Geometry

java.lang.Object
- org.dyn4j.geometry.Geometry

```
public final class Geometry
extends java.lang.Object
```
Contains static methods to perform standard geometric operations.
This class can be used to create Shapes of varying types via the create* methods. While Shapes can be created using their constructors as well, the methods here can place their centers on the origin and also make copies of the given input to avoid reuse issues.
This class also contains various helper methods for cleaning vector arrays and lists and performing various operations on Shapes.

Since:

1.0.0

Version:

3.2.2

Author:

William Bittle

Field Summary

Fields
Modifier and Type	Field and Description
`static double`	`INV_3` The value of 1/3
`static double`	`INV_SQRT_3` The value of the inverse of the square root of 3; 1/sqrt(3)
`static double`	`TWO_PI` 2 * PI constant

Constructor Summary

Constructors
Constructor and Description

Geometry()

Constructors
Constructor and Description
`Geometry()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static java.util.List<Vector2>`	`cleanse(java.util.List<Vector2> points)` Returns a new list containing the 'cleansed' version of the given listing of polygon points.
`static Vector2[]`	`cleanse(Vector2... points)` Returns a new array containing the 'cleansed' version of the given array of polygon points.
`static Capsule`	`createCapsule(double width, double height)` Creates a new `Capsule` bounded by the given rectangle width and height.
`static Circle`	`createCircle(double radius)` Returns a new `Circle` with the given radius centered on the origin.
`static Ellipse`	`createEllipse(double width, double height)` Creates a new `Ellipse` bounded by the given rectangle width and height.
`static Triangle`	`createEquilateralTriangle(double height)` Creates an equilateral `Triangle` with the center at the origin.
`static HalfEllipse`	`createHalfEllipse(double width, double height)` Creates a new `HalfEllipse` bounded by the given rectangle width and height.
`static HalfEllipse`	`createHalfEllipseAtOrigin(double width, double height)` Creates a new `HalfEllipse` bounded by the given rectangle width and height.
`static Segment`	`createHorizontalSegment(double length)` Creates a new `Segment` with the given length with the center at the origin.
`static Triangle`	`createIsoscelesTriangle(double width, double height)` Creates an isosceles `Triangle` with the center at the origin.
`static java.util.List<Link>`	`createLinks(java.util.List<Vector2> vertices, boolean closed)` Creates a list of `Link`s for the given vertices.
`static java.util.List<Link>`	`createLinks(Vector2[] vertices, boolean closed)` Creates a `Link` chain for the given vertices.
`static Polygon`	`createPolygon(Vector2... vertices)` Returns a new `Polygon` with the given vertices.
`static Polygon`	`createPolygonalCapsule(int count, double width, double height)` Creates a new `Polygon` in the shape of a capsule using count number of vertices on each cap, centered on the origin.
`static Polygon`	`createPolygonalCircle(int count, double radius)` Creates a new `Polygon` in the shape of a circle with count number of vertices centered on the origin.
`static Polygon`	`createPolygonalCircle(int count, double radius, double theta)` Creates a new `Polygon` in the shape of a circle with count number of vertices centered on the origin.
`static Polygon`	`createPolygonalEllipse(int count, double width, double height)` Creates a new `Polygon` in the shape of an ellipse with count number of vertices centered on the origin.
`static Polygon`	`createPolygonalHalfEllipse(int count, double width, double height)` Creates a new `Polygon` in the shape of a half ellipse with count number of vertices with the base at the origin.
`static Polygon`	`createPolygonalHalfEllipseAtOrigin(int count, double width, double height)` Creates a new `Polygon` in the shape of a half ellipse with count number of vertices centered on the origin.
`static Polygon`	`createPolygonalSlice(int count, double radius, double theta)` Creates a new `Polygon` in the shape of a `Slice` with count number of vertices with the circle center centered on the origin.
`static Polygon`	`createPolygonalSliceAtOrigin(int count, double radius, double theta)` Creates a new `Polygon` in the shape of a `Slice` with count number of vertices centered on the origin.
`static Polygon`	`createPolygonAtOrigin(Vector2... vertices)` Returns a new `Polygon`, using the given vertices, centered at the origin.
`static Rectangle`	`createRectangle(double width, double height)` Creates a new `Rectangle` with the given width and height centered at the origin.
`static Triangle`	`createRightTriangle(double width, double height)` Creates a right angle `Triangle` with the center at the origin.
`static Triangle`	`createRightTriangle(double width, double height, boolean mirror)` Creates a right angle `Triangle` with the center at the origin.
`static Segment`	`createSegment(Vector2 end)` Creates a new `Segment` from the origin to the given end point
`static Segment`	`createSegment(Vector2 p1, Vector2 p2)` Creates a new `Segment` with the given points.
`static Segment`	`createSegmentAtOrigin(Vector2 p1, Vector2 p2)` Creates a new `Segment` with the given points.
`static Slice`	`createSlice(double radius, double theta)` Creates a new `Slice` with the given circle radius and arc length theta.
`static Slice`	`createSliceAtOrigin(double radius, double theta)` Creates a new `Slice` with the given circle radius and arc length theta.
`static Rectangle`	`createSquare(double size)` Creates a square (equal height and width `Rectangle`) with the given size centered at the origin.
`static Triangle`	`createTriangle(Vector2 p1, Vector2 p2, Vector2 p3)` Creates a new `Triangle`, using the given points.
`static Triangle`	`createTriangleAtOrigin(Vector2 p1, Vector2 p2, Vector2 p3)` Creates a new `Triangle` with the given points centered at the origin.
`static Polygon`	`createUnitCirclePolygon(int count, double radius)` Returns a new `Polygon` with count number of points, where the points are evenly distributed around the unit circle.
`static Polygon`	`createUnitCirclePolygon(int count, double radius, double theta)` Returns a new `Polygon` with count number of points, where the points are evenly distributed around the unit circle.
`static Segment`	`createVerticalSegment(double length)` Creates a new `Segment` with the given length with the center at the origin.
`static Polygon`	`flip(Polygon polygon, Vector2 axis)` Flips the given polygon about the given line and returns the result as a new polygon.
`static Polygon`	`flip(Polygon polygon, Vector2 axis, Vector2 point)` Flips the given polygon about the given line and returns the result as a new polygon.
`static Polygon`	`flipAlongTheXAxis(Polygon polygon)` Flips the given polygon about its center along the x-axis and returns the result as a new polygon.
`static Polygon`	`flipAlongTheXAxis(Polygon polygon, Vector2 point)` Flips the given polygon about the given point along the x-axis and returns the result as a new polygon.
`static Polygon`	`flipAlongTheYAxis(Polygon polygon)` Flips the given polygon about its center along the y-axis and returns the result as a new polygon.
`static Polygon`	`flipAlongTheYAxis(Polygon polygon, Vector2 point)` Flips the given polygon about the given point along the y-axis and returns the result as a new polygon.
`static Vector2`	`getAreaWeightedCenter(java.util.List<Vector2> points)` Returns the area weighted centroid for the given points.
`static Vector2`	`getAreaWeightedCenter(Vector2... points)` Returns the area weighted centroid for the given points.
`static Vector2`	`getAverageCenter(java.util.List<Vector2> points)` Returns the centroid of the given points by performing an average.
`static Vector2`	`getAverageCenter(Vector2... points)` Returns the centroid of the given points by performing an average.
`static Vector2[]`	`getCounterClockwiseEdgeNormals(Vector2... vertices)` Returns an array of normalized vectors representing the normals of all the edges given the vertices.
`static double`	`getRotationRadius(Vector2... vertices)` Returns the maximum radius of the given vertices rotated about the origin.
`static double`	`getRotationRadius(Vector2 center, Vector2... vertices)` Returns the maximum radius of the given vertices rotated about the given center.
`static double`	`getWinding(java.util.List<Vector2> points)` Returns the winding, Clockwise or Counter-Clockwise, for the given list of points of a polygon.
`static double`	`getWinding(Vector2... points)` Returns the winding, Clockwise or Counter-Clockwise, for the given array of points of a polygon.
`static Polygon`	`minkowskiSum(Circle circle, Polygon polygon, int count)` Performs the Minkowski Sum of the given `Polygon` and `Circle`.
`static <E extends Wound & Convex> Polygon`	`minkowskiSum(E convex1, E convex2)` Returns the Minkowski Sum of the given convex shapes.
`static Polygon`	`minkowskiSum(Polygon polygon, Circle circle, int count)` Performs the Minkowski Sum of the given `Polygon` and `Circle`.
`static Polygon`	`minkowskiSum(Polygon polygon, double radius, int count)` Returns a new polygon that has been radially expanded.
`static void`	`reverseWinding(java.util.List<Vector2> points)` Reverses the order of the polygon points within the given list.
`static void`	`reverseWinding(Vector2... points)` Reverses the order of the polygon points within the given array.
`static Capsule`	`scale(Capsule capsule, double scale)` Returns a scaled version of the given capsule.
`static Circle`	`scale(Circle circle, double scale)` Returns a scaled version of the given circle.
`static Ellipse`	`scale(Ellipse ellipse, double scale)` Returns a scaled version of the given ellipse.
`static HalfEllipse`	`scale(HalfEllipse halfEllipse, double scale)` Returns a scaled version of the given half-ellipse.
`static Polygon`	`scale(Polygon polygon, double scale)` Returns a scaled version of the given polygon.
`static Segment`	`scale(Segment segment, double scale)` Returns a scaled version of the given segment.
`static Slice`	`scale(Slice slice, double scale)` Returns a scaled version of the given slice.

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - TWO_PI
```
public static final double TWO_PI
```
    2 * PI constant
    
    See Also:
    
    Constant Field Values
  - INV_3
```
public static final double INV_3
```
    The value of 1/3
    
    See Also:
    
    Constant Field Values
  - INV_SQRT_3
```
public static final double INV_SQRT_3
```
    The value of the inverse of the square root of 3; 1/sqrt(3)
- Constructor Detail
  - Geometry
```
public Geometry()
```
- Method Detail
  - getWinding
```
public static final double getWinding(java.util.List<Vector2> points)
```
    Returns the winding, Clockwise or Counter-Clockwise, for the given list of points of a polygon.
    This method determines the winding by computing a signed "area".
    
    Parameters:
    
    points - the points of a polygon
    
    Returns:
    
    double negative for Clockwise winding; positive for Counter-Clockwise winding
    
    Throws:
    
    java.lang.NullPointerException - if points is null or an element of points is null
    
    java.lang.IllegalArgumentException - if points contains less than 2 elements
    
    Since:
    
    2.2.0
  - getWinding
```
public static final double getWinding(Vector2... points)
```
    Returns the winding, Clockwise or Counter-Clockwise, for the given array of points of a polygon.
    
    Parameters:
    
    points - the points of a polygon
    
    Returns:
    
    double negative for Clockwise winding; positive for Counter-Clockwise winding
    
    Throws:
    
    java.lang.NullPointerException - if points is null or an element of points is null
    
    java.lang.IllegalArgumentException - if points contains less than 2 elements
    
    Since:
    
    2.2.0
  - reverseWinding
```
public static final void reverseWinding(Vector2... points)
```
    Reverses the order of the polygon points within the given array.
    This method performs a simple array reverse.
    
    Parameters:
    
    points - the polygon points
    
    Throws:
    
    java.lang.NullPointerException - if points is null
    
    Since:
    
    2.2.0
  - reverseWinding
```
public static final void reverseWinding(java.util.List<Vector2> points)
```
    Reverses the order of the polygon points within the given list.
    This method performs a simple list reverse.
    
    Parameters:
    
    points - the polygon points
    
    Throws:
    
    java.lang.NullPointerException - if points is null
    
    Since:
    
    2.2.0
  - getAverageCenter
```
public static final Vector2 getAverageCenter(java.util.List<Vector2> points)
```
    Returns the centroid of the given points by performing an average.
    
    Parameters:
    
    points - the list of points
    
    Returns:
    
    Vector2 the centroid
    
    Throws:
    
    java.lang.NullPointerException - if points is null or an element of points is null
    
    java.lang.IllegalArgumentException - if points is an empty list
  - getAverageCenter
```
public static final Vector2 getAverageCenter(Vector2... points)
```
    Returns the centroid of the given points by performing an average.
    
    Parameters:
    
    points - the array of points
    
    Returns:
    
    Vector2 the centroid
    
    Throws:
    
    java.lang.NullPointerException - if points is null or an element of points is null
    
    java.lang.IllegalArgumentException - if points is an empty array
    
    See Also:
    
    getAverageCenter(List)
  - getAreaWeightedCenter
```
public static final Vector2 getAreaWeightedCenter(java.util.List<Vector2> points)
```
    Returns the area weighted centroid for the given points.
    A Polygon's centroid must be computed by the area weighted method since the average method can be bias to one side if there are more points on that one side than another.
    Finding the area of a Polygon can be done by using the following summation:
    0.5 * ∑(x_i * y_{i + 1} - x_{i + 1} * y_i)
    Finding the area weighted centroid can be done by using the following summation:
    1 / (6 * A) * ∑(p_i + p_{i + 1}) * (x_i * y_{i + 1} - x_{i + 1} * y_i)
    
    Parameters:
    
    points - the Polygon points
    
    Returns:
    
    Vector2 the area weighted centroid
    
    Throws:
    
    java.lang.NullPointerException - if points is null or an element of points is null
    
    java.lang.IllegalArgumentException - if points is empty
  - getAreaWeightedCenter
```
public static final Vector2 getAreaWeightedCenter(Vector2... points)
```
    Returns the area weighted centroid for the given points.
    
    Parameters:
    
    points - the Polygon points
    
    Returns:
    
    Vector2 the area weighted centroid
    
    Throws:
    
    java.lang.NullPointerException - if points is null or an element of points is null
    
    java.lang.IllegalArgumentException - if points is empty
    
    See Also:
    
    getAreaWeightedCenter(List)
  - getRotationRadius
```
public static final double getRotationRadius(Vector2... vertices)
```
    Returns the maximum radius of the given vertices rotated about the origin.
    If the vertices array is null or empty, zero is returned.
    
    Parameters:
    
    vertices - the polygon vertices
    
    Returns:
    
    double
    
    Since:
    
    3.2.0
    
    See Also:
    
    getRotationRadius(Vector2, Vector2...)
  - getRotationRadius
```
public static final double getRotationRadius(Vector2 center,
                                             Vector2... vertices)
```
    Returns the maximum radius of the given vertices rotated about the given center.
    If the vertices array is null or empty, zero is returned. If center is null the origin will be used instead.
    
    Parameters:
    
    center - the center point
    
    vertices - the polygon vertices
    
    Returns:
    
    double
    
    Since:
    
    3.2.0
  - getCounterClockwiseEdgeNormals
```
public static final Vector2[] getCounterClockwiseEdgeNormals(Vector2... vertices)
```
    Returns an array of normalized vectors representing the normals of all the edges given the vertices.
    This method assumes counter-clockwise ordering.
    Returns null if the given vertices array is null or empty.
    
    Parameters:
    
    vertices - the vertices
    
    Returns:
    
    Vector2[]
    
    Throws:
    
    java.lang.NullPointerException - if vertices contains a null element
    
    Since:
    
    3.2.0
  - createCircle
```
public static final Circle createCircle(double radius)
```
    Returns a new Circle with the given radius centered on the origin.
    
    Parameters:
    
    radius - the radius in meters
    
    Returns:
    
    Circle
    
    Throws:
    
    java.lang.IllegalArgumentException - if radius is less than or equal to zero
  - createPolygon
```
public static final Polygon createPolygon(Vector2... vertices)
```
    Returns a new Polygon with the given vertices.
    This method makes a copy of both the array and the vertices within the array to create the new Polygon.
    The center of the Polygon will be computed using the area weighted method.
    
    Parameters:
    
    vertices - the array of vertices
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if vertices is null or an element of vertices is null
    
    java.lang.IllegalArgumentException - if vertices contains less than 3 non-null vertices
    
    See Also:
    
    to create a new {@link Polygon} that is centered on the origin
  - createPolygonAtOrigin
```
public static final Polygon createPolygonAtOrigin(Vector2... vertices)
```
    Returns a new Polygon, using the given vertices, centered at the origin.
    This method makes a copy of both the array and the vertices within the array to create the new Polygon.
    This method translates the Polygon vertices so that the center is at the origin.
    
    Parameters:
    
    vertices - the array of vertices
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if vertices is null or an element of vertices is null
    
    java.lang.IllegalArgumentException - if vertices contains less than 3 non-null vertices
  - createUnitCirclePolygon
```
public static final Polygon createUnitCirclePolygon(int count,
                                                    double radius)
```
    Returns a new Polygon with count number of points, where the points are evenly distributed around the unit circle. The resulting Polygon will be centered on the origin.
    The radius parameter is the distance from the center of the polygon to each vertex.
    
    Parameters:
    
    count - the number of vertices
    
    radius - the radius from the center to each vertex in meters
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.IllegalArgumentException - if count is less than 3 or radius is less than or equal to zero
    
    See Also:
    
    createUnitCirclePolygon(int, double, double), createPolygonalCircle(int, double), createPolygonalCircle(int, double, double)
  - createUnitCirclePolygon
```
public static final Polygon createUnitCirclePolygon(int count,
                                                    double radius,
                                                    double theta)
```
    Returns a new Polygon with count number of points, where the points are evenly distributed around the unit circle. The resulting Polygon will be centered on the origin.
    The radius parameter is the distance from the center of the polygon to each vertex.
    The theta parameter is a vertex angle offset used to rotate all the vertices by the given amount.
    
    Parameters:
    
    count - the number of vertices
    
    radius - the radius from the center to each vertex in meters
    
    theta - the vertex angle offset in radians
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.IllegalArgumentException - if count is less than 3 or radius is less than or equal to zero
    
    See Also:
    
    createPolygonalCircle(int, double, double)
  - createSquare
```
public static final Rectangle createSquare(double size)
```
    Creates a square (equal height and width Rectangle) with the given size centered at the origin.
    
    Parameters:
    
    size - the size in meters
    
    Returns:
    
    Rectangle
    
    Throws:
    
    java.lang.IllegalArgumentException - if size is less than or equal to zero
  - createRectangle
```
public static final Rectangle createRectangle(double width,
                                              double height)
```
    Creates a new Rectangle with the given width and height centered at the origin.
    
    Parameters:
    
    width - the width in meters
    
    height - the height in meters
    
    Returns:
    
    Rectangle
    
    Throws:
    
    java.lang.IllegalArgumentException - if width or height is less than or equal to zero
  - createTriangle
```
public static final Triangle createTriangle(Vector2 p1,
                                            Vector2 p2,
                                            Vector2 p3)
```
    Creates a new Triangle, using the given points.
    This method makes a copy of the given points to create the Triangle.
    The center of the Triangle will be computed using the area weighted method.
    
    Parameters:
    
    p1 - the first point
    
    p2 - the second point
    
    p3 - the third point
    
    Returns:
    
    Triangle
    
    Throws:
    
    java.lang.NullPointerException - if p1, p2, or p3 is null
    
    See Also:
    
    to create a new {@link Triangle} that is centered on the origin
  - createTriangleAtOrigin
```
public static final Triangle createTriangleAtOrigin(Vector2 p1,
                                                    Vector2 p2,
                                                    Vector2 p3)
```
    Creates a new Triangle with the given points centered at the origin.
    This method makes a copy of the given points to create the Triangle.
    
    Parameters:
    
    p1 - the first point
    
    p2 - the second point
    
    p3 - the third point
    
    Returns:
    
    Triangle
    
    Throws:
    
    java.lang.NullPointerException - if p1, p2, or p3 is null
  - createRightTriangle
```
public static final Triangle createRightTriangle(double width,
                                                 double height)
```
    Creates a right angle Triangle with the center at the origin.
    
    Parameters:
    
    width - the width of the base in meters
    
    height - the height in meters
    
    Returns:
    
    Triangle
    
    Throws:
    
    java.lang.IllegalArgumentException - if width or height is less than or equal to zero
  - createRightTriangle
```
public static final Triangle createRightTriangle(double width,
                                                 double height,
                                                 boolean mirror)
```
    Creates a right angle Triangle with the center at the origin.
    
    Parameters:
    
    width - the width of the base in meters
    
    height - the height in meters
    
    mirror - true if the triangle should be mirrored along the y-axis
    
    Returns:
    
    Triangle
    
    Throws:
    
    java.lang.IllegalArgumentException - if width or height is less than or equal to zero
  - createEquilateralTriangle
```
public static final Triangle createEquilateralTriangle(double height)
```
    Creates an equilateral Triangle with the center at the origin.
    
    Parameters:
    
    height - the height of the triangle in meters
    
    Returns:
    
    Triangle
    
    Throws:
    
    java.lang.IllegalArgumentException - if height is less than or equal to zero
  - createIsoscelesTriangle
```
public static final Triangle createIsoscelesTriangle(double width,
                                                     double height)
```
    Creates an isosceles Triangle with the center at the origin.
    
    Parameters:
    
    width - the width of the base in meters
    
    height - the height in meters
    
    Returns:
    
    Triangle
    
    Throws:
    
    java.lang.IllegalArgumentException - if width or height is less than or equal to zero
  - createSegment
```
public static final Segment createSegment(Vector2 p1,
                                          Vector2 p2)
```
    Creates a new Segment with the given points.
    This method makes a copy of the given points to create the Segment.
    The center of the Segment will be the average of the two points.
    
    Parameters:
    
    p1 - the first point
    
    p2 - the second point
    
    Returns:
    
    Segment
    
    Throws:
    
    java.lang.NullPointerException - if p1 or p2 is null
    
    See Also:
    
    to create a {@link Segment} centered on the origin
  - createSegmentAtOrigin
```
public static final Segment createSegmentAtOrigin(Vector2 p1,
                                                  Vector2 p2)
```
    Creates a new Segment with the given points.
    This method makes a copy of the given points to create the Segment.
    This method translates the Segment vertices so that the center is at the origin.
    
    Parameters:
    
    p1 - the first point
    
    p2 - the second point
    
    Returns:
    
    Segment
    
    Throws:
    
    java.lang.NullPointerException - if p1 or p2 is null
  - createSegment
```
public static final Segment createSegment(Vector2 end)
```
    Creates a new Segment from the origin to the given end point
    This method makes a copy of the given point to create the Segment.
    
    Parameters:
    
    end - the end point
    
    Returns:
    
    Segment
    
    Throws:
    
    java.lang.NullPointerException - if end is null
  - createHorizontalSegment
```
public static final Segment createHorizontalSegment(double length)
```
    Creates a new Segment with the given length with the center at the origin.
    Renamed from createSegment(double).
    
    Parameters:
    
    length - the length of the segment in meters
    
    Returns:
    
    Segment
    
    Throws:
    
    java.lang.IllegalArgumentException - if length is less than or equal to zero
    
    Since:
    
    2.2.3
  - createVerticalSegment
```
public static final Segment createVerticalSegment(double length)
```
    Creates a new Segment with the given length with the center at the origin.
    
    Parameters:
    
    length - the length of the segment in meters
    
    Returns:
    
    Segment
    
    Throws:
    
    java.lang.IllegalArgumentException - if length is less than or equal to zero
    
    Since:
    
    2.2.3
  - createCapsule
```
public static final Capsule createCapsule(double width,
                                          double height)
```
    Creates a new Capsule bounded by the given rectangle width and height.
    The capsule will be axis-aligned and centered on the origin with the caps on the ends of the largest dimension.
    If width and height are equal use a Circle shape instead.
    
    Parameters:
    
    width - the bounding rectangle width
    
    height - the bounding rectangle height
    
    Returns:
    
    Capsule
    
    Throws:
    
    java.lang.IllegalArgumentException - if width or height are less than or equal to zero
    
    Since:
    
    3.1.5
  - createSlice
```
public static final Slice createSlice(double radius,
                                      double theta)
```
    Creates a new Slice with the given circle radius and arc length theta.
    A Slice is an arbitrary slice of a circle. The specified radius is the radius of the circle. The slice will be positioned with the circle center on the origin.
    Theta is the total arc length of the slice specified in radians. Theta is halved, putting half the arc length below the x-axis and half above.
    Theta cannot be greater than π.
    
    Parameters:
    
    radius - the circle radius
    
    theta - the total arc length in radians
    
    Returns:
    
    Slice
    
    Throws:
    
    java.lang.IllegalArgumentException - if radius is less than or equal to zero; if theta is less than or equal to zero or is greater than π
    
    Since:
    
    3.1.5
  - createSliceAtOrigin
```
public static final Slice createSliceAtOrigin(double radius,
                                              double theta)
```
    Creates a new Slice with the given circle radius and arc length theta.
    A Slice is an arbitrary slice of a circle. The specified radius is the radius of the circle. The slice will be positioned with the centroid at the origin.
    Theta is the total arc length of the slice specified in radians. Theta is halved, putting half the arc length below the x-axis and half above.
    Theta cannot be greater than π.
    
    Parameters:
    
    radius - the circle radius
    
    theta - the total arc length in radians
    
    Returns:
    
    Slice
    
    Throws:
    
    java.lang.IllegalArgumentException - if radius is less than or equal to zero; if theta is less than or equal to zero or is greater than π
    
    Since:
    
    3.1.5
  - createEllipse
```
public static final Ellipse createEllipse(double width,
                                          double height)
```
    Creates a new Ellipse bounded by the given rectangle width and height.
    The ellipse will be axis-aligned and centered on the origin.
    If width and height are equal use a Circle shape instead.
    
    Parameters:
    
    width - the bounding rectangle width
    
    height - the bounding rectangle height
    
    Returns:
    
    Ellipse
    
    Throws:
    
    java.lang.IllegalArgumentException - if width or height are less than or equal to zero
    
    Since:
    
    3.1.5
  - createHalfEllipse
```
public static final HalfEllipse createHalfEllipse(double width,
                                                  double height)
```
    Creates a new HalfEllipse bounded by the given rectangle width and height.
    The ellipse will be axis-aligned with the base of the half ellipse on the x-axis. The given height is the height of the half, not the height of the full ellipse.
    If width and height are equal use a Slice shape with theta = Math.PI instead.
    
    Parameters:
    
    width - the bounding rectangle width
    
    height - the bounding rectangle height
    
    Returns:
    
    HalfEllipse
    
    Throws:
    
    java.lang.IllegalArgumentException - if width or height are less than or equal to zero
    
    Since:
    
    3.1.5
  - createHalfEllipseAtOrigin
```
public static final HalfEllipse createHalfEllipseAtOrigin(double width,
                                                          double height)
```
    Creates a new HalfEllipse bounded by the given rectangle width and height.
    The ellipse will be axis-aligned with the base of the half ellipse on the x-axis. The given height is the height of the half, not the height of the full ellipse.
    If width and height are equal use a Slice shape with theta = Math.PI instead.
    
    Parameters:
    
    width - the bounding rectangle width
    
    height - the bounding rectangle height
    
    Returns:
    
    HalfEllipse
    
    Throws:
    
    java.lang.IllegalArgumentException - if width or height are less than or equal to zero
    
    Since:
    
    3.1.5
  - createPolygonalCircle
```
public static final Polygon createPolygonalCircle(int count,
                                                  double radius)
```
    Creates a new Polygon in the shape of a circle with count number of vertices centered on the origin.
    
    Parameters:
    
    count - the number of vertices to use; must be greater than 2
    
    radius - the radius of the circle; must be greater than zero
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.IllegalArgumentException - thrown if count is less than 3 or the radius is less than or equal to zero
    
    Since:
    
    3.1.5
  - createPolygonalCircle
```
public static final Polygon createPolygonalCircle(int count,
                                                  double radius,
                                                  double theta)
```
    Creates a new Polygon in the shape of a circle with count number of vertices centered on the origin.
    
    Parameters:
    
    count - the number of vertices to use; must be greater than or equal to 3
    
    radius - the radius of the circle; must be greater than zero
    
    theta - the radial offset for the points in radians
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.IllegalArgumentException - thrown if count is less than 3 or the radius is less than or equal to zero
    
    Since:
    
    3.1.5
  - createPolygonalSlice
```
public static final Polygon createPolygonalSlice(int count,
                                                 double radius,
                                                 double theta)
```
    Creates a new Polygon in the shape of a Slice with count number of vertices with the circle center centered on the origin.
    This method returns a polygon with count + 3 vertices.
    
    Parameters:
    
    count - the number of vertices to use; must be greater than or equal to 1
    
    radius - the radius of the circle; must be greater than zero
    
    theta - the arc length of the slice in radians; must be greater than zero
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.IllegalArgumentException - thrown if count is less than 1 or the radius is less than or equal to zero or theta is less than or equal to zero
    
    Since:
    
    3.1.5
  - createPolygonalSliceAtOrigin
```
public static final Polygon createPolygonalSliceAtOrigin(int count,
                                                         double radius,
                                                         double theta)
```
    Creates a new Polygon in the shape of a Slice with count number of vertices centered on the origin.
    This method returns a polygon with count + 3 vertices.
    
    Parameters:
    
    count - the number of vertices to use; must be greater than or equal to 1
    
    radius - the radius of the circle; must be greater than zero
    
    theta - the arc length of the slice in radians; must be greater than zero
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.IllegalArgumentException - thrown if count is less than 1 or the radius is less than or equal to zero or theta is less than or equal to zero
    
    Since:
    
    3.1.5
  - createPolygonalEllipse
```
public static final Polygon createPolygonalEllipse(int count,
                                                   double width,
                                                   double height)
```
    Creates a new Polygon in the shape of an ellipse with count number of vertices centered on the origin.
    The count should be greater than or equal to 4 and a multiple of 2. If not, the returned polygon will have count - 1 vertices.
    
    Parameters:
    
    count - the number of vertices to use; must be greater than or equal to 4; should be even, if not, count - 1 vertices will be generated
    
    width - the width of the ellipse
    
    height - the height of the ellipse
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.IllegalArgumentException - thrown if count is less than 4 or the width or height are less than or equal to zero
    
    Since:
    
    3.1.5
  - createPolygonalHalfEllipse
```
public static final Polygon createPolygonalHalfEllipse(int count,
                                                       double width,
                                                       double height)
```
    Creates a new Polygon in the shape of a half ellipse with count number of vertices with the base at the origin.
    Returns a polygon with count + 2 vertices.
    The height is the total height of the half not the half height.
    
    Parameters:
    
    count - the number of vertices to use; must be greater than or equal to 1
    
    width - the width of the half ellipse
    
    height - the height of the half ellipse; should be the total height
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.IllegalArgumentException - thrown if count is less than 1 or the width or height are less than or equal to zero
    
    Since:
    
    3.1.5
  - createPolygonalHalfEllipseAtOrigin
```
public static final Polygon createPolygonalHalfEllipseAtOrigin(int count,
                                                               double width,
                                                               double height)
```
    Creates a new Polygon in the shape of a half ellipse with count number of vertices centered on the origin.
    Returns a polygon with count + 2 vertices.
    The height is the total height of the half not the half height.
    
    Parameters:
    
    count - the number of vertices to use; should be even, if not, count - 1 vertices will be generated
    
    width - the width of the half ellipse
    
    height - the height of the half ellipse; should be the total height
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.IllegalArgumentException - thrown if count is less than 1 or the width or height are less than or equal to zero
    
    Since:
    
    3.1.5
  - createPolygonalCapsule
```
public static final Polygon createPolygonalCapsule(int count,
                                                   double width,
                                                   double height)
```
    Creates a new Polygon in the shape of a capsule using count number of vertices on each cap, centered on the origin. The caps will be on the ends of the largest dimension.
    The returned polygon will have 4 + 2 * count number of vertices.
    
    Parameters:
    
    count - the number of vertices to use for one cap; must be greater than or equal to 1
    
    width - the bounding rectangle width
    
    height - the bounding rectangle height
    
    Returns:
    
    Polygon
    
    Since:
    
    3.1.5
  - cleanse
```
public static final java.util.List<Vector2> cleanse(java.util.List<Vector2> points)
```
    Returns a new list containing the 'cleansed' version of the given listing of polygon points.
    This method ensures the polygon has CCW winding, removes colinear vertices, and removes coincident vertices.
    If the given list is empty, the list is returned.
    
    Parameters:
    
    points - the list polygon points
    
    Returns:
    
    List<Vector2>
    
    Throws:
    
    java.lang.NullPointerException - if points is null or if points contains null elements
  - cleanse
```
public static final Vector2[] cleanse(Vector2... points)
```
    Returns a new array containing the 'cleansed' version of the given array of polygon points.
    This method ensures the polygon has CCW winding, removes colinear vertices, and removes coincident vertices.
    
    Parameters:
    
    points - the list polygon points
    
    Returns:
    
    Vector2[]
    
    Throws:
    
    java.lang.NullPointerException - if points is null or points contains null elements
  - flipAlongTheXAxis
```
public static final Polygon flipAlongTheXAxis(Polygon polygon)
```
    Flips the given polygon about its center along the x-axis and returns the result as a new polygon.
    This method assumes that the line is through the origin.
    
    Parameters:
    
    polygon - the polygon to flip
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if the given polygon is null
    
    Since:
    
    3.1.4
    
    See Also:
    
    flip(Polygon, Vector2), flip(Polygon, Vector2, Vector2)
  - flipAlongTheYAxis
```
public static final Polygon flipAlongTheYAxis(Polygon polygon)
```
    Flips the given polygon about its center along the y-axis and returns the result as a new polygon.
    This method assumes that the line is through the origin.
    
    Parameters:
    
    polygon - the polygon to flip
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if the given polygon is null
    
    Since:
    
    3.1.4
    
    See Also:
    
    flip(Polygon, Vector2), flip(Polygon, Vector2, Vector2)
  - flipAlongTheXAxis
```
public static final Polygon flipAlongTheXAxis(Polygon polygon,
                                              Vector2 point)
```
    Flips the given polygon about the given point along the x-axis and returns the result as a new polygon.
    
    Parameters:
    
    polygon - the polygon to flip
    
    point - the point to flip about
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if the given polygon is null
    
    Since:
    
    3.1.4
    
    See Also:
    
    flip(Polygon, Vector2), flip(Polygon, Vector2, Vector2)
  - flipAlongTheYAxis
```
public static final Polygon flipAlongTheYAxis(Polygon polygon,
                                              Vector2 point)
```
    Flips the given polygon about the given point along the y-axis and returns the result as a new polygon.
    
    Parameters:
    
    polygon - the polygon to flip
    
    point - the point to flip about
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if the given polygon is null
    
    Since:
    
    3.1.4
    
    See Also:
    
    flip(Polygon, Vector2), flip(Polygon, Vector2, Vector2)
  - flip
```
public static final Polygon flip(Polygon polygon,
                                 Vector2 axis)
```
    Flips the given polygon about the given line and returns the result as a new polygon.
    This method assumes that the line is through the origin.
    
    Parameters:
    
    polygon - the polygon to flip
    
    axis - the axis to flip about
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if the given polygon or axis is null
    
    java.lang.IllegalArgumentException - if the given axis is the zero vector
    
    Since:
    
    3.1.4
    
    See Also:
    
    flip(Polygon, Vector2, Vector2)
  - flip
```
public static final Polygon flip(Polygon polygon,
                                 Vector2 axis,
                                 Vector2 point)
```
    Flips the given polygon about the given line and returns the result as a new polygon.
    
    Parameters:
    
    polygon - the polygon to flip
    
    axis - the axis to flip about
    
    point - the point to flip about; if null, the polygon center is used
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if the given polygon or axis is null
    
    java.lang.IllegalArgumentException - if the given axis is the zero vector
    
    Since:
    
    3.1.4
  - minkowskiSum
```
public static final <E extends Wound & Convex> Polygon minkowskiSum(E convex1,
                                                                    E convex2)
```
    Returns the Minkowski Sum of the given convex shapes.
    This method computes the Minkowski Sum in O(n + m) time where n and m are the number of vertices of the first and second convex respectively.
    This method accepts any Convex Wound shape which basically means Polygons or Segments.
    This method throws an IllegalArgumentException if two Segments are supplied that are colinear (in this case the resulting Minkowski Sum would be another segment rather than a polygon).
    
    Type Parameters:
    
    E - either a Wound or Convex type
    
    Parameters:
    
    convex1 - the first convex
    
    convex2 - the second convex
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if convex1 or convex2 are null
    
    java.lang.IllegalArgumentException - if both convex1 and convex2 are Segments and are colinear
    
    Since:
    
    3.1.5
  - minkowskiSum
```
public static final Polygon minkowskiSum(Circle circle,
                                         Polygon polygon,
                                         int count)
```
    Performs the Minkowski Sum of the given Polygon and Circle.
    Use the count parameter to specify the number of vertices to use per round corner.
    If the given polygon has n number of vertices, the returned polygon will have n * 2 + n * count number of vertices.
    This method is O(n) where n is the number of vertices in the given polygon.
    
    Parameters:
    
    polygon - the polygon
    
    circle - the circle to add to the polygon
    
    count - the number of vertices to add for each rounded corner; must be greater than zero
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if the given polygon or circle is null
    
    java.lang.IllegalArgumentException - if the given radius or count is less than or equal to zero
    
    Since:
    
    3.1.5
    
    See Also:
    
    minkowskiSum(Polygon, double, int)
  - minkowskiSum
```
public static final Polygon minkowskiSum(Polygon polygon,
                                         Circle circle,
                                         int count)
```
    Performs the Minkowski Sum of the given Polygon and Circle.
    Use the count parameter to specify the number of vertices to use per round corner.
    If the given polygon has n number of vertices, the returned polygon will have n * 2 + n * count number of vertices.
    This method is O(n) where n is the number of vertices in the given polygon.
    
    Parameters:
    
    polygon - the polygon
    
    circle - the circle to add to the polygon
    
    count - the number of vertices to add for each rounded corner; must be greater than zero
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if the given polygon or circle is null
    
    java.lang.IllegalArgumentException - if the given radius or count is less than or equal to zero
    
    Since:
    
    3.1.5
    
    See Also:
    
    minkowskiSum(Polygon, double, int)
  - minkowskiSum
```
public static final Polygon minkowskiSum(Polygon polygon,
                                         double radius,
                                         int count)
```
    Returns a new polygon that has been radially expanded. This is equivalent to the Minkowski sum of a circle, of the given radius, and the given polygon.
    Use the count parameter to specify the number of vertices to use per round corner.
    If the given polygon has n number of vertices, the returned polygon will have n * 2 + n * count number of vertices.
    This method is O(n) where n is the number of vertices in the given polygon.
    
    Parameters:
    
    polygon - the polygon to expand radially
    
    radius - the radial expansion; must be greater than zero
    
    count - the number of vertices to add for each rounded corner; must be greater than zero
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if the given polygon is null
    
    java.lang.IllegalArgumentException - if the given radius or count is less than or equal to zero
    
    Since:
    
    3.1.5
  - scale
```
public static final Circle scale(Circle circle,
                                 double scale)
```
    Returns a scaled version of the given circle.
    
    Parameters:
    
    circle - the circle
    
    scale - the scale; must be greater than zero
    
    Returns:
    
    Circle
    
    Throws:
    
    java.lang.NullPointerException - if the given circle is null
    
    java.lang.IllegalArgumentException - if the given scale is less than or equal to zero
    
    Since:
    
    3.1.5
  - scale
```
public static final Capsule scale(Capsule capsule,
                                  double scale)
```
    Returns a scaled version of the given capsule.
    
    Parameters:
    
    capsule - the capsule
    
    scale - the scale; must be greater than zero
    
    Returns:
    
    Capsule
    
    Throws:
    
    java.lang.NullPointerException - if the given capsule is null
    
    java.lang.IllegalArgumentException - if the given scale is less than or equal to zero
    
    Since:
    
    3.1.5
  - scale
```
public static final Ellipse scale(Ellipse ellipse,
                                  double scale)
```
    Returns a scaled version of the given ellipse.
    
    Parameters:
    
    ellipse - the ellipse
    
    scale - the scale; must be greater than zero
    
    Returns:
    
    Ellipse
    
    Throws:
    
    java.lang.NullPointerException - if the given ellipse is null
    
    java.lang.IllegalArgumentException - if the given scale is less than or equal to zero
    
    Since:
    
    3.1.5
  - scale
```
public static final HalfEllipse scale(HalfEllipse halfEllipse,
                                      double scale)
```
    Returns a scaled version of the given half-ellipse.
    
    Parameters:
    
    halfEllipse - the half-ellipse
    
    scale - the scale; must be greater than zero
    
    Returns:
    
    HalfEllipse
    
    Throws:
    
    java.lang.NullPointerException - if the given half-ellipse is null
    
    java.lang.IllegalArgumentException - if the given scale is less than or equal to zero
    
    Since:
    
    3.1.5
  - scale
```
public static final Slice scale(Slice slice,
                                double scale)
```
    Returns a scaled version of the given slice.
    
    Parameters:
    
    slice - the slice
    
    scale - the scale; must be greater than zero
    
    Returns:
    
    Slice
    
    Throws:
    
    java.lang.NullPointerException - if the given slice is null
    
    java.lang.IllegalArgumentException - if the given scale is less than or equal to zero
    
    Since:
    
    3.1.5
  - scale
```
public static final Polygon scale(Polygon polygon,
                                  double scale)
```
    Returns a scaled version of the given polygon.
    
    Parameters:
    
    polygon - the polygon
    
    scale - the scale; must be greater than zero
    
    Returns:
    
    Polygon
    
    Throws:
    
    java.lang.NullPointerException - if the given polygon is null
    
    java.lang.IllegalArgumentException - if the given scale is less than or equal to zero
    
    Since:
    
    3.1.5
  - scale
```
public static final Segment scale(Segment segment,
                                  double scale)
```
    Returns a scaled version of the given segment.
    
    Parameters:
    
    segment - the segment
    
    scale - the scale; must be greater than zero
    
    Returns:
    
    Segment
    
    Throws:
    
    java.lang.NullPointerException - if the given segment is null
    
    java.lang.IllegalArgumentException - if the given scale is less than or equal to zero
    
    Since:
    
    3.1.5
  - createLinks
```
public static final java.util.List<Link> createLinks(java.util.List<Vector2> vertices,
                                                     boolean closed)
```
    Creates a list of Links for the given vertices.
    If the closed parameter is true, an extra link is created joining the last and first vertices in the list.
    
    Parameters:
    
    vertices - the poly-line vertices
    
    closed - true if the shape should be enclosed
    
    Returns:
    
    List<Link>
    
    Throws:
    
    java.lang.NullPointerException - if the list of vertices is null or an element of the vertex list is null
    
    java.lang.IllegalArgumentException - if the list of vertices doesn't contain 2 or more elements
    
    Since:
    
    3.2.2
  - createLinks
```
public static final java.util.List<Link> createLinks(Vector2[] vertices,
                                                     boolean closed)
```
    Creates a Link chain for the given vertices.
    If the closed parameter is true, an extra link is created joining the last and first vertices in the array.
    
    Parameters:
    
    vertices - the poly-line vertices
    
    closed - true if the shape should be enclosed
    
    Returns:
    
    List<Link>
    
    Throws:
    
    java.lang.NullPointerException - if the array of vertices is null or an element of the vertex array is null
    
    java.lang.IllegalArgumentException - if the array of vertices doesn't contain 2 or more elements
    
    Since:
    
    3.2.2

Class Geometry

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

TWO_PI

INV_3

INV_SQRT_3

Constructor Detail

Geometry

Method Detail

getWinding

getWinding

reverseWinding

reverseWinding

getAverageCenter

getAverageCenter

getAreaWeightedCenter

getAreaWeightedCenter

getRotationRadius

getRotationRadius

getCounterClockwiseEdgeNormals

createCircle

createPolygon

createPolygonAtOrigin

createUnitCirclePolygon

createUnitCirclePolygon

createSquare

createRectangle

createTriangle

createTriangleAtOrigin

createRightTriangle

createRightTriangle

createEquilateralTriangle

createIsoscelesTriangle

createSegment

createSegmentAtOrigin

createSegment

createHorizontalSegment

createVerticalSegment

createCapsule

createSlice

createSliceAtOrigin

createEllipse

createHalfEllipse

createHalfEllipseAtOrigin

createPolygonalCircle

createPolygonalCircle

createPolygonalSlice

createPolygonalSliceAtOrigin

createPolygonalEllipse

createPolygonalHalfEllipse

createPolygonalHalfEllipseAtOrigin

createPolygonalCapsule

cleanse

cleanse

flipAlongTheXAxis

flipAlongTheYAxis

flipAlongTheXAxis

flipAlongTheYAxis

flip

flip

minkowskiSum

minkowskiSum

minkowskiSum

minkowskiSum

scale

scale

scale

scale

scale

scale

scale

createLinks

createLinks