (b != a) // necessary + nNodes += a.splitIntersections(b); + b = b.next; + } + while (b != A); + a = a.next; // move to the next segment + } + while (a != A); // until one wrap. + + return (nNodes); + } + + /** + * Deletes paths which are redundant from a list, (i.e. solid areas within + * solid areas) Clears any nodes. Sorts the remaining paths into solids + * and holes, sets their orientation and sets the solids and holes lists. + */ + private void deleteRedundantPaths(Vector paths) + { + int npaths = paths.size(); + + int[][] contains = new int[npaths][npaths]; + int[][] windingNumbers = new int[npaths][2]; + int neg; + Rectangle2D[] bb = new Rectangle2D[npaths]; // path bounding boxes + + neg = ((windingRule == PathIterator.WIND_NON_ZERO) ? -1 : 1); + + for (int i = 0; i < npaths; i++) + bb[i] = ((Segment) paths.elementAt(i)).getPathBounds(); + + // Find which path contains which, assign winding numbers + for (int i = 0; i < npaths; i++) + { + Segment pathA = (Segment) paths.elementAt(i); + pathA.nullNodes(); // remove any now-redundant nodes, in case. + int windingA = pathA.hasClockwiseOrientation() ? 1 : neg; + + for (int j = 0; j < npaths; j++) + if (i != j) + { + Segment pathB = (Segment) paths.elementAt(j); + + // A contains B + if (bb[i].intersects(bb[j])) + { + Segment s = pathB.next; + while (s.P1.getY() == s.P2.getY() && s != pathB) + s = s.next; + Point2D p = s.getMidPoint(); + if (pathA.contains(p.getX(), p.getY())) + contains[i][j] = windingA; + } + else + // A does not contain B + contains[i][j] = 0; + } + else + contains[i][j] = windingA; // i == j + } + + for (int i = 0; i < npaths; i++) + { + windingNumbers[i][0] = 0; + for (int j = 0; j < npaths; j++) + windingNumbers[i][0] += contains[j][i]; + windingNumbers[i][1] = contains[i][i]; + } + + Vector solids = new Vector(); + Vector holes = new Vector(); + + if (windingRule == PathIterator.WIND_NON_ZERO) + { + for (int i = 0; i < npaths; i++) + { + if (windingNumbers[i][0] == 0) + holes.add(paths.elementAt(i)); + else if (windingNumbers[i][0] - windingNumbers[i][1] == 0 + && Math.abs(windingNumbers[i][0]) == 1) + solids.add(paths.elementAt(i)); + } + } + else + { + windingRule = PathIterator.WIND_NON_ZERO; + for (int i = 0; i < npaths; i++) + { + if ((windingNumbers[i][0] & 1) == 0) + holes.add(paths.elementAt(i)); + else if ((windingNumbers[i][0] & 1) == 1) + solids.add(paths.elementAt(i)); + } + } + + setDirection(holes, false); + setDirection(solids, true); + this.holes = holes; + this.solids = solids; + } + + /** + * Sets the winding direction of a Vector of paths + * @param clockwise gives the direction, + * true = clockwise, false = counter-clockwise + */ + private void setDirection(Vector paths, boolean clockwise) + { + Segment v; + for (int i = 0; i < paths.size(); i++) + { + v = (Segment) paths.elementAt(i); + if (clockwise != v.hasClockwiseOrientation()) + v.reverseAll(); + } + } + + /** + * Class representing a linked-list of vertices forming a closed polygon, + * convex or concave, without holes. + */ + private abstract class Segment implements Cloneable + { + // segment type, PathIterator segment types are used. + Point2D P1; + Point2D P2; + Segment next; + Segment node; + + Segment() + { + P1 = P2 = null; + node = next = null; + } + + /** + * Reverses the direction of a single segment + */ + abstract void reverseCoords(); + + /** + * Returns the segment's midpoint + */ + abstract Point2D getMidPoint(); + + /** + * Returns the bounding box of this segment + */ + abstract Rectangle2D getBounds(); + + /** + * Transforms a single segment + */ + abstract void transform(AffineTransform at); + + /** + * Returns the PathIterator type of a segment + */ + abstract int getType(); + + /** + */ + abstract int splitIntersections(Segment b); + + /** + * Returns the PathIterator coords of a segment + */ + abstract int pathIteratorFormat(double[] coords); + + /** + * Returns the number of intersections on the positive X axis, + * with the origin at (x,y), used for contains()-testing + * + * (Although that could be done by the line-intersect methods, + * a dedicated method is better to guarantee consitent handling + * of endpoint-special-cases) + */ + abstract int rayCrossing(double x, double y); + + /** + * Subdivides the segment at parametric value t, inserting + * the new segment into the linked list after this, + * such that this becomes [0,t] and this.next becomes [t,1] + */ + abstract void subdivideInsert(double t); + + /** + * Returns twice the area of a curve, relative the P1-P2 line + * Used for area calculations. + */ + abstract double curveArea(); + + /** + * Compare two segments. + */ + abstract boolean equals(Segment b); + + /** + * Determines if this path of segments contains the point (x,y) + */ + boolean contains(double x, double y) + { + Segment v = this; + int crossings = 0; + do + { + int n = v.rayCrossing(x, y); + crossings += n; + v = v.next; + } + while (v != this); + return ((crossings & 1) == 1); + } + + /** + * Nulls all nodes of the path. Clean up any 'hairs'. + */ + void nullNodes() + { + Segment v = this; + do + { + v.node = null; + v = v.next; + } + while (v != this); + } + + /** + * Transforms each segment in the closed path + */ + void transformSegmentList(AffineTransform at) + { + Segment v = this; + do + { + v.transform(at); + v = v.next; + } + while (v != this); + } + + /** + * Determines the winding direction of the path + * By the sign of the area. + */ + boolean hasClockwiseOrientation() + { + return (getSignedArea() > 0.0); + } + + /** + * Returns the bounds of this path + */ + public Rectangle2D getPathBounds() + { + double xmin; + double xmax; + double ymin; + double ymax; + xmin = xmax = P1.getX(); + ymin = ymax = P1.getY(); + + Segment v = this; + do + { + Rectangle2D r = v.getBounds(); + xmin = Math.min(r.getMinX(), xmin); + ymin = Math.min(r.getMinY(), ymin); + xmax = Math.max(r.getMaxX(), xmax); + ymax = Math.max(r.getMaxY(), ymax); + v = v.next; + } + while (v != this); + + return (new Rectangle2D.Double(xmin, ymin, (xmax - xmin), (ymax - ymin))); + } + + /** + * Calculates twice the signed area of the path; + */ + double getSignedArea() + { + Segment s; + double area = 0.0; + + s = this; + do + { + area += s.curveArea(); + + area += s.P1.getX() * s.next.P1.getY() + - s.P1.getY() * s.next.P1.getX(); + s = s.next; + } + while (s != this); + + return area; + } + + /** + * Reverses the orientation of the whole polygon + */ + void reverseAll() + { + reverseCoords(); + Segment v = next; + Segment former = this; + while (v != this) + { + v.reverseCoords(); + Segment vnext = v.next; + v.next = former; + former = v; + v = vnext; + } + next = former; + } + + /** + * Inserts a Segment after this one + */ + void insert(Segment v) + { + Segment n = next; + next = v; + v.next = n; + } + + /** + * Returns if this segment path is polygonal + */ + boolean isPolygonal() + { + Segment v = this; + do + { + if (! (v instanceof LineSegment)) + return false; + v = v.next; + } + while (v != this); + return true; + } + + /** + * Clones this path + */ + Segment cloneSegmentList() throws CloneNotSupportedException + { + Vector list = new Vector(); + Segment v = next; + + while (v != this) + { + list.add(v); + v = v.next; + } + + Segment clone = (Segment) this.clone(); + v = clone; + for (int i = 0; i < list.size(); i++) + { + clone.next = (Segment) ((Segment) list.elementAt(i)).clone(); + clone = clone.next; + } + clone.next = v; + return v; + } + + /** + * Creates a node between this segment and segment b + * at the given intersection + * @return the number of nodes created (0 or 1) + */ + int createNode(Segment b, Intersection i) + { + Point2D p = i.p; + if ((pointEquals(P1, p) || pointEquals(P2, p)) + && (pointEquals(b.P1, p) || pointEquals(b.P2, p))) + return 0; + + subdivideInsert(i.ta); + b.subdivideInsert(i.tb); + + // snap points + b.P2 = b.next.P1 = P2 = next.P1 = i.p; + + node = b.next; + b.node = next; + return 1; + } + + /** + * Creates multiple nodes from a list of intersections, + * This must be done in the order of ascending parameters, + * and the parameters must be recalculated in accordance + * with each split. + * @return the number of nodes created + */ + protected int createNodes(Segment b, Intersection[] x) + { + Vector v = new Vector(); + for (int i = 0; i < x.length; i++) + { + Point2D p = x[i].p; + if (! ((pointEquals(P1, p) || pointEquals(P2, p)) + && (pointEquals(b.P1, p) || pointEquals(b.P2, p)))) + v.add(x[i]); + } + + int nNodes = v.size(); + Intersection[] A = new Intersection[nNodes]; + Intersection[] B = new Intersection[nNodes]; + for (int i = 0; i < nNodes; i++) + A[i] = B[i] = (Intersection) v.elementAt(i); + + // Create two lists sorted by the parameter + // Bubble sort, OK I suppose, since the number of intersections + // cannot be larger than 9 (cubic-cubic worst case) anyway + for (int i = 0; i < nNodes - 1; i++) + { + for (int j = i + 1; j < nNodes; j++) + { + if (A[i].ta > A[j].ta) + { + Intersection swap = A[i]; + A[i] = A[j]; + A[j] = swap; + } + if (B[i].tb > B[j].tb) + { + Intersection swap = B[i]; + B[i] = B[j]; + B[j] = swap; + } + } + } + // subdivide a + Segment s = this; + for (int i = 0; i < nNodes; i++) + { + s.subdivideInsert(A[i].ta); + + // renormalize the parameters + for (int j = i + 1; j < nNodes; j++) + A[j].ta = (A[j].ta - A[i].ta) / (1.0 - A[i].ta); + + A[i].seg = s; + s = s.next; + } + + // subdivide b, set nodes + s = b; + for (int i = 0; i < nNodes; i++) + { + s.subdivideInsert(B[i].tb); + + for (int j = i + 1; j < nNodes; j++) + B[j].tb = (B[j].tb - B[i].tb) / (1.0 - B[i].tb); + + // set nodes + B[i].seg.node = s.next; // node a -> b + s.node = B[i].seg.next; // node b -> a + + // snap points + B[i].seg.P2 = B[i].seg.next.P1 = s.P2 = s.next.P1 = B[i].p; + s = s.next; + } + return nNodes; + } + + /** + * Determines if two paths are equal. + * Colinear line segments are ignored in the comparison. + */ + boolean pathEquals(Segment B) + { + if (! getPathBounds().equals(B.getPathBounds())) + return false; + + Segment startA = getTopLeft(); + Segment startB = B.getTopLeft(); + Segment a = startA; + Segment b = startB; + do + { + if (! a.equals(b)) + return false; + + if (a instanceof LineSegment) + a = ((LineSegment) a).lastCoLinear(); + if (b instanceof LineSegment) + b = ((LineSegment) b).lastCoLinear(); + + a = a.next; + b = b.next; + } + while (a != startA && b != startB); + return true; + } + + /** + * Return the segment with the top-leftmost first point + */ + Segment getTopLeft() + { + Segment v = this; + Segment tl = this; + do + { + if (v.P1.getY() < tl.P1.getY()) + tl = v; + else if (v.P1.getY() == tl.P1.getY()) + { + if (v.P1.getX() < tl.P1.getX()) + tl = v; + } + v = v.next; + } + while (v != this); + return tl; + } + + /** + * Returns if the path has a segment outside a shape + */ + boolean isSegmentOutside(Shape shape) + { + return ! shape.contains(getMidPoint()); + } + } // class Segment + + private class LineSegment extends Segment + { + public LineSegment(double x1, double y1, double x2, double y2) + { + super(); + P1 = new Point2D.Double(x1, y1); + P2 = new Point2D.Double(x2, y2); + } + + public LineSegment(Point2D p1, Point2D p2) + { + super(); + P1 = (Point2D) p1.clone(); + P2 = (Point2D) p2.clone(); + } + + /** + * Clones this segment + */ + public Object clone() + { + return new LineSegment(P1, P2); + } + + /** + * Transforms the segment + */ + void transform(AffineTransform at) + { + P1 = at.transform(P1, null); + P2 = at.transform(P2, null); + } + + /** + * Swap start and end points + */ + void reverseCoords() + { + Point2D p = P1; + P1 = P2; + P2 = p; + } + + /** + * Returns the segment's midpoint + */ + Point2D getMidPoint() + { + return (new Point2D.Double(0.5 * (P1.getX() + P2.getX()), + 0.5 * (P1.getY() + P2.getY()))); + } + + /** + * Returns twice the area of a curve, relative the P1-P2 line + * Obviously, a line does not enclose any area besides the line + */ + double curveArea() + { + return 0; + } + + /** + * Returns the PathIterator type of a segment + */ + int getType() + { + return (PathIterator.SEG_LINETO); + } + + /** + * Subdivides the segment at parametric value t, inserting + * the new segment into the linked list after this, + * such that this becomes [0,t] and this.next becomes [t,1] + */ + void subdivideInsert(double t) + { + Point2D p = new Point2D.Double((P2.getX() - P1.getX()) * t + P1.getX(), + (P2.getY() - P1.getY()) * t + P1.getY()); + insert(new LineSegment(p, P2)); + P2 = p; + next.node = node; + node = null; + } + + /** + * Determines if two line segments are strictly colinear + */ + boolean isCoLinear(LineSegment b) + { + double x1 = P1.getX(); + double y1 = P1.getY(); + double x2 = P2.getX(); + double y2 = P2.getY(); + double x3 = b.P1.getX(); + double y3 = b.P1.getY(); + double x4 = b.P2.getX(); + double y4 = b.P2.getY(); + + if ((y1 - y3) * (x4 - x3) - (x1 - x3) * (y4 - y3) != 0.0) + return false; + + return ((x2 - x1) * (y4 - y3) - (y2 - y1) * (x4 - x3) == 0.0); + } + + /** + * Return the last segment colinear with this one. + * Used in comparing paths. + */ + Segment lastCoLinear() + { + Segment prev = this; + Segment v = next; + + while (v instanceof LineSegment) + { + if (isCoLinear((LineSegment) v)) + { + prev = v; + v = v.next; + } + else + return prev; + } + return prev; + } + + /** + * Compare two segments. + * We must take into account that the lines may be broken into colinear + * subsegments and ignore them. + */ + boolean equals(Segment b) + { + if (! (b instanceof LineSegment)) + return false; + Point2D p1 = P1; + Point2D p3 = b.P1; + + if (! p1.equals(p3)) + return false; + + Point2D p2 = lastCoLinear().P2; + Point2D p4 = ((LineSegment) b).lastCoLinear().P2; + return (p2.equals(p4)); + } + + /** + * Returns a line segment + */ + int pathIteratorFormat(double[] coords) + { + coords[0] = P2.getX(); + coords[1] = P2.getY(); + return (PathIterator.SEG_LINETO); + } + + /** + * Returns if the line has intersections. + */ + boolean hasIntersections(Segment b) + { + if (b instanceof LineSegment) + return (linesIntersect(this, (LineSegment) b) != null); + + if (b instanceof QuadSegment) + return (lineQuadIntersect(this, (QuadSegment) b) != null); + + if (b instanceof CubicSegment) + return (lineCubicIntersect(this, (CubicSegment) b) != null); + + return false; + } + + /** + * Splits intersections into nodes, + * This one handles line-line, line-quadratic, line-cubic + */ + int splitIntersections(Segment b) + { + if (b instanceof LineSegment) + { + Intersection i = linesIntersect(this, (LineSegment) b); + + if (i == null) + return 0; + + return createNode(b, i); + } + + Intersection[] x = null; + + if (b instanceof QuadSegment) + x = lineQuadIntersect(this, (QuadSegment) b); + + if (b instanceof CubicSegment) + x = lineCubicIntersect(this, (CubicSegment) b); + + if (x == null) + return 0; + + if (x.length == 1) + return createNode(b, (Intersection) x[0]); + + return createNodes(b, x); + } + + /** + * Returns the bounding box of this segment + */ + Rectangle2D getBounds() + { + return (new Rectangle2D.Double(Math.min(P1.getX(), P2.getX()), + Math.min(P1.getY(), P2.getY()), + Math.abs(P1.getX() - P2.getX()), + Math.abs(P1.getY() - P2.getY()))); + } + + /** + * Returns the number of intersections on the positive X axis, + * with the origin at (x,y), used for contains()-testing + */ + int rayCrossing(double x, double y) + { + double x0 = P1.getX() - x; + double y0 = P1.getY() - y; + double x1 = P2.getX() - x; + double y1 = P2.getY() - y; + + if (y0 * y1 > 0) + return 0; + + if (x0 < 0 && x1 < 0) + return 0; + + if (y0 == 0.0) + y0 -= EPSILON; + + if (y1 == 0.0) + y1 -= EPSILON; + + if (Line2D.linesIntersect(x0, y0, x1, y1, + EPSILON, 0.0, Double.MAX_VALUE, 0.0)) + return 1; + return 0; + } + } // class LineSegment + + /** + * Quadratic Bezier curve segment + * + * Note: Most peers don't support quadratics directly, so it might make + * sense to represent them as cubics internally and just be done with it. + * I think we should be peer-agnostic, however, and stay faithful to the + * input geometry types as far as possible. + */ + private class QuadSegment extends Segment + { + Point2D cp; // control point + + /** + * Constructor, takes the coordinates of the start, control, + * and end point, respectively. + */ + QuadSegment(double x1, double y1, double cx, double cy, double x2, + double y2) + { + super(); + P1 = new Point2D.Double(x1, y1); + P2 = new Point2D.Double(x2, y2); + cp = new Point2D.Double(cx, cy); + } + + /** + * Clones this segment + */ + public Object clone() + { + return new QuadSegment(P1.getX(), P1.getY(), cp.getX(), cp.getY(), + P2.getX(), P2.getY()); + } + + /** + * Returns twice the area of a curve, relative the P1-P2 line + * + * The area formula can be derived by using Green's formula in the + * plane on the parametric form of the bezier. + */ + double curveArea() + { + double x0 = P1.getX(); + double y0 = P1.getY(); + double x1 = cp.getX(); + double y1 = cp.getY(); + double x2 = P2.getX(); + double y2 = P2.getY(); + + double P = (y2 - 2 * y1 + y0); + double Q = 2 * (y1 - y0); + + double A = (x2 - 2 * x1 + x0); + double B = 2 * (x1 - x0); + + double area = (B * P - A * Q) / 3.0; + return (area); + } + + /** + * Compare two segments. + */ + boolean equals(Segment b) + { + if (! (b instanceof QuadSegment)) + return false; + + return (P1.equals(b.P1) && cp.equals(((QuadSegment) b).cp) + && P2.equals(b.P2)); + } + + /** + * Returns a Point2D corresponding to the parametric value t + * of the curve + */ + Point2D evaluatePoint(double t) + { + double x0 = P1.getX(); + double y0 = P1.getY(); + double x1 = cp.getX(); + double y1 = cp.getY(); + double x2 = P2.getX(); + double y2 = P2.getY(); + + return new Point2D.Double(t * t * (x2 - 2 * x1 + x0) + 2 * t * (x1 - x0) + + x0, + t * t * (y2 - 2 * y1 + y0) + 2 * t * (y1 - y0) + + y0); + } + + /** + * Returns the bounding box of this segment + */ + Rectangle2D getBounds() + { + double x0 = P1.getX(); + double y0 = P1.getY(); + double x1 = cp.getX(); + double y1 = cp.getY(); + double x2 = P2.getX(); + double y2 = P2.getY(); + double r0; + double r1; + + double xmax = Math.max(x0, x2); + double ymax = Math.max(y0, y2); + double xmin = Math.min(x0, x2); + double ymin = Math.min(y0, y2); + + r0 = 2 * (y1 - y0); + r1 = 2 * (y2 - 2 * y1 + y0); + if (r1 != 0.0) + { + double t = -r0 / r1; + if (t > 0.0 && t < 1.0) + { + double y = evaluatePoint(t).getY(); + ymax = Math.max(y, ymax); + ymin = Math.min(y, ymin); + } + } + r0 = 2 * (x1 - x0); + r1 = 2 * (x2 - 2 * x1 + x0); + if (r1 != 0.0) + { + double t = -r0 / r1; + if (t > 0.0 && t < 1.0) + { + double x = evaluatePoint(t).getY(); + xmax = Math.max(x, xmax); + xmin = Math.min(x, xmin); + } + } + + return (new Rectangle2D.Double(xmin, ymin, xmax - xmin, ymax - ymin)); + } + + /** + * Returns a cubic segment corresponding to this curve + */ + CubicSegment getCubicSegment() + { + double x1 = P1.getX() + 2.0 * (cp.getX() - P1.getX()) / 3.0; + double y1 = P1.getY() + 2.0 * (cp.getY() - P1.getY()) / 3.0; + double x2 = cp.getX() + (P2.getX() - cp.getX()) / 3.0; + double y2 = cp.getY() + (P2.getY() - cp.getY()) / 3.0; + + return new CubicSegment(P1.getX(), P1.getY(), x1, y1, x2, y2, P2.getX(), + P2.getY()); + } + + /** + * Returns the segment's midpoint + */ + Point2D getMidPoint() + { + return evaluatePoint(0.5); + } + + /** + * Returns the PathIterator type of a segment + */ + int getType() + { + return (PathIterator.SEG_QUADTO); + } + + /** + * Returns the PathIterator coords of a segment + */ + int pathIteratorFormat(double[] coords) + { + coords[0] = cp.getX(); + coords[1] = cp.getY(); + coords[2] = P2.getX(); + coords[3] = P2.getY(); + return (PathIterator.SEG_QUADTO); + } + + /** + * Returns the number of intersections on the positive X axis, + * with the origin at (x,y), used for contains()-testing + */ + int rayCrossing(double x, double y) + { + double x0 = P1.getX() - x; + double y0 = P1.getY() - y; + double x1 = cp.getX() - x; + double y1 = cp.getY() - y; + double x2 = P2.getX() - x; + double y2 = P2.getY() - y; + double[] r = new double[3]; + int nRoots; + int nCrossings = 0; + + /* check if curve may intersect X+ axis. */ + if ((x0 > 0.0 || x1 > 0.0 || x2 > 0.0) && (y0 * y1 <= 0 || y1 * y2 <= 0)) + { + if (y0 == 0.0) + y0 -= EPSILON; + if (y2 == 0.0) + y2 -= EPSILON; + + r[0] = y0; + r[1] = 2 * (y1 - y0); + r[2] = (y2 - 2 * y1 + y0); + + nRoots = QuadCurve2D.solveQuadratic(r); + for (int i = 0; i < nRoots; i++) + if (r[i] > 0.0f && r[i] < 1.0f) + { + double t = r[i]; + if (t * t * (x2 - 2 * x1 + x0) + 2 * t * (x1 - x0) + x0 > 0.0) + nCrossings++; + } + } + return nCrossings; + } + + /** + * Swap start and end points + */ + void reverseCoords() + { + Point2D temp = P1; + P1 = P2; + P2 = temp; + } + + /** + * Splits intersections into nodes, + * This one handles quadratic-quadratic only, + * Quadratic-line is passed on to the LineSegment class, + * Quadratic-cubic is passed on to the CubicSegment class + */ + int splitIntersections(Segment b) + { + if (b instanceof LineSegment) + return (b.splitIntersections(this)); + + if (b instanceof CubicSegment) + return (b.splitIntersections(this)); + + if (b instanceof QuadSegment) + { + // Use the cubic-cubic intersection routine for quads as well, + // Since a quadratic can be exactly described as a cubic, this + // should not be a problem; + // The recursion depth will be the same in any case. + Intersection[] x = cubicCubicIntersect(getCubicSegment(), + ((QuadSegment) b) + .getCubicSegment()); + if (x == null) + return 0; + + if (x.length == 1) + return createNode(b, (Intersection) x[0]); + + return createNodes(b, x); + } + return 0; + } + + /** + * Subdivides the segment at parametric value t, inserting + * the new segment into the linked list after this, + * such that this becomes [0,t] and this.next becomes [t,1] + */ + void subdivideInsert(double t) + { + double x0 = P1.getX(); + double y0 = P1.getY(); + double x1 = cp.getX(); + double y1 = cp.getY(); + double x2 = P2.getX(); + double y2 = P2.getY(); + + double p10x = x0 + t * (x1 - x0); + double p10y = y0 + t * (y1 - y0); + double p11x = x1 + t * (x2 - x1); + double p11y = y1 + t * (y2 - y1); + double p20x = p10x + t * (p11x - p10x); + double p20y = p10y + t * (p11y - p10y); + + insert(new QuadSegment(p20x, p20y, p11x, p11y, x2, y2)); + P2 = next.P1; + cp.setLocation(p10x, p10y); + + next.node = node; + node = null; + } + + /** + * Transforms the segment + */ + void transform(AffineTransform at) + { + P1 = at.transform(P1, null); + P2 = at.transform(P2, null); + cp = at.transform(cp, null); + } + } // class QuadSegment + + /** + * Cubic Bezier curve segment + */ + private class CubicSegment extends Segment + { + Point2D cp1; // control points + Point2D cp2; // control points + + /** + * Constructor - takes coordinates of the starting point, + * first control point, second control point and end point, + * respecively. + */ + public CubicSegment(double x1, double y1, double c1x, double c1y, + double c2x, double c2y, double x2, double y2) + { + super(); + P1 = new Point2D.Double(x1, y1); + P2 = new Point2D.Double(x2, y2); + cp1 = new Point2D.Double(c1x, c1y); + cp2 = new Point2D.Double(c2x, c2y); + } + + /** + * Clones this segment + */ + public Object clone() + { + return new CubicSegment(P1.getX(), P1.getY(), cp1.getX(), cp1.getY(), + cp2.getX(), cp2.getY(), P2.getX(), P2.getY()); + } + + /** + * Returns twice the area of a curve, relative the P1-P2 line + * + * The area formula can be derived by using Green's formula in the + * plane on the parametric form of the bezier. + */ + double curveArea() + { + double x0 = P1.getX(); + double y0 = P1.getY(); + double x1 = cp1.getX(); + double y1 = cp1.getY(); + double x2 = cp2.getX(); + double y2 = cp2.getY(); + double x3 = P2.getX(); + double y3 = P2.getY(); + + double P = y3 - 3 * y2 + 3 * y1 - y0; + double Q = 3 * (y2 + y0 - 2 * y1); + double R = 3 * (y1 - y0); + + double A = x3 - 3 * x2 + 3 * x1 - x0; + double B = 3 * (x2 + x0 - 2 * x1); + double C = 3 * (x1 - x0); + + double area = (B * P - A * Q) / 5.0 + (C * P - A * R) / 2.0 + + (C * Q - B * R) / 3.0; + + return (area); + } + + /** + * Compare two segments. + */ + boolean equals(Segment b) + { + if (! (b instanceof CubicSegment)) + return false; + + return (P1.equals(b.P1) && cp1.equals(((CubicSegment) b).cp1) + && cp2.equals(((CubicSegment) b).cp2) && P2.equals(b.P2)); + } + + /** + * Returns a Point2D corresponding to the parametric value t + * of the curve + */ + Point2D evaluatePoint(double t) + { + double x0 = P1.getX(); + double y0 = P1.getY(); + double x1 = cp1.getX(); + double y1 = cp1.getY(); + double x2 = cp2.getX(); + double y2 = cp2.getY(); + double x3 = P2.getX(); + double y3 = P2.getY(); + + return new Point2D.Double(-(t * t * t) * (x0 - 3 * x1 + 3 * x2 - x3) + + 3 * t * t * (x0 - 2 * x1 + x2) + + 3 * t * (x1 - x0) + x0, + -(t * t * t) * (y0 - 3 * y1 + 3 * y2 - y3) + + 3 * t * t * (y0 - 2 * y1 + y2) + + 3 * t * (y1 - y0) + y0); + } + + /** + * Returns the bounding box of this segment + */ + Rectangle2D getBounds() + { + double x0 = P1.getX(); + double y0 = P1.getY(); + double x1 = cp1.getX(); + double y1 = cp1.getY(); + double x2 = cp2.getX(); + double y2 = cp2.getY(); + double x3 = P2.getX(); + double y3 = P2.getY(); + double[] r = new double[3]; + + double xmax = Math.max(x0, x3); + double ymax = Math.max(y0, y3); + double xmin = Math.min(x0, x3); + double ymin = Math.min(y0, y3); + + r[0] = 3 * (y1 - y0); + r[1] = 6.0 * (y2 + y0 - 2 * y1); + r[2] = 3.0 * (y3 - 3 * y2 + 3 * y1 - y0); + + int n = QuadCurve2D.solveQuadratic(r); + for (int i = 0; i < n; i++) + { + double t = r[i]; + if (t > 0 && t < 1.0) + { + double y = evaluatePoint(t).getY(); + ymax = Math.max(y, ymax); + ymin = Math.min(y, ymin); + } + } + + r[0] = 3 * (x1 - x0); + r[1] = 6.0 * (x2 + x0 - 2 * x1); + r[2] = 3.0 * (x3 - 3 * x2 + 3 * x1 - x0); + n = QuadCurve2D.solveQuadratic(r); + for (int i = 0; i < n; i++) + { + double t = r[i]; + if (t > 0 && t < 1.0) + { + double x = evaluatePoint(t).getX(); + xmax = Math.max(x, xmax); + xmin = Math.min(x, xmin); + } + } + return (new Rectangle2D.Double(xmin, ymin, (xmax - xmin), (ymax - ymin))); + } + + /** + * Returns a CubicCurve2D object corresponding to this segment. + */ + CubicCurve2D getCubicCurve2D() + { + return new CubicCurve2D.Double(P1.getX(), P1.getY(), cp1.getX(), + cp1.getY(), cp2.getX(), cp2.getY(), + P2.getX(), P2.getY()); + } + + /** + * Returns the parametric points of self-intersection if the cubic + * is self-intersecting, null otherwise. + */ + double[] getLoop() + { + double x0 = P1.getX(); + double y0 = P1.getY(); + double x1 = cp1.getX(); + double y1 = cp1.getY(); + double x2 = cp2.getX(); + double y2 = cp2.getY(); + double x3 = P2.getX(); + double y3 = P2.getY(); + double[] r = new double[4]; + double k; + double R; + double T; + double A; + double B; + double[] results = new double[2]; + + R = x3 - 3 * x2 + 3 * x1 - x0; + T = y3 - 3 * y2 + 3 * y1 - y0; + + // A qudratic + if (R == 0.0 && T == 0.0) + return null; + + // true cubic + if (R != 0.0 && T != 0.0) + { + A = 3 * (x2 + x0 - 2 * x1) / R; + B = 3 * (x1 - x0) / R; + + double P = 3 * (y2 + y0 - 2 * y1) / T; + double Q = 3 * (y1 - y0) / T; + + if (A == P || Q == B) + return null; + + k = (Q - B) / (A - P); + } + else + { + if (R == 0.0) + { + // quadratic in x + k = -(3 * (x1 - x0)) / (3 * (x2 + x0 - 2 * x1)); + A = 3 * (y2 + y0 - 2 * y1) / T; + B = 3 * (y1 - y0) / T; + } + else + { + // quadratic in y + k = -(3 * (y1 - y0)) / (3 * (y2 + y0 - 2 * y1)); + A = 3 * (x2 + x0 - 2 * x1) / R; + B = 3 * (x1 - x0) / R; + } + } + + r[0] = -k * k * k - A * k * k - B * k; + r[1] = 3 * k * k + 2 * k * A + 2 * B; + r[2] = -3 * k; + r[3] = 2; + + int n = CubicCurve2D.solveCubic(r); + if (n != 3) + return null; + + // sort r + double t; + for (int i = 0; i < 2; i++) + for (int j = i + 1; j < 3; j++) + if (r[j] < r[i]) + { + t = r[i]; + r[i] = r[j]; + r[j] = t; + } + + if (Math.abs(r[0] + r[2] - k) < 1E-13) + if (r[0] >= 0.0 && r[0] <= 1.0 && r[2] >= 0.0 && r[2] <= 1.0) + if (evaluatePoint(r[0]).distance(evaluatePoint(r[2])) < PE_EPSILON * 10) + { // we snap the points anyway + results[0] = r[0]; + results[1] = r[2]; + return (results); + } + return null; + } + + /** + * Returns the segment's midpoint + */ + Point2D getMidPoint() + { + return evaluatePoint(0.5); + } + + /** + * Returns the PathIterator type of a segment + */ + int getType() + { + return (PathIterator.SEG_CUBICTO); + } + + /** + * Returns the PathIterator coords of a segment + */ + int pathIteratorFormat(double[] coords) + { + coords[0] = cp1.getX(); + coords[1] = cp1.getY(); + coords[2] = cp2.getX(); + coords[3] = cp2.getY(); + coords[4] = P2.getX(); + coords[5] = P2.getY(); + return (PathIterator.SEG_CUBICTO); + } + + /** + * Returns the number of intersections on the positive X axis, + * with the origin at (x,y), used for contains()-testing + */ + int rayCrossing(double x, double y) + { + double x0 = P1.getX() - x; + double y0 = P1.getY() - y; + double x1 = cp1.getX() - x; + double y1 = cp1.getY() - y; + double x2 = cp2.getX() - x; + double y2 = cp2.getY() - y; + double x3 = P2.getX() - x; + double y3 = P2.getY() - y; + double[] r = new double[4]; + int nRoots; + int nCrossings = 0; + + /* check if curve may intersect X+ axis. */ + if ((x0 > 0.0 || x1 > 0.0 || x2 > 0.0 || x3 > 0.0) + && (y0 * y1 <= 0 || y1 * y2 <= 0 || y2 * y3 <= 0)) + { + if (y0 == 0.0) + y0 -= EPSILON; + if (y3 == 0.0) + y3 -= EPSILON; + + r[0] = y0; + r[1] = 3 * (y1 - y0); + r[2] = 3 * (y2 + y0 - 2 * y1); + r[3] = y3 - 3 * y2 + 3 * y1 - y0; + + if ((nRoots = CubicCurve2D.solveCubic(r)) > 0) + for (int i = 0; i < nRoots; i++) + { + if (r[i] > 0.0 && r[i] < 1.0) + { + double t = r[i]; + if (-(t * t * t) * (x0 - 3 * x1 + 3 * x2 - x3) + + 3 * t * t * (x0 - 2 * x1 + x2) + 3 * t * (x1 - x0) + + x0 > 0.0) + nCrossings++; + } + } + } + return nCrossings; + } + + /** + * Swap start and end points + */ + void reverseCoords() + { + Point2D p = P1; + P1 = P2; + P2 = p; + p = cp1; // swap control points + cp1 = cp2; + cp2 = p; + } + + /** + * Splits intersections into nodes, + * This one handles cubic-cubic and cubic-quadratic intersections + */ + int splitIntersections(Segment b) + { + if (b instanceof LineSegment) + return (b.splitIntersections(this)); + + Intersection[] x = null; + + if (b instanceof QuadSegment) + x = cubicCubicIntersect(this, ((QuadSegment) b).getCubicSegment()); + + if (b instanceof CubicSegment) + x = cubicCubicIntersect(this, (CubicSegment) b); + + if (x == null) + return 0; + + if (x.length == 1) + return createNode(b, x[0]); + + return createNodes(b, x); + } + + /** + * Subdivides the segment at parametric value t, inserting + * the new segment into the linked list after this, + * such that this becomes [0,t] and this.next becomes [t,1] + */ + void subdivideInsert(double t) + { + CubicSegment s = (CubicSegment) clone(); + double p1x = (s.cp1.getX() - s.P1.getX()) * t + s.P1.getX(); + double p1y = (s.cp1.getY() - s.P1.getY()) * t + s.P1.getY(); + + double px = (s.cp2.getX() - s.cp1.getX()) * t + s.cp1.getX(); + double py = (s.cp2.getY() - s.cp1.getY()) * t + s.cp1.getY(); + + s.cp2.setLocation((s.P2.getX() - s.cp2.getX()) * t + s.cp2.getX(), + (s.P2.getY() - s.cp2.getY()) * t + s.cp2.getY()); + + s.cp1.setLocation((s.cp2.getX() - px) * t + px, + (s.cp2.getY() - py) * t + py); + + double p2x = (px - p1x) * t + p1x; + double p2y = (py - p1y) * t + p1y; + + double p3x = (s.cp1.getX() - p2x) * t + p2x; + double p3y = (s.cp1.getY() - p2y) * t + p2y; + s.P1.setLocation(p3x, p3y); + + // insert new curve + insert(s); + + // set this curve + cp1.setLocation(p1x, p1y); + cp2.setLocation(p2x, p2y); + P2 = s.P1; + next.node = node; + node = null; + } + + /** + * Transforms the segment + */ + void transform(AffineTransform at) + { + P1 = at.transform(P1, null); + P2 = at.transform(P2, null); + cp1 = at.transform(cp1, null); + cp2 = at.transform(cp2, null); + } + } // class CubicSegment +} // class Area |