com.yworks.yfiles.algorithms

Class Geom

java.lang.Object

com.yworks.yfiles.algorithms.Geom

public final class Geom
extends Object

This class provides useful geometric primitives and advanced geometric algorithms.

Method Summary

Modifier and Type	Method and Description
static YList	calcConvexHull(YList points) Calculates the convex hull for a set of points.
static YPoint	calcIntersection(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4) Calculates the intersection point of two affine lines.
static Rectangle2D	calcIntersection(Rectangle2D r1, Rectangle2D r2, Rectangle2D dest) Intersects the pair of specified source Rectangle2D objects and puts the result into the specified destination Rectangle2D object.
static YPoint	calcIntersection(YPoint p1, YPoint p2, YPoint p3, YPoint p4) Calculates the intersection point of two affine lines.
static YPoint	calcIntersection(YPoint p1, YVector d1, YPoint p2, YVector d2) Calculates the intersection point of two affine lines.
static Rectangle2D	calcUnion(Rectangle2D r1, Rectangle2D r2, Rectangle2D dest) Unions the pair of source Rectangle2D objects and puts the result into the specified destination Rectangle2D object.
static boolean	collinear(YPoint p, YPoint q, YPoint r) Returns true iff the given points are collinear, i.e.
static double	distanceToLineSegment(double pointX, double pointY, double lineX1, double lineY1, double lineX2, double lineY2) Determines the distance of the point p to the line segment [l1, l2].
static boolean	leftTurn(YPoint p, YPoint q, YPoint r) Same as orientation(p,q,r) > 0.
static boolean	linesIntersect(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4) Returns whether the two lines defined by the given coordinates intersect or not.
static int	orientation(double px, double py, double qx, double qy, double rx, double ry) Same as orientation(YPoint, YPoint, YPoint) with double values as arguments.
static int	orientation(YPoint p, YPoint q, YPoint r) Returns the orientation of point r relative to the directed line from point p to point q.
static YPoint	projection(double pointX, double pointY, double lineX1, double lineY1, double lineX2, double lineY2) Determines the projection of the point p onto the line segment [l1, l2].
static boolean	rightTurn(YPoint p, YPoint q, YPoint r) Same as orientation(p,q,r) < 0.
static int	sideOfCircle(YPoint a, YPoint b, YPoint c, YPoint d) Returns +1 if point d lies left of the directed circle through points a, b, and c, 0 if a,b,c and d are cocircular, and -1 otherwise.
static double	toDegrees(double angrad) Converts the given degree value from radian to angular.
static double	toRadians(double angdeg) Converts the given degree value from angular to radian.

Methods inherited from class java.lang.Object

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

Method Detail

calcConvexHull

public static final YList calcConvexHull(YList points)

Calculates the convex hull for a set of points.

Complexity:

O(n)*log(n), n := points.size()

Parameters:

points - a list of YPoint objects

Returns:

a list of YPoint objects that constitute the convex hull of the given points. The list contains points in counter clockwise order around the hull. The first point is the one with the smallest x coordinate. If two such points exist then of these points the one with the smallest y coordinate is chosen as the first one.

calcIntersection

public static final YPoint calcIntersection(double x1,
                                            double y1,
                                            double x2,
                                            double y2,
                                            double x3,
                                            double y3,
                                            double x4,
                                            double y4)

Calculates the intersection point of two affine lines.

Each line is given by the coordinates of two points.

Parameters:

x1 - x-coordinate of one point on the first line.

y1 - y-coordinate of one point on the first line.

x2 - x-coordinate of another point on the first line.

y2 - y-coordinate of another point on the first line.

x3 - x-coordinate of one point on the second line.

y3 - y-coordinate of one point on the second line.

x4 - x-coordinate of another point on the second line.

y4 - y-coordinate of another point on the second line.

Returns:

the intersection point of the specified lines or null if there is no intersection.

calcIntersection

public static final Rectangle2D calcIntersection(Rectangle2D r1,
                                                 Rectangle2D r2,
                                                 Rectangle2D dest)

Intersects the pair of specified source Rectangle2D objects and puts the result into the specified destination Rectangle2D object.

If one or both of the source rectangles have negative width or height, the resulting rectangle will be located at (0,0) with a width and height of -1. One of the source rectangles can also be the destination to avoid creating a third Rectangle2D object, but in this case the original points of this source rectangle will be overwritten by this method.

Parameters:

r1 - the first of a pair of Rectangle2D objects to be intersected with each other

r2 - the second of a pair of Rectangle2D objects to be intersected with each other

dest - the Rectangle2D that holds the results of the intersection of r1 and r2

calcIntersection

public static final YPoint calcIntersection(YPoint p1,
                                            YPoint p2,
                                            YPoint p3,
                                            YPoint p4)

Calculates the intersection point of two affine lines.

Each line is given by two points.

Parameters:

p1 - one point on the first line.

p2 - another point on the first line.

p3 - one point on the second line.

p4 - another point on the second line.

Returns:

the intersection point of the specified lines or null if there is no intersection.

calcIntersection

public static final YPoint calcIntersection(YPoint p1,
                                            YVector d1,
                                            YPoint p2,
                                            YVector d2)

Calculates the intersection point of two affine lines.

Each line is given by a point and a direction vector.

Parameters:

p1 - origin point of the first line.

d1 - direction vector of the first line.

p2 - origin point of the second line.

d2 - direction vector of the second line.

Returns:

the intersection point of the specified lines or null if there is no intersection.

calcUnion

public static final Rectangle2D calcUnion(Rectangle2D r1,
                                          Rectangle2D r2,
                                          Rectangle2D dest)

Unions the pair of source Rectangle2D objects and puts the result into the specified destination Rectangle2D object.

If one of the source rectangles has negative width or height, it is excluded from the union. If both source rectangles have negative width or height, the destination rectangle will become a copy of r1. One of the source rectangles can also be the destination to avoid creating a third Rectangle2D object, but in this case the original points of this source rectangle will be overwritten by this method. If the destination is null, a new Rectangle2D is created.

Parameters:

r1 - the first of a pair of Rectangle2D objects to be combined with each other

r2 - the second of a pair of Rectangle2D objects to be combined with each other

dest - the Rectangle2D that holds the results of the union of r1 and r2

collinear

public static final boolean collinear(YPoint p,
                                      YPoint q,
                                      YPoint r)

Returns true iff the given points are collinear, i.e.

all three points lie on a common line.

Same as orientation(p,q,r) == 0

distanceToLineSegment

public static final double distanceToLineSegment(double pointX,
                                                 double pointY,
                                                 double lineX1,
                                                 double lineY1,
                                                 double lineX2,
                                                 double lineY2)

Determines the distance of the point p to the line segment [l1, l2].

Parameters:

pointX - the x coordinate of p

pointY - the y coordinate of p

lineX1 - the x coordinate of l1

lineY1 - the y coordinate of l1

lineX2 - the x coordinate of l2

lineY2 - the y coordinate of l2

leftTurn

public static final boolean leftTurn(YPoint p,
                                     YPoint q,
                                     YPoint r)

Same as orientation(p,q,r) > 0.

linesIntersect

public static final boolean linesIntersect(double x1,
                                           double y1,
                                           double x2,
                                           double y2,
                                           double x3,
                                           double y3,
                                           double x4,
                                           double y4)

Returns whether the two lines defined by the given coordinates intersect or not.

orientation

public static final int orientation(double px,
                                    double py,
                                    double qx,
                                    double qy,
                                    double rx,
                                    double ry)

Same as orientation(YPoint, YPoint, YPoint) with double values as arguments.

orientation

public static final int orientation(YPoint p,
                                    YPoint q,
                                    YPoint r)

Returns the orientation of point r relative to the directed line from point p to point q.

The given tuple of points is said to have positive orientation if p and q are distinct and r lies to the left of the oriented line passing through p and q and oriented from p to q.

The tuple is said to have negative orientation if p and q are distinct and r lies to the right of the line, and the tuple is said to have orientation zero if the three points are collinear.

Returns:

+1 in the case of positive orientation, -1 in the case of negative orientation and 0 in the case of zero orientation.

projection

public static final YPoint projection(double pointX,
                                      double pointY,
                                      double lineX1,
                                      double lineY1,
                                      double lineX2,
                                      double lineY2)

Determines the projection of the point p onto the line segment [l1, l2].

The resulting point is

• the orthogonal projection of p onto the line through l1 and l2, iff the projection lies on the line segment [l1, l2]
• the end point of the line segment [l1, l2] that is closest to p, otherwise

Parameters:

pointX - the x coordinate of p

pointY - the y coordinate of p

lineX1 - the x coordinate of l1

lineY1 - the y coordinate of l1

lineX2 - the x coordinate of l2

lineY2 - the y coordinate of l2

rightTurn

public static final boolean rightTurn(YPoint p,
                                      YPoint q,
                                      YPoint r)

Same as orientation(p,q,r) < 0.

sideOfCircle

public static final int sideOfCircle(YPoint a,
                                     YPoint b,
                                     YPoint c,
                                     YPoint d)

Returns +1 if point d lies left of the directed circle through points a, b, and c, 0 if a,b,c and d are cocircular, and -1 otherwise.

toDegrees

public static final double toDegrees(double angrad)

Converts the given degree value from radian to angular.

toRadians

public static final double toRadians(double angdeg)

Converts the given degree value from angular to radian.