The contains and intersects() methods are also more accurate than the specification of #Shape requires.

Please note that constructing an Area can be slow (Self-intersection resolving is proportional to the square of the number of segments).

Since:

1.2

Nested Class Summary
private  class	Area.AreaIterator           Private pathiterator object.
private  class	Area.CubicSegment           Cubic Bezier curve segment
private  class	Area.Intersection           A small wrapper class to store intersection points
private  class	Area.LineSegment
private  class	Area.QuadSegment           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.
private  class	Area.Segment           Class representing a linked-list of vertices forming a closed polygon, convex or concave, without holes.

 

Field Summary
private  java.util.Vector	cc_intersections           Vector (temporary) storing curve-curve intersections
private static double	EPSILON           General numerical precision
(package private)  java.util.Vector	holes           Segment vectors containing solid areas and holes This is package-private to avoid an accessor method.
private static double	PE_EPSILON           Snap distance - points within this distance are considered equal
private static double	RS_EPSILON           recursive subdivision epsilon - (see getRecursionDepth)
(package private)  java.util.Vector	solids           Segment vectors containing solid areas and holes This is package-private to avoid an accessor method.
private  int	windingRule           Winding rule WIND_NON_ZERO used, after construction, this is irrelevant.

 

Constructor Summary

Area()           Constructs an empty Area

Area(java.awt.Shape s)           Constructs an Area from any given Shape.

 

Method Summary
void	add(Area area)           Performs an add (union) operation on this area with another Area.
java.lang.Object	clone()           Create a new area of the same run-time type with the same contents as this one.
boolean	contains(double x, double y)           Determines if the point (x,y) is contained within this Area.
boolean	contains(double x, double y, double w, double h)           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.
boolean	contains(Point2D p)           Determines if the Point2D p is contained within this Area.
boolean	contains(Rectangle2D r)           Determines if the Rectangle2D specified by r is completely contained within this Area, returns false otherwise.
private  int	createNodes(Area.Segment A, Area.Segment B)           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	createNodesSelf(Area.Segment A)           Find the intersections of a path with itself.
Area	createTransformedArea(AffineTransform at)           Returns a new Area equal to this one, transformed by the AffineTransform at.
(package private)  Area.Intersection[]	cubicCubicIntersect(Area.CubicSegment curve1, Area.CubicSegment curve2)           Returns a set of interesections between two Cubic segments Or null if no intersections were found.
private  void	deleteRedundantPaths(java.util.Vector paths)           Deletes paths which are redundant from a list, (i.e.
boolean	equals(Area area)           Compares two Areas.
void	exclusiveOr(Area area)           Performs an exclusive-or operation on this Area.
java.awt.Rectangle	getBounds()           Returns the bounds of this object in Rectangle format.
Rectangle2D	getBounds2D()           Returns the bounding box of the Area.
PathIterator	getPathIterator(AffineTransform at)           Returns a PathIterator object defining the contour of this Area, transformed by at.
PathIterator	getPathIterator(AffineTransform at, double flatness)           Returns a flattened PathIterator object defining the contour of this Area, transformed by at and with a defined flatness.
private  int	getRecursionDepth(Area.CubicSegment curve)           Returns the recursion depth necessary to approximate the curve by line segments within the error RS_EPSILON.
void	intersect(Area area)           Performs an intersection operation on this Area.
boolean	intersects(double x, double y, double w, double h)           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.
boolean	intersects(Rectangle2D r)           Determines if the Rectangle2D specified by r intersects any part of this Area.
boolean	isEmpty()           Returns whether this area encloses any area.
boolean	isPolygonal()           Determines whether the Area consists entirely of line segments
boolean	isRectangular()           Determines if the Area is rectangular.
boolean	isSingular()           Returns whether the Area consists of more than one simple (non self-intersecting) subpath.
(package private)  Area.Intersection[]	lineCubicIntersect(Area.LineSegment l, Area.CubicSegment c)           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.
(package private)  Area.Intersection[]	lineQuadIntersect(Area.LineSegment l, Area.QuadSegment c)           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.
(package private)  Area.Intersection	linesIntersect(Area.LineSegment a, Area.LineSegment b)           Returns the intersection between two lines, or null if there is no intersection.
private  java.util.Vector	makeSegment(java.awt.Shape s)           Helper method Turns a shape into a Vector of Segments
(package private)  boolean	pointEquals(Point2D a, Point2D b)           Determines if two points are equal, within an error margin 'snap distance' This is package-private to avoid an accessor method.
private  void	recursiveSubdivide(CubicCurve2D c1, CubicCurve2D c2, int depth1, int depth2, double t1, double t2, double w1, double w2)           Performs recursive subdivision:
void	reset()           Clears the Area object, creating an empty area.
private  void	setDirection(java.util.Vector paths, boolean clockwise)           Sets the winding direction of a Vector of paths
void	subtract(Area area)           Performs a subtraction operation on this Area.
void	transform(AffineTransform at)           Transforms this area by the AffineTransform at.
private  java.util.Vector	weilerAtherton(java.util.Vector segments)           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.

 

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

 

Field Detail

EPSILON

private static final double EPSILON

General numerical precision

See Also:

Constant Field Values

RS_EPSILON

private static final double RS_EPSILON

recursive subdivision epsilon - (see getRecursionDepth)

See Also:

Constant Field Values

PE_EPSILON

private static final double PE_EPSILON

Snap distance - points within this distance are considered equal

See Also:

Constant Field Values

solids

java.util.Vector solids

Segment vectors containing solid areas and holes This is package-private to avoid an accessor method.

holes

java.util.Vector holes

Segment vectors containing solid areas and holes This is package-private to avoid an accessor method.

cc_intersections

private java.util.Vector cc_intersections

Vector (temporary) storing curve-curve intersections

windingRule

private int windingRule

Winding rule WIND_NON_ZERO used, after construction, this is irrelevant.

Area

public Area()

Constructs an empty Area

Area

public Area(java.awt.Shape s)

Constructs an Area from any given Shape.

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.

add

public void add(Area area)

Performs an add (union) operation on this area with another Area.

subtract

public void subtract(Area area)

Performs a subtraction operation on this Area.

intersect

public void intersect(Area area)

Performs an intersection operation on this Area.

exclusiveOr

public void exclusiveOr(Area area)

Performs an exclusive-or operation on this Area.

reset

public void reset()

Clears the Area object, creating an empty area.

isEmpty

public boolean isEmpty()

Returns whether this area encloses any area.

isPolygonal

public boolean isPolygonal()

Determines whether the Area consists entirely of line segments

isRectangular

public boolean isRectangular()

Determines if the Area is rectangular.

This is strictly qualified. An area is considered rectangular if:

It consists of a single polygonal path.

It is oriented parallel/perpendicular to the xy axis

It must be exactly rectangular, i.e. small errors induced by transformations may cause a false result, although the area is visibly rectangular.

isSingular

public boolean isSingular()

Returns whether the Area consists of more than one simple (non self-intersecting) subpath.

getBounds2D

public Rectangle2D getBounds2D()

Returns the bounding box of the Area.

Unlike the CubicCurve2D and QuadraticCurve2D classes, this method will return the tightest possible bounding box, evaluating the extreme points of each curved segment.

Specified by:

getBounds2D in interface java.awt.Shape

getBounds

public java.awt.Rectangle getBounds()

Returns the bounds of this object in Rectangle format. Please note that this may lead to loss of precision.

Specified by:

getBounds in interface java.awt.Shape

clone

public java.lang.Object clone()

Create a new area of the same run-time type with the same contents as this one.

equals

public boolean equals(Area area)

Compares two Areas.

transform

public void transform(AffineTransform at)

Transforms this area by the AffineTransform at.

createTransformedArea

public Area createTransformedArea(AffineTransform at)

Returns a new Area equal to this one, transformed by the AffineTransform at.

contains

public boolean contains(double x,
                        double y)

Determines if the point (x,y) is contained within this Area.

Specified by:

contains in interface java.awt.Shape

contains

public boolean contains(Point2D p)

Determines if the Point2D p is contained within this Area.

Specified by:

contains in interface java.awt.Shape

contains

public boolean contains(double x,
                        double y,
                        double w,
                        double h)

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.

This method should always produce the correct results, unlike for other classes in geom.

Specified by:

contains in interface java.awt.Shape

contains

public boolean contains(Rectangle2D r)

Determines if the Rectangle2D specified by r is completely contained within this Area, returns false otherwise.

This method should always produce the correct results, unlike for other classes in geom.

Specified by:

contains in interface java.awt.Shape

intersects

public boolean intersects(double x,
                          double y,
                          double w,
                          double h)

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.

Specified by:

intersects in interface java.awt.Shape

intersects

public boolean intersects(Rectangle2D r)

Determines if the Rectangle2D specified by r intersects any part of this Area.

Specified by:

intersects in interface java.awt.Shape

getPathIterator

public PathIterator getPathIterator(AffineTransform at)

Returns a PathIterator object defining the contour of this Area, transformed by at.

Specified by:

getPathIterator in interface java.awt.Shape

getPathIterator

public PathIterator getPathIterator(AffineTransform at,
                                    double flatness)

Returns a flattened PathIterator object defining the contour of this Area, transformed by at and with a defined flatness.

Specified by:

getPathIterator in interface java.awt.Shape

weilerAtherton

private java.util.Vector weilerAtherton(java.util.Vector segments)

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.

getRecursionDepth

private int getRecursionDepth(Area.CubicSegment curve)

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)

recursiveSubdivide

private void recursiveSubdivide(CubicCurve2D c1,
                                CubicCurve2D c2,
                                int depth1,
                                int depth2,
                                double t1,
                                double t2,
                                double w1,
                                double w2)

Performs recursive subdivision:

cubicCubicIntersect

Area.Intersection[] cubicCubicIntersect(Area.CubicSegment curve1,
                                        Area.CubicSegment curve2)

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.

lineQuadIntersect

Area.Intersection[] lineQuadIntersect(Area.LineSegment l,
                                      Area.QuadSegment c)

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.

lineCubicIntersect

Area.Intersection[] lineCubicIntersect(Area.LineSegment l,
                                       Area.CubicSegment c)

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.

linesIntersect

Area.Intersection linesIntersect(Area.LineSegment a,
                                 Area.LineSegment b)

Returns the intersection between two lines, or null if there is no intersection. This is package-private to avoid an accessor method.

pointEquals

boolean pointEquals(Point2D a,
                    Point2D b)

Determines if two points are equal, within an error margin 'snap distance' This is package-private to avoid an accessor method.

makeSegment

private java.util.Vector makeSegment(java.awt.Shape s)

Helper method Turns a shape into a Vector of Segments

createNodes

private int createNodes(Area.Segment A,
                        Area.Segment B)

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

createNodesSelf

private int createNodesSelf(Area.Segment A)

Find the intersections of a path with itself. Splits the segments at the intersection points, and create nodes pointing from one to the other.

deleteRedundantPaths

private void deleteRedundantPaths(java.util.Vector paths)

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.

setDirection

private void setDirection(java.util.Vector paths,
                          boolean clockwise)

Sets the winding direction of a Vector of paths

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