Class RobustPredicates

Adaptive exact arithmetic geometric predicates.

Inheritance

System.Object

RobustPredicates

Inherited Members

System.Object.ToString()

System.Object.Equals(System.Object)

System.Object.Equals(System.Object, System.Object)

System.Object.ReferenceEquals(System.Object, System.Object)

System.Object.GetHashCode()

System.Object.GetType()

System.Object.MemberwiseClone()

Namespace: UnityEngine.Experimental.U2D.TriangleNet

Syntax

public class RobustPredicates : IPredicates

Remarks

The adaptive exact arithmetic geometric predicates implemented herein are described in detail in the paper "Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates." by Jonathan Richard Shewchuk, see http://www.cs.cmu.edu/~quake/robust.html

The macros of the original C code were automatically expanded using the Visual Studio command prompt with the command "CL /P /C EXACT.C", see http://msdn.microsoft.com/en-us/library/8z9z0bx6.aspx

Constructors

RobustPredicates()

Declaration

public RobustPredicates()

Properties

Default

Gets the default configuration instance.

Declaration

public static RobustPredicates Default { get; }

Property Value

Type	Description
RobustPredicates

Methods

CounterClockwise(Point, Point, Point)

Check, if the three points appear in counterclockwise order. The result is also a rough approximation of twice the signed area of the triangle defined by the three points.

Declaration

public double CounterClockwise(Point pa, Point pb, Point pc)

Parameters

Type	Name	Description
Point	pa	Point a.
Point	pb	Point b.
Point	pc	Point c.

Returns

Type	Description
System.Double	Return a positive value if the points pa, pb, and pc occur in counterclockwise order; a negative value if they occur in clockwise order; and zero if they are collinear.

Implements

IPredicates.CounterClockwise(Point, Point, Point)

FindCircumcenter(Point, Point, Point, ref Double, ref Double)

Find the circumcenter of a triangle.

Declaration

public Point FindCircumcenter(Point org, Point dest, Point apex, ref double xi, ref double eta)

Parameters

Type	Name	Description
Point	org	Triangle point.
Point	dest	Triangle point.
Point	apex	Triangle point.
System.Double	xi	Relative coordinate of new location.
System.Double	eta	Relative coordinate of new location.

Returns

Type	Description
Point	Coordinates of the circumcenter

Implements

IPredicates.FindCircumcenter(Point, Point, Point, ref Double, ref Double)

Remarks

The result is returned both in terms of x-y coordinates and xi-eta (barycentric) coordinates. The xi-eta coordinate system is defined in terms of the triangle: the origin of the triangle is the origin of the coordinate system; the destination of the triangle is one unit along the xi axis; and the apex of the triangle is one unit along the eta axis. This procedure also returns the square of the length of the triangle's shortest edge.

FindCircumcenter(Point, Point, Point, ref Double, ref Double, Double)

Find the circumcenter of a triangle.

Declaration

public Point FindCircumcenter(Point org, Point dest, Point apex, ref double xi, ref double eta, double offconstant)

Parameters

Type	Name	Description
Point	org	Triangle point.
Point	dest	Triangle point.
Point	apex	Triangle point.
System.Double	xi	Relative coordinate of new location.
System.Double	eta	Relative coordinate of new location.
System.Double	offconstant	Off-center constant.

Returns

Type	Description
Point	Coordinates of the circumcenter (or off-center)

Implements

IPredicates.FindCircumcenter(Point, Point, Point, ref Double, ref Double, Double)

InCircle(Point, Point, Point, Point)

Check if the point pd lies inside the circle passing through pa, pb, and pc. The points pa, pb, and pc must be in counterclockwise order, or the sign of the result will be reversed.

Declaration

public double InCircle(Point pa, Point pb, Point pc, Point pd)

Parameters

Type	Name	Description
Point	pa	Point a.
Point	pb	Point b.
Point	pc	Point c.
Point	pd	Point d.

Returns

Type	Description
System.Double	Return a positive value if the point pd lies inside the circle passing through pa, pb, and pc; a negative value if it lies outside; and zero if the four points are cocircular.

Implements

IPredicates.InCircle(Point, Point, Point, Point)

NonRegular(Point, Point, Point, Point)

Return a positive value if the point pd is incompatible with the circle or plane passing through pa, pb, and pc (meaning that pd is inside the circle or below the plane); a negative value if it is compatible; and zero if the four points are cocircular/coplanar. The points pa, pb, and pc must be in counterclockwise order, or the sign of the result will be reversed.

Declaration

public double NonRegular(Point pa, Point pb, Point pc, Point pd)

Parameters

Type	Name	Description
Point	pa	Point a.
Point	pb	Point b.
Point	pc	Point c.
Point	pd	Point d.

Returns

Type	Description
System.Double	Return a positive value if the point pd lies inside the circle passing through pa, pb, and pc; a negative value if it lies outside; and zero if the four points are cocircular.