PointI (tektosyne API)

java.lang.Object
- org.kynosarges.tektosyne.geometry.PointI

```
public final class PointI
extends java.lang.Object
```
Represents a location in two-dimensional space, using Integer coordinates. PointI contains two immutable non-negative Integer dimensions, representing either a two-dimensional location or a two-dimensional vector. Use PointD to represent points with Double dimensions.

Field Summary

Fields
Modifier and Type Field and Description

static PointI EMPTY
An empty read-only PointI.

int x
The x-coordinate of the PointI.

int y
The y-coordinate of the PointI.

Fields
Modifier and Type	Field and Description
`static PointI`	`EMPTY` An empty read-only `PointI`.
`int`	`x` The x-coordinate of the `PointI`.
`int`	`y` The y-coordinate of the `PointI`.

Constructor Summary

Constructors
Constructor and Description

PointI()
Creates a PointI with the coordinate origin.

PointI(int x, int y)
Creates a PointI with the specified Integer coordinates.

Constructors
Constructor and Description
`PointI()` Creates a `PointI` with the coordinate origin.
`PointI(int x, int y)` Creates a `PointI` with the specified `Integer` coordinates.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`PointI`	`add(PointI point)` Adds the location of the specified `PointI` to this instance.
`double`	`angle()` Gets the polar angle of the vector represented by the `PointI`, in radians.
`double`	`angleBetween(PointI vector)` Computes the angle between the vector represented by the `PointI` and the specified vector.
`double`	`angleBetween(PointI a, PointI b)` Computes the angle between the vectors from the `PointI` to the specified locations.
`long`	`crossProductLength(PointI vector)` Computes the length of the cross-product of the vector represented by the `PointI` and the specified vector.
`long`	`crossProductLength(PointI a, PointI b)` Computes the length of the cross-product of the vectors from the `PointI` to the specified locations.
`boolean`	`equals(java.lang.Object obj)` Compares the specified `Object` to this `PointI` instance.
`static PointI[]`	`fromInts(int... points)` Converts the specified `Integer` array to a `PointI` array.
`static PointI`	`fromPolar(double length, double angle)` Creates a `PointI` from the specified polar coordinates.
`int`	`hashCode()` Returns a hash code for the `PointI`.
`boolean`	`isCollinear(PointI a, PointI b)` Determines if the `PointI` is collinear with the specified instances.
`double`	`length()` Gets the absolute length of the vector represented by the `PointI`.
`long`	`lengthSquared()` Gets the squared absolute length of the vector represented by the `PointI`.
`long`	`multiply(PointI vector)` Multiplies the vectors represented by the specified `PointI` and this instance.
`PointI`	`restrict(int minX, int minY, int maxX, int maxY)` Restricts the `PointI` to the specified location range.
`PointI`	`subtract(PointI point)` Subtracts the location of the specified `PointI` from this instance.
`static int[]`	`toInts(PointI... points)` Converts the specified `PointI` array to an `Integer` array.
`PointD`	`toPointD()` Converts the `PointI` to a `PointD`.
`java.lang.String`	`toString()` Returns a `String` representation of the `PointI`.

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

- Field Detail
  - x
```
public final int x
```
    The x-coordinate of the PointI.
  - y
```
public final int y
```
    The y-coordinate of the PointI.
  - EMPTY
```
public static final PointI EMPTY
```
    An empty read-only PointI. Both x and y are set to zero.
- Constructor Detail
  - PointI
```
public PointI()
```
    Creates a PointI with the coordinate origin. Both x and y are set to zero.
  - PointI
```
public PointI(int x,
              int y)
```
    Creates a PointI with the specified Integer coordinates.
    
    Parameters:
    
    x - the x-coordinate of the PointI
    
    y - the y-coordinate of the PointI
- Method Detail
  - add
```
public PointI add(PointI point)
```
    Adds the location of the specified PointI to this instance.
    
    Parameters:
    
    point - the PointI whose location to add to this instance
    
    Returns:
    
    a PointI whose x and y equal the addition of the corresponding dimensions of the specified point to this instance
    
    Throws:
    
    java.lang.ArithmeticException - if the sum in any dimension overflows Integer
    
    java.lang.NullPointerException - if point is null
  - angle
```
public double angle()
```
    Gets the polar angle of the vector represented by the PointI, in radians. Returns the result of Math.atan2(double, double) for y and x, within the interval [-Math.PI, +Math.PI].
    
    Returns:
    
    the polar angle, in radians, of the vector represented by the PointI, or zero if x and y both equal zero
  - angleBetween
```
public double angleBetween(PointI vector)
```
    Computes the angle between the vector represented by the PointI and the specified vector. Returns the result of Math.atan2(double, double) for the cross-product length and the scalar dot product of the two vectors. The possible range of values is [-Math.PI, +Math.PI]. Coordinates are widened to Double to avoid Integer overflow.
    
    Parameters:
    
    vector - the PointI vector to compare with this instance
    
    Returns:
    
    the angle, in radians, between this instance and the specified vector, in that order
    
    Throws:
    
    java.lang.NullPointerException - if vector is null
  - angleBetween
```
public double angleBetween(PointI a,
                           PointI b)
```
    Computes the angle between the vectors from the PointI to the specified locations. Returns the result of Math.atan2(double, double) for the cross-product length and the scalar dot product of the two vectors. The possible range of values is [-Math.PI, +Math.PI].
    
    Parameters:
    
    a - the PointI location where the first vector ends
    
    b - the PointI location where the second vector ends
    
    Returns:
    
    the angle, in radians, between the vectors from this instance to a and from this instance to b, in that order
    
    Throws:
    
    java.lang.NullPointerException - if a or b is null
  - crossProductLength
```
public long crossProductLength(PointI vector)
```
    Computes the length of the cross-product of the vector represented by the PointI and the specified vector. The absolute value equals the area of the parallelogram spanned by the PointI and the specified vector. The sign indicates their spatial relationship, as described in crossProductLength(PointI, PointI). Coordinates are widened to Long to avoid Integer overflow.
    
    Parameters:
    
    vector - the PointI vector to multiply with this instance
    
    Returns:
    
    a Long value indicating the length of the cross-product of this instance and the specified vector, in that order
    
    Throws:
    
    java.lang.NullPointerException - if vector is null
  - crossProductLength
```
public long crossProductLength(PointI a,
                               PointI b)
```
    Computes the length of the cross-product of the vectors from the PointI to the specified locations. The absolute value equals the area of the parallelogram spanned by the vectors from the PointI to a and b. The sign indicates their spatial relationship of the two vectors, as follows:
    - Less than zero — The sequence from this instance to a and then b constitutes a right-hand turn, assuming y-coordinates increase upward.
    - Zero — This instance, a, and b are collinear.
    - Greater than zero — The sequence from this instance to a and then b constitutes a left-hand turn, assuming y-coordinates increase upward.
    Coordinates are widened to Long to avoid Integer overflow.
    Parameters:
    
    a - the PointI location where the first vector ends
    
    b - the PointI location where the second vector ends
    
    Returns:
    
    a Long value indicating the length of the cross-product of the vectors from this instance to a and from this instance to b, in that order
    
    Throws:
    
    java.lang.NullPointerException - if a or b is null
  - fromInts
```
public static PointI[] fromInts(int... points)
```
    Converts the specified Integer array to a PointI array. The returned array has half as many elements as the specified points and retains the same coordinate sequence.
    
    Parameters:
    
    points - an array containing the x and y components of PointI instances, stored in alternating index positions
    
    Returns:
    
    the PointI array created from points
    
    Throws:
    
    java.lang.IllegalArgumentException - if points has an odd number of elements
    
    java.lang.NullPointerException - if points is null
  - fromPolar
```
public static PointI fromPolar(double length,
                               double angle)
```
    Creates a PointI from the specified polar coordinates. The calculated x and y coordinates are converted to the nearest Integer values using Fortran.nint(double) rounding. The resulting length() and angle() may differ accordingly from the specified arguments.
    
    Parameters:
    
    length - the distance from the coordinate origin to the PointI
    
    angle - the polar angle, in radians, of the PointI
    
    Returns:
    
    a PointI whose length() and angle() approximately equal the specified length and angle
    
    Throws:
    
    java.lang.ArithmeticException - if any resulting Cartesian coordinate overflows Integer
  - isCollinear
```
public boolean isCollinear(PointI a,
                           PointI b)
```
    Determines if the PointI is collinear with the specified instances. Returns true exactly if crossProductLength(PointI, PointI) is zero for a and b.
    
    Parameters:
    
    a - the first PointI to examine
    
    b - the second PointI to examine
    
    Returns:
    
    true if the PointI is collinear with a and b, else false
    
    Throws:
    
    java.lang.NullPointerException - if a or b is null
  - length
```
public double length()
```
    Gets the absolute length of the vector represented by the PointI. Returns the square root of the sum of the squares of x and y.
    
    Returns:
    
    the non-negative absolute length of the vector represented by the PointI
  - lengthSquared
```
public long lengthSquared()
```
    Gets the squared absolute length of the vector represented by the PointI. Returns the sum of the squares of x and y, widened to Long to avoid Integer overflow. Use instead of length() if you only need the squared value.
    
    Returns:
    
    a non-negative Long value that equals the square of length()
  - multiply
```
public long multiply(PointI vector)
```
    Multiplies the vectors represented by the specified PointI and this instance. Returns the sum of the pairwise products of both instances' x and y, widened to Long to avoid Integer overflow. That sum equals lengthSquared() if the specified vector equals this instance.
    
    Parameters:
    
    vector - the PointI to multiply with this instance
    
    Returns:
    
    a Long value that represents the scalar dot product of the specified vector and this instance
    
    Throws:
    
    java.lang.NullPointerException - if vector is null
  - restrict
```
public PointI restrict(int minX,
                       int minY,
                       int maxX,
                       int maxY)
```
    Restricts the PointI to the specified location range.
    
    Parameters:
    
    minX - the smallest permissible x
    
    minY - the smallest permissible y
    
    maxX - the greatest permissible x
    
    maxY - the greatest permissible y
    
    Returns:
    
    a PointI whose x and y coordinates equal those of this instance, restricted to the specified location range
  - subtract
```
public PointI subtract(PointI point)
```
    Subtracts the location of the specified PointI from this instance.
    
    Parameters:
    
    point - the PointI location to subtract from this instance
    
    Returns:
    
    a PointI whose x and y equal the subtraction of the corresponding dimensions of the specified point from this instance
    
    Throws:
    
    java.lang.ArithmeticException - if the difference in any dimension overflows Integer
    
    java.lang.NullPointerException - if point is null
  - toInts
```
public static int[] toInts(PointI... points)
```
    Converts the specified PointI array to an Integer array. The returned array has twice as many elements as the specified points and retains the same coordinate sequence.
    
    Parameters:
    
    points - the PointI array to convert
    
    Returns:
    
    an array containing the x and y components of all points, stored in alternating index positions
    
    Throws:
    
    java.lang.NullPointerException - if points or any of its elements is null
  - toPointD
```
public PointD toPointD()
```
    Converts the PointI to a PointD.
    
    Returns:
    
    a PointD whose PointD.x and PointD.y equal the corresponding dimensions of the PointI
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Compares the specified Object to this PointI instance.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    obj - the Object to compare to this instance
    
    Returns:
    
    true if obj is not null and a PointI instance whose x and y equal those of this instance, else false
  - hashCode
```
public int hashCode()
```
    Returns a hash code for the PointI.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    an Integer hash code for the PointI
  - toString
```
public java.lang.String toString()
```
    Returns a String representation of the PointI.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    a String containing the values of x and y

Class PointI

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

x

y

EMPTY

Constructor Detail

PointI

PointI

Method Detail

add

angle

angleBetween

angleBetween

crossProductLength

crossProductLength

fromInts

fromPolar

isCollinear

length

lengthSquared

multiply

restrict

subtract

toInts

toPointD

equals

hashCode

toString