Package org.openjump.core.graph.delauneySimplexInsert

Class Pnt

java.lang.Object

org.openjump.core.graph.delauneySimplexInsert.Pnt

public class Pnt
extends Object

Points in Euclidean space, implemented as double[]. Includes simple geometric operations. Uses matrices; a matrix is represented as an array of Pnts. Uses simplices; a simplex is represented as an array of Pnts.

Author:

Paul Chew Created July 2005. Derived from an earlier, messier version.

Constructor Summary

Constructors

Constructor	Description
Pnt(double[] coords)	Constructor.
Pnt(double coordA, double coordB)	Constructor.
Pnt(double coordA, double coordB, double coordC)	Constructor.

Method Summary

Modifier and Type	Method	Description
Pnt	add(Pnt p)	Add.
double	angle(Pnt p)	Angle (in radians) between two Pnts (treated as vectors).
Pnt	bisector(Pnt point)	Perpendicular bisector of two Pnts.
static Pnt	circumcenter(Pnt[] simplex)	Circumcenter of a simplex.
static double	content(Pnt[] simplex)	Determine the signed content (i.e., area or volume, etc.) of a simplex.
double	coord(int i)
static Pnt	cross(Pnt[] matrix)	Compute generalized cross-product of the rows of a matrix.
static double	determinant(Pnt[] matrix)	Compute the determinant of a matrix (array of Pnts).
int	dimCheck(Pnt p)	Check that dimensions match.
int	dimension()
double	dot(Pnt p)	Dot product.
boolean	equals(Object other)	Equality.
Pnt	extend(double[] coords)	Create a new Pnt by adding additional coordinates to this Pnt.
int	hashCode()	HashCode.
boolean	isInside(Pnt[] simplex)	Test if this Pnt is inside a simplex.
Pnt	isOn(Pnt[] simplex)	Test if this Pnt is on a simplex.
Pnt	isOutside(Pnt[] simplex)	Test if this Pnt is outside of simplex.
double	magnitude()	Magnitude (as a vector).
static void	main(String[] args)	Main program (used for testing).
int[]	relation(Pnt[] simplex)	Relation between this Pnt and a simplex (represented as an array of Pnts).
Pnt	subtract(Pnt p)	Subtract.
String	toString()	Create a String for this Pnt.
static String	toString(Pnt[] matrix)	Create a String for a matrix.
int	vsCircumcircle(Pnt[] simplex)	Test relation between this Pnt and circumcircle of a simplex.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

Pnt

public Pnt(double[] coords)

Constructor.

Parameters:

coords - the coordinates

Pnt

public Pnt(double coordA,
           double coordB)

Constructor.

Parameters:

coordA - first ordinate of the point

coordB - second ordinate of the point

Pnt

public Pnt(double coordA,
           double coordB,
           double coordC)

Constructor.

Parameters:

coordA - first ordinate of the point

coordB - second ordinate of the point

coordC - third ordinate of the point

Method Detail

toString

public String toString()

Create a String for this Pnt.

Overrides:

toString in class Object

Returns:

a String representation of this Pnt.

equals

public boolean equals(Object other)

Equality.

Overrides:

equals in class Object

Parameters:

other - the other Object to compare to

Returns:

true iff the Pnts have the same coordinates

hashCode

public int hashCode()

HashCode.

Overrides:

hashCode in class Object

Returns:

the hashCode for this Pnt

coord

public double coord(int i)

Returns:

the specified coordinate of this Pnt

Throws:

ArrayIndexOutOfBoundsException - for bad coordinate

dimension

public int dimension()

Returns:

this Pnt's dimension.

dimCheck

public int dimCheck(Pnt p)

Check that dimensions match.

Parameters:

p - the Pnt to check (against this Pnt)

Returns:

the dimension of the Pnts

Throws:

IllegalArgumentException - if dimension fail to match

extend

public Pnt extend(double[] coords)

Create a new Pnt by adding additional coordinates to this Pnt.

Parameters:

coords - the new coordinates (added on the right end)

Returns:

a new Pnt with the additional coordinates

dot

public double dot(Pnt p)

Dot product.

Parameters:

p - the other Pnt

Returns:

dot product of this Pnt and p

magnitude

public double magnitude()

Magnitude (as a vector).

Returns:

the Euclidean length of this vector

subtract

public Pnt subtract(Pnt p)

Subtract.

Parameters:

p - the other Pnt

Returns:

a new Pnt = this - p

add

public Pnt add(Pnt p)

Add.

Parameters:

p - the other Pnt

Returns:

a new Pnt = this + p

angle

public double angle(Pnt p)

Angle (in radians) between two Pnts (treated as vectors).

Parameters:

p - the other Pnt

Returns:

the angle (in radians) between the two Pnts

bisector

public Pnt bisector(Pnt point)

Perpendicular bisector of two Pnts. Works in any dimension. The coefficients are returned as a Pnt of one higher dimension (e.g., (A,B,C,D) for an equation of the form Ax + By + Cz + D = 0).

Parameters:

point - the other point

Returns:

the coefficients of the perpendicular bisector

toString

public static String toString(Pnt[] matrix)

Create a String for a matrix.

Parameters:

matrix - the matrix (an array of Pnts)

Returns:

a String represenation of the matrix

determinant

public static double determinant(Pnt[] matrix)

Compute the determinant of a matrix (array of Pnts). This is not an efficient implementation, but should be adequate for low dimension.

Parameters:

matrix - the matrix as an array of Pnts

Returns:

the determinnant of the input matrix

Throws:

IllegalArgumentException - if dimensions are wrong

cross

public static Pnt cross(Pnt[] matrix)

Compute generalized cross-product of the rows of a matrix. The result is a Pnt perpendicular (as a vector) to each row of the matrix. This is not an efficient implementation, but should be adequate for low dimension.

Parameters:

matrix - the matrix of Pnts (one less row than the Pnt dimension)

Returns:

a Pnt perpendicular to each row Pnt

Throws:

IllegalArgumentException - if matrix is wrong shape

content

public static double content(Pnt[] simplex)

Determine the signed content (i.e., area or volume, etc.) of a simplex.

Parameters:

simplex - the simplex (as an array of Pnts)

Returns:

the signed content of the simplex

relation

public int[] relation(Pnt[] simplex)

Relation between this Pnt and a simplex (represented as an array of Pnts). Result is an array of signs, one for each vertex of the simplex, indicating the relation between the vertex, the vertex's opposite facet, and this Pnt.

   -1 means Pnt is on same side of facet
    0 means Pnt is on the facet
   +1 means Pnt is on opposite side of facet

Parameters:

simplex - an array of Pnts representing a simplex

Returns:

an array of signs showing relation between this Pnt and the simplex

isOutside

public Pnt isOutside(Pnt[] simplex)

Test if this Pnt is outside of simplex.

Parameters:

simplex - the simplex (an array of Pnts)

Returns:

the simplex Pnt that "witnesses" outsideness (or null if not outside)

isOn

public Pnt isOn(Pnt[] simplex)

Test if this Pnt is on a simplex.

Parameters:

simplex - the simplex (an array of Pnts)

Returns:

the simplex Pnt that "witnesses" on-ness (or null if not on)

isInside

public boolean isInside(Pnt[] simplex)

Test if this Pnt is inside a simplex.

Parameters:

simplex - the simplex (an arary of Pnts)

Returns:

true iff this Pnt is inside simplex.

vsCircumcircle

public int vsCircumcircle(Pnt[] simplex)

Test relation between this Pnt and circumcircle of a simplex.

Parameters:

simplex - the simplex (as an array of Pnts)

Returns:

-1, 0, or +1 for inside, on, or outside of circumcircle

circumcenter

public static Pnt circumcenter(Pnt[] simplex)

Circumcenter of a simplex.

Parameters:

simplex - the simplex (as an array of Pnts)

Returns:

the circumcenter (a Pnt) of simplex

main

public static void main(String[] args)

Main program (used for testing).