Package arc.math.geom

Class Geometry

java.lang.Object

arc.math.geom.Geometry

public final class Geometry
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static interface	Geometry.Raycaster
static interface	Geometry.SolidChecker

Field Summary

Fields

Modifier and Type	Field	Description
static final Point2[]	d4	Points representing cardinal directions, starting at the left and going counter-clockwise.
static final Point2[]	d4c	Points representing cardinal directions, starting at the left and going counter-clockwise.
static final int[]	d4x
static final int[]	d4y
static final Point2[]	d8
static final Point2[]	d8edge

Constructor Summary

Constructors

Constructor	Description
Geometry()

Method Summary

Modifier and Type	Method	Description
static boolean	barycoordInsideTriangle(Vec2 barycentric)	Returns true if the barycentric coordinates are inside the triangle.
static void	circle(int x, int y, int width, int height, int radius, Intc2 cons)
static void	circle(int x, int y, int radius, Intc2 cons)
static boolean	colinear(float x1, float y1, float x2, float y2, float x3, float y3)
static Point2	d4(int i)
static int	d4x(int i)
static int	d4y(int i)
static Point2	d8(int i)
static Point2	d8edge(int i)
static void	ensureCCW(float[] polygon)
static void	ensureCCW(float[] polygon, int offset, int count)
static <T extends Position> T	findClosest(float x, float y, Iterable<T> list)
static <T extends Position> T	findClosest(float x, float y, T[] list)
static <T extends Position> T	findFurthest(float x, float y, Iterable<T> list)
static float	fromBarycoord(Vec2 barycentric, float a, float b, float c)	Returns an interpolated value given the barycentric coordinates of a point in a triangle and the values at each vertex.
static Vec2	fromBarycoord(Vec2 barycentric, Vec2 a, Vec2 b, Vec2 c, Vec2 interpolatedOut)	Returns interpolated values given the barycentric coordinates of a point in a triangle and the values at each vertex.
static Point2[]	getD4Points()
static Point2[]	getD8EdgePoints()
static Point2[]	getD8Points()
static boolean	isClockwise(float[] polygon, int offset, int count)
static float	iterateLine(float start, float x1, float y1, float x2, float y2, float segment, Floatc2 pos)
static void	iteratePolygon(Floatc2 path, float[] vertices)
static void	iteratePolySegments(float[] vertices, Floatc4 it)
static float	lowestPositiveRoot(float a, float b, float c)	Returns the lowest positive root of the quadric equation given by a* x * x + b * x + c = 0.
static Vec2	overlap(Rect a, Rect b, boolean x)	Checks for collisions between two rectangles, and returns the correct delta vector of A.
static Vec2[]	pixelCircle(float tindex)
static Vec2[]	pixelCircle(float index, Geometry.SolidChecker checker)
static float	polygonArea(float[] polygon, int offset, int count)	Computes the area for a convex polygon.
static Vec2	polygonCentroid(float[] polygon, int offset, int count, Vec2 centroid)	Returns the centroid for the specified non-self-intersecting polygon.
static Vec2	quadrilateralCentroid(float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4, Vec2 centroid)
static boolean	raycast(int x0f, int y0f, int x1, int y1, Geometry.Raycaster cons)
static Vec2	raycastRect(float startx, float starty, float endx, float endy, float x, float y, float halfx, float halfy)
static Vec2	raycastRect(float startx, float starty, float endx, float endy, Rect rect)
static float[]	regPoly(int amount, float size)	returns a regular polygon with {amount} sides
static Vec2	toBarycoord(Vec2 p, Vec2 a, Vec2 b, Vec2 c, Vec2 barycentricOut)	Computes the barycentric coordinates v,w for the specified point in the triangle.
static float	triangleArea(float x1, float y1, float x2, float y2, float x3, float y3)
static Vec2	triangleCentroid(float x1, float y1, float x2, float y2, float x3, float y3, Vec2 centroid)
static Vec2	triangleCircumcenter(float x1, float y1, float x2, float y2, float x3, float y3, Vec2 circumcenter)	Returns the circumcenter of the triangle.
static float	triangleCircumradius(float x1, float y1, float x2, float y2, float x3, float y3)
static float	triangleQuality(float x1, float y1, float x2, float y2, float x3, float y3)	Ratio of circumradius to shortest edge as a measure of triangle quality.
static FloatSeq	vectorsToFloats(Seq<Vec2> result)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

d4

public static final Point2[] d4

Points representing cardinal directions, starting at the left and going counter-clockwise.

d4c

public static final Point2[] d4c

Points representing cardinal directions, starting at the left and going counter-clockwise. Also contains a center point: 0,0.

d4x

public static final int[] d4x

d4y

public static final int[] d4y

d8

public static final Point2[] d8

d8edge

public static final Point2[] d8edge

Constructor Details

Geometry

public Geometry()

Method Details

d4

public static Point2 d4(int i)

d4x

public static int d4x(int i)

d4y

public static int d4y(int i)

d8

public static Point2 d8(int i)

d8edge

public static Point2 d8edge(int i)

circle

public static void circle(int x,
 int y,
 int radius,
 Intc2 cons)

circle

public static void circle(int x,
 int y,
 int width,
 int height,
 int radius,
 Intc2 cons)

vectorsToFloats

public static FloatSeq vectorsToFloats(Seq<Vec2> result)

findClosest

public static <T extends Position> T findClosest(float x,
 float y,
 T[] list)

findClosest

public static <T extends Position> T findClosest(float x,
 float y,
 Iterable<T> list)

findFurthest

public static <T extends Position> T findFurthest(float x,
 float y,
 Iterable<T> list)

pixelCircle

public static Vec2[] pixelCircle(float tindex)

pixelCircle

public static Vec2[] pixelCircle(float index,
 Geometry.SolidChecker checker)

regPoly

public static float[] regPoly(int amount,
 float size)

returns a regular polygon with {amount} sides

iterateLine

public static float iterateLine(float start,
 float x1,
 float y1,
 float x2,
 float y2,
 float segment,
 Floatc2 pos)

iteratePolySegments

public static void iteratePolySegments(float[] vertices,
 Floatc4 it)

iteratePolygon

public static void iteratePolygon(Floatc2 path,
 float[] vertices)

getD4Points

public static Point2[] getD4Points()

getD8Points

public static Point2[] getD8Points()

getD8EdgePoints

public static Point2[] getD8EdgePoints()

raycast

public static boolean raycast(int x0f,
 int y0f,
 int x1,
 int y1,
 Geometry.Raycaster cons)

raycastRect

public static Vec2 raycastRect(float startx,
 float starty,
 float endx,
 float endy,
 Rect rect)

raycastRect

public static Vec2 raycastRect(float startx,
 float starty,
 float endx,
 float endy,
 float x,
 float y,
 float halfx,
 float halfy)

overlap

public static Vec2 overlap(Rect a,
 Rect b,
 boolean x)

Checks for collisions between two rectangles, and returns the correct delta vector of A. Note: The same vector instance is returned each time!

toBarycoord

public static Vec2 toBarycoord(Vec2 p,
 Vec2 a,
 Vec2 b,
 Vec2 c,
 Vec2 barycentricOut)

Computes the barycentric coordinates v,w for the specified point in the triangle.

If barycentric.x >= 0 && barycentric.y >= 0 && barycentric.x + barycentric.y <= 1 then the point is inside the triangle.

If vertices a,b,c have values aa,bb,cc then to get an interpolated value at point p:

 Geometry.barycentric(p, a, b, c, barycentric);
 float u = 1.f - barycentric.x - barycentric.y;
 float x = u * aa.x + barycentric.x * bb.x + barycentric.y * cc.x;
 float y = u * aa.y + barycentric.x * bb.y + barycentric.y * cc.y;
 

Returns:

barycentricOut

barycoordInsideTriangle

public static boolean barycoordInsideTriangle(Vec2 barycentric)

Returns true if the barycentric coordinates are inside the triangle.

fromBarycoord

public static Vec2 fromBarycoord(Vec2 barycentric,
 Vec2 a,
 Vec2 b,
 Vec2 c,
 Vec2 interpolatedOut)

Returns interpolated values given the barycentric coordinates of a point in a triangle and the values at each vertex.

Returns:

interpolatedOut

fromBarycoord

public static float fromBarycoord(Vec2 barycentric,
 float a,
 float b,
 float c)

Returns an interpolated value given the barycentric coordinates of a point in a triangle and the values at each vertex.

Returns:

interpolatedOut

lowestPositiveRoot

public static float lowestPositiveRoot(float a,
 float b,
 float c)

Returns the lowest positive root of the quadric equation given by a* x * x + b * x + c = 0. If no solution is given Float.Nan is returned.

Parameters:

a - the first coefficient of the quadric equation

b - the second coefficient of the quadric equation

c - the third coefficient of the quadric equation

Returns:

the lowest positive root or Float.Nan

colinear

public static boolean colinear(float x1,
 float y1,
 float x2,
 float y2,
 float x3,
 float y3)

triangleCentroid

public static Vec2 triangleCentroid(float x1,
 float y1,
 float x2,
 float y2,
 float x3,
 float y3,
 Vec2 centroid)

triangleCircumcenter

public static Vec2 triangleCircumcenter(float x1,
 float y1,
 float x2,
 float y2,
 float x3,
 float y3,
 Vec2 circumcenter)

Returns the circumcenter of the triangle. The input points must not be colinear.

triangleCircumradius

public static float triangleCircumradius(float x1,
 float y1,
 float x2,
 float y2,
 float x3,
 float y3)

triangleQuality

public static float triangleQuality(float x1,
 float y1,
 float x2,
 float y2,
 float x3,
 float y3)

Ratio of circumradius to shortest edge as a measure of triangle quality.

Gary L. Miller, Dafna Talmor, Shang-Hua Teng, and Noel Walkington. A Delaunay Based Numerical Method for Three Dimensions: Generation, Formulation, and Partition.

triangleArea

public static float triangleArea(float x1,
 float y1,
 float x2,
 float y2,
 float x3,
 float y3)

quadrilateralCentroid

public static Vec2 quadrilateralCentroid(float x1,
 float y1,
 float x2,
 float y2,
 float x3,
 float y3,
 float x4,
 float y4,
 Vec2 centroid)

polygonCentroid

public static Vec2 polygonCentroid(float[] polygon,
 int offset,
 int count,
 Vec2 centroid)

Returns the centroid for the specified non-self-intersecting polygon.

polygonArea

public static float polygonArea(float[] polygon,
 int offset,
 int count)

Computes the area for a convex polygon.

ensureCCW

public static void ensureCCW(float[] polygon)

ensureCCW

public static void ensureCCW(float[] polygon,
 int offset,
 int count)

isClockwise

public static boolean isClockwise(float[] polygon,
 int offset,
 int count)