Point

java.lang.Object
- Point

All Implemented Interfaces:

java.io.Serializable
```
public class Point
extends java.lang.Object
implements java.io.Serializable
```
Represents a point in the module generated by the nth roots of unity in the complex plane. Each Point can be expressed as an integer combination of the vectors (cos (k pi/n), sin(k pi/n)). The main field is an int array, the kth entry of which is the coefficient of (cos (k pi/n), sin(k pi/n)).

See Also:
Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

static long serialVersionUID
For serialization.

Fields
Modifier and Type	Field and Description
`static long`	`serialVersionUID` For serialization.

Method Summary

Methods
Modifier and Type	Method and Description
`static Point`	`createPoint(int i)` Public static factory method.
`boolean`	`equals(java.lang.Object obj)` Two Points are equal if they are of the same length and have the same entries in each position.
`static java.lang.String`	`gapString()` Output a gap-readable String representing a rotation matrix.
`static java.lang.String`	`gapString(int[] angles)` Output a gap-readable String representing an inflation matrix.
`Point2D`	`getPoint2D()` Output this Point as a Point2D.
`int`	`hashCode()` Currently broken.
`static Point[]`	`inflation(int[] seq)` Produce an inflation matrix (i.e., a sequence of `N()`-1 Points) corresponding to a given edge sequence.
`static void`	`main(java.lang.String[] args)` For testing.
`java.lang.String`	`matrixString()` Output a String consisting of the coefficients of the Point in a comma-separated list with no brackets.
`static java.lang.String`	`matrixString(int[] angles)` Same as `gapString(int[])`, but with row breaks indicated by new lines instead of square brackets.
`Point`	`minus(Point p)` Subtract another point from this one and return the result.
`Point`	`multiply(Point[] mat)` View the given array of Points as a matrix, and multiply this Point by it.
`static int`	`N()` Get the order of symmetry.
`static java.lang.String`	`order()` Output a String describing the order of symmetry.
`Point`	`plus(Point p)` Add another point to this one and return the result.
`java.lang.String`	`postscriptString()` Output a String consisting of the coefficients of the Point in a space-separated list.
`double[]`	`project()` Output 2d Cartesian coordinates.
`Point`	`rotate(int angle)` Rotate this Point about the origin by the given angle.
`static void`	`setN(int n)` Set the order of symmetry.
`java.lang.String`	`toString()` Output a String consisting of the coefficients of the Point in a comma-separated list, enclosed in square brackets.
`static Point`	`ZERO()` Get the zero vector.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - serialVersionUID
```
public static final long serialVersionUID
```
    For serialization.
    
    See Also:
    Constant Field Values
- Method Detail
  - setN
```
public static void setN(int n)
```
    Set the order of symmetry.
    
    Parameters:
    n - The new order of symmetry.
  - N
```
public static int N()
```
    Get the order of symmetry.
    
    Returns:
    N.
  - ZERO
```
public static Point ZERO()
```
    Get the zero vector.
    
    Returns:
    A point representing the origin.
  - createPoint
```
public static Point createPoint(int i)
```
    Public static factory method. Returns the element of the unit circle that makes an angle of i pi/N with the positive x-axis.
    
    Parameters:
    i - The angle between the Point returned and the positive x-axis.
    
    Returns:
    The point on the unit circle that makes an angle of i with the positive x-axis.
  - toString
```
public java.lang.String toString()
```
    Output a String consisting of the coefficients of the Point in a comma-separated list, enclosed in square brackets.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    The coefficients of the Point in a comma-separated list enclosed in square brackets.
  - postscriptString
```
public java.lang.String postscriptString()
```
    Output a String consisting of the coefficients of the Point in a space-separated list.
    
    Returns:
    The coefficients of the Point in a space-separated list.
  - order
```
public static java.lang.String order()
```
    Output a String describing the order of symmetry.
    
    Returns:
    "pent" if N == 5, "hept" if N == 11, etc.
  - matrixString
```
public java.lang.String matrixString()
```
    Output a String consisting of the coefficients of the Point in a comma-separated list with no brackets.
    
    Returns:
    The coefficients of the Point in a comma-separated list.
  - project
```
public double[] project()
```
    Output 2d Cartesian coordinates.
    
    Returns:
    An array of two doubles representing x- and y-coordinates of this point.
  - getPoint2D
```
public Point2D getPoint2D()
```
    Output this Point as a Point2D.
    
    Returns:
    A Point2D representation of this point.
  - gapString
```
public static java.lang.String gapString(int[] angles)
```
    Output a gap-readable String representing an inflation matrix. This square matrix has N-1 rows, each enclosed in square brackets, with comma-separated entries.
    
    Parameters:
    angles - A list of angles, given as integer multiples of pi/N. The sum of the points on the unit circle corresponding to these angles is the inflation factor of the matrix.
    
    Returns:
    The matrix representation of multiplication by the inflation factor, expressed in terms of the N-1 vectors (cos(k pi/n), sin(k pi/n)).
  - matrixString
```
public static java.lang.String matrixString(int[] angles)
```
    Same as gapString(int[]), but with row breaks indicated by new lines instead of square brackets.
  - gapString
```
public static java.lang.String gapString()
```
    Output a gap-readable String representing a rotation matrix. This square matrix has N-1 rows, each enclosed in square brackets, with comma-separated entries.
    
    Returns:
    The matrix representation of rotation by pi/n, expressed in terms of the N-1 vectors (cos(k pi/n), sin(k pi/n)).
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Two Points are equal if they are of the same length and have the same entries in each position.
    
    Overrides:
    
    equals in class java.lang.Object
  - hashCode
```
public int hashCode()
```
    Currently broken.
    
    Overrides:
    
    hashCode in class java.lang.Object
  - plus
```
public Point plus(Point p)
```
    Add another point to this one and return the result. The two original Points remain unchanged.
    
    Parameters:
    p - The Point we add to this one.
    
    Returns:
    The sum of this an p.
  - minus
```
public Point minus(Point p)
```
    Subtract another point from this one and return the result. The two original Points remain unchanged.
    
    Parameters:
    p - The Point we subtract from this one.
    
    Returns:
    The difference of this an p.
  - rotate
```
public Point rotate(int angle)
```
    Rotate this Point about the origin by the given angle.
    
    Parameters:
    angle - The angle of rotation.
    
    Returns:
    The Point that results from the rotation.
  - inflation
```
public static Point[] inflation(int[] seq)
```
    Produce an inflation matrix (i.e., a sequence of N()-1 Points) corresponding to a given edge sequence.
    
    Parameters:
    seq - A sequence of angles representing a vector reached by taking steps of unit length, starting at the origin. This vector should lie on the positive x-axis, and therefore represent a length.
    
    Returns:
    A matrix (array of Points), multiplication by which corresponds to inflation by the length represented by the given sequence.
  - multiply
```
public Point multiply(Point[] mat)
```
    View the given array of Points as a matrix, and multiply this Point by it. Intended for use in computing inflated Points.
    
    Parameters:
    mat - An Array of Points representing an inflation matrix.
    
    Returns:
    The inflation of this point by the given matrix.
  - main
```
public static void main(java.lang.String[] args)
```
    For testing.

Class Point

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

serialVersionUID

Method Detail

setN

N

ZERO

createPoint

toString

postscriptString

order

matrixString

project

getPoint2D

gapString

matrixString

gapString

equals

hashCode

plus

minus

rotate

inflation

multiply

main