Static Public Member Functions
static void	point_to_line_dist (double nearness)

static boolean	is_point_near_line (Vector2D v0, Vector2D v1, Vector2D p)

static boolean	is_point_near_line (Vector2D v0, Vector2D v1, Vector2D p, Vector2D vp)

static boolean	is_point_near_infinite_line (Vector2D v0, Vector2D v1, Vector2D p)

static boolean	is_point_near_infinite_line (Vector2D v0, Vector2D v1, Vector2D p, Vector2D vp)

static Vector2D	point_nearest_line (Vector2D v0, Vector2D v1, Vector2D p)

static Vector2D	point_nearest_infinite_line (Vector2D v0, Vector2D v1, Vector2D p)

static boolean	line_circle (double x0, double y0, double x1, double y1, double cx, double cy, double r)

static double[]	line_circle_p (double x0, double y0, double x1, double y1, double cx, double cy, double r)

static boolean	line_line (double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)

static Vector2D	line_line_p (Vector2D v0, Vector2D v1, Vector2D v2, Vector2D v3)

static Vector2D	line_line_infinite_p (Vector2D v0, Vector2D v1, Vector2D v2, Vector2D v3)

static double[]	line_line_p (double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)

static double[]	line_line_infinite_p (double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)

static double[]	line_lines_p (double x0, double y0, double x1, double y1, double[] xy, boolean continuous)

static boolean	circle_circle (double cx0, double cy0, double r0, double cx1, double cy1, double r1)

static double[]	circle_circle_p (double cx0, double cy0, double r0, double cx1, double cy1, double r1)

static double[]	tangents_to_circle (double x, double y, double cx, double cy, double r)

static double[]	tangents_between_circles (double cx0, double cy0, double r0, double cx1, double cy1, double r1)

static int	which_side_pp (double x0, double y0, double x1, double y1, double px, double py)

static int	which_side_pn (double x0, double y0, double nx, double ny, double px, double py)

static boolean	line_box_xyxy (double lx0, double ly0, double lx1, double ly1, double rx0, double ry0, double rx1, double ry1)

static boolean	line_box_xywh (double lx0, double ly0, double lx1, double ly1, double rx0, double ry0, double rWidth, double rHeight)

static boolean	box_box (double ax0, double ay0, double ax1, double ay1, double bx0, double by0, double bx1, double by1)

static double[]	box_box_p (double ax0, double ay0, double ax1, double ay1, double bx0, double by0, double bx1, double by1)

static boolean	isInsideTriangle (double aX, double aY, double bX, double bY, double cX, double cY, double pX, double pY)

static boolean	isInsideTriangle (Vector2D a, Vector2D b, Vector2D c, Vector2D p)

static boolean	isInsideTriangle (Vector2D a, Vector2D b, Vector2D c, double pX, double pY)

static boolean	isInsideRectangle_xyxy (double x0, double y0, double x1, double y1, double pX, double pY)

static boolean	isInsideRectangle_xyxy (Vector2D v0, Vector2D v1, Vector2D p)

static boolean	isInsideRectangle_xywh (double x0, double y0, double width, double height, double pX, double pY)

static boolean	isInsideRectangle_xywh (Vector2D v0, double width, double height, Vector2D p)

static boolean	isInsidePolygon (Vector2D[] verts, double x0, double y0)

static double	distance_sq (double x0, double y0, double x1, double y1)

static double	distance (double x0, double y0, double x1, double y1)

Static Public Attributes
static final int	ON_PLANE = 16

static final int	PLANE_INSIDE = 17

static final int	PLANE_OUTSIDE = 18

Static Private Member Functions
static int	outcode (double pX, double pY, double rectX, double rectY, double rectWidth, double rectHeight)

Static Private Attributes
static final double	ACCY = 1E-30

static final double[]	NONE = new double[0]

static final int	OUT_LEFT = 1

static final int	OUT_TOP = 2

static final int	OUT_RIGHT = 4

static final int	OUT_BOTTOM = 8

static double	NEARNESS = 1.0

Member Function Documentation

◆ box_box()

static boolean game2dai.maths.Geometry2D.box_box	(	double	ax0,
		double	ay0,
		double	ax1,
		double	ay1,
		double	bx0,
		double	by0,
		double	bx1,
		double	by1
	)

static

Determine whether two boxes intersect.
The boxes are represented by the top-left and bottom-right corner coordinates.

Parameters

ax0	top-left corner of rectangle A
ay0	top-left corner of rectangle A
ax1	bottom-right corner of rectangle A
ay1	bottom-right corner of rectangle A
bx0	top-left corner of rectangle B
by0	top-left corner of rectangle B
bx1	bottom-right corner of rectangle B
by1	bottom-right corner of rectangle B

Returns: true if the boxes intersect

◆ box_box_p()

static double[] game2dai.maths.Geometry2D.box_box_p	(	double	ax0,
		double	ay0,
		double	ax1,
		double	ay1,
		double	bx0,
		double	by0,
		double	bx1,
		double	by1
	)

static

If two boxes overlap then the overlap region is another box. This method is used to calculate the coordinates of the overlap.
The boxes are represented by the top-left and bottom-right corner coordinates. If the returned array has a length: 0 then they do not overlap
4 then these are the coordinates of the top-left and bottom-right corners of the overlap region.

Parameters

ax0	top-left corner of rectangle A
ay0	top-left corner of rectangle A
ax1	bottom-right corner of rectangle A
ay1	bottom-right corner of rectangle A
bx0	top-left corner of rectangle B
by0	top-left corner of rectangle B
bx1	bottom-right corner of rectangle B
by1	bottom-right corner of rectangle B

Returns: an array with the overlap box coordinates (if any)

◆ circle_circle()

static boolean game2dai.maths.Geometry2D.circle_circle	(	double	cx0,
		double	cy0,
		double	r0,
		double	cx1,
		double	cy1,
		double	r1
	)

static

Determine if two circles overlap

Parameters

cx0	centre of first circle x position
cy0	centre of first circle y position
r0	radius of first circle
cx1	centre of second circle x position
cy1	centre of second circle y position
r1	radius of second circle

Returns: true if the circles overlap else false

◆ circle_circle_p()

static double[] game2dai.maths.Geometry2D.circle_circle_p	(	double	cx0,
		double	cy0,
		double	r0,
		double	cx1,
		double	cy1,
		double	r1
	)

static

Calculate the intersection points between two circles.
If the array is of length:
0 then there is no intersection
2 there is just one intersection (the circles are touching)
4 there are two intersections

Parameters

cx0	centre of first circle x position
cy0	centre of first circle y position
r0	radius of first circle
cx1	centre of second circle x position
cy1	centre of second circle y position
r1	radius of second circle

Returns: an array with the intersection points

◆ distance()

static double game2dai.maths.Geometry2D.distance	(	double	x0,
		double	y0,
		double	x1,
		double	y1
	)

static

Calculates the distance between 2 points

Parameters

x0	point 1
y0	point 1
x1	point 2
y1	point 2

Returns: the distance between the points squared

◆ distance_sq()

static double game2dai.maths.Geometry2D.distance_sq	(	double	x0,
		double	y0,
		double	x1,
		double	y1
	)

static

Calculates the squared distance between 2 points

Parameters

x0	point 1
y0	point 1
x1	point 2
y1	point 2

Returns: the distance between the points squared

◆ is_point_near_infinite_line() [1/2]

static boolean game2dai.maths.Geometry2D.is_point_near_infinite_line	(	Vector2D	v0,
		Vector2D	v1,
		Vector2D	p
	)

static

See if point is near the infinite line.

Parameters

v0	line passes through this point
v1	line passes through this point
p	point to consider

Returns: true if p is near the line

◆ is_point_near_infinite_line() [2/2]

static boolean game2dai.maths.Geometry2D.is_point_near_infinite_line	(	Vector2D	v0,
		Vector2D	v1,
		Vector2D	p,
		Vector2D	vp
	)

static

See if point is near the infinite line.

Parameters

v0	line passes through this point
v1	line passes through this point
p	point to consider
vp	filled with xy position of the nearest point on line (must not be null)

Returns: true if p is near the line

◆ is_point_near_line() [1/2]

static boolean game2dai.maths.Geometry2D.is_point_near_line	(	Vector2D	v0,
		Vector2D	v1,
		Vector2D	p
	)

static

See if point is near the finite line.

Parameters

v0	line start
v1	line end
p	point to consider

Returns: true if p is near the line

◆ is_point_near_line() [2/2]

static boolean game2dai.maths.Geometry2D.is_point_near_line	(	Vector2D	v0,
		Vector2D	v1,
		Vector2D	p,
		Vector2D	vp
	)

static

See if point is near the finite line.

Parameters

v0	line start
v1	line end
p	point to consider
vp	filled with xy position of the nearest point on finite line (must not be null)

Returns: true if p is near the line

◆ isInsidePolygon()

static boolean game2dai.maths.Geometry2D.isInsidePolygon	(	Vector2D[]	verts,
		double	x0,
		double	y0
	)

static

See if the given point is inside a polygon defined by the vertices provided.

Parameters

verts	the vertices of the shape
x0
y0

Returns: true if x0, y0 is inside polygon else returns false

◆ isInsideRectangle_xywh() [1/2]

static boolean game2dai.maths.Geometry2D.isInsideRectangle_xywh	(	double	x0,
		double	y0,
		double	width,
		double	height,
		double	pX,
		double	pY
	)

static

See if a point is inside the rectangle defined by top-left and bottom right coordinates

Parameters

x0	top-left corner of rectangle
y0	top-left corner of rectangle
width	width of rectangle
height	height of rectangle
pX	x position of point of interest
pY	y position of point of interest

Returns: true if inside rectangle else false

◆ isInsideRectangle_xywh() [2/2]

static boolean game2dai.maths.Geometry2D.isInsideRectangle_xywh	(	Vector2D	v0,
		double	width,
		double	height,
		Vector2D	p
	)

static

See if this a is inside the rectangle defined by top-left and bottom right coordinates

Parameters

v0	top-left corner of rectangle
width	width of rectangle
height	height of rectangle
p	point of interest

Returns: true if inside rectangle else false

◆ isInsideRectangle_xyxy() [1/2]

static boolean game2dai.maths.Geometry2D.isInsideRectangle_xyxy	(	double	x0,
		double	y0,
		double	x1,
		double	y1,
		double	pX,
		double	pY
	)

static

See if a point is inside the rectangle defined by top-left and bottom right coordinates

Parameters

x0	top-left corner of rectangle
y0	top-left corner of rectangle
x1	bottom-right corner of rectangle
y1	bottom-right corner of rectangle
pX	x position of point of interest
pY	y position of point of interest

Returns: true if inside rectangle else false

◆ isInsideRectangle_xyxy() [2/2]

static boolean game2dai.maths.Geometry2D.isInsideRectangle_xyxy	(	Vector2D	v0,
		Vector2D	v1,
		Vector2D	p
	)

static

See if this a is inside the rectangle defined by top-left and bottom right coordinates

Parameters

v0	top-left corner of rectangle
v1	bottom-right corner of rectangle
p	point of interest

Returns: true if inside rectangle else false

◆ isInsideTriangle() [1/3]

static boolean game2dai.maths.Geometry2D.isInsideTriangle	(	double	aX,
		double	aY,
		double	bX,
		double	bY,
		double	cX,
		double	cY,
		double	pX,
		double	pY
	)

static

Determine if the point pX/pY is inside triangle defined by triangle ABC whose vertices are given by [ax,ay] [bx,by] [cx,cy]

Returns: true if the point is inside

◆ isInsideTriangle() [2/3]

static boolean game2dai.maths.Geometry2D.isInsideTriangle	(	Vector2D	a,
		Vector2D	b,
		Vector2D	c,
		double	pX,
		double	pY
	)

static

Determine if the point pX/pY is inside triangle defined by triangle ABC

Parameters

a	triangle vertex 1
b	triangle vertex 2
c	triangle vertex 3
pX	x position for point of interest
pY	y position for point of interest

Returns: true if inside triangle else false

◆ isInsideTriangle() [3/3]

static boolean game2dai.maths.Geometry2D.isInsideTriangle	(	Vector2D	a,
		Vector2D	b,
		Vector2D	c,
		Vector2D	p
	)

static

Determine if the point (p) is inside triangle defined by triangle ABC

Parameters

a	triangle vertex 1
b	triangle vertex 2
c	triangle vertex 3
p	point of interest

Returns: true if inside triangle else false

◆ line_box_xywh()

static boolean game2dai.maths.Geometry2D.line_box_xywh	(	double	lx0,
		double	ly0,
		double	lx1,
		double	ly1,
		double	rx0,
		double	ry0,
		double	rWidth,
		double	rHeight
	)

static

Determine whether a line intersects with a box.
The box is represented by the top-left corner coordinates and the box width and height.

Parameters

lx0	start of line
ly0	start of line
lx1	end of line
ly1	end of line
rx0	top-left corner of rectangle
ry0	top-left corner of rectangle
rWidth	width of rectangle
rHeight	height of rectangle

Returns: true if they intersect else false

◆ line_box_xyxy()

static boolean game2dai.maths.Geometry2D.line_box_xyxy	(	double	lx0,
		double	ly0,
		double	lx1,
		double	ly1,
		double	rx0,
		double	ry0,
		double	rx1,
		double	ry1
	)

static

Determine whether a line intersects with a box.
The box is represented by the top-left and bottom-right corner coordinates.

Parameters

lx0	start of line
ly0	start of line
lx1	end of line
ly1	end of line
rx0	top-left corner of rectangle
ry0	top-left corner of rectangle
rx1	bottom-right corner of rectangle
ry1	bottom-right corner of rectangle

Returns: true if they intersect else false

◆ line_circle()

static boolean game2dai.maths.Geometry2D.line_circle	(	double	x0,
		double	y0,
		double	x1,
		double	y1,
		double	cx,
		double	cy,
		double	r
	)

static

Sees if a line intersects with the circumference of a circle.

Parameters

x0
y0
x1
y1
cx	centre of circle x position
cy	centre of circle y position
r	radius of circle

Returns: true if the line intersects the circle else false

◆ line_circle_p()

static double[] game2dai.maths.Geometry2D.line_circle_p	(	double	x0,
		double	y0,
		double	x1,
		double	y1,
		double	cx,
		double	cy,
		double	r
	)

static

Calculate the points of intersection between a line and a circle.
An array is returned that contains the intersection points in x, y order. If the array is of length:
0 then there is no intersection
2 there is just one intersection (the line is a tangent to the circle)
4 there are two intersections

Parameters

x0	start of line
y0	start of line
x1	end of line
y1	end of line
cx	centre of circle x position
cy	centre of circle y position
r	radius of circle

Returns: the intersection points as an array (2 elements per intersection)

◆ line_line()

static boolean game2dai.maths.Geometry2D.line_line	(	double	x0,
		double	y0,
		double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x3,
		double	y3
	)

static

See if two lines intersect

Parameters

x0	start of line 1
y0	start of line 1
x1	end of line 1
y1	end of line 1
x2	start of line 2
y2	start of line 2
x3	end of line 2
y3	end of line 2

Returns: true if the lines intersect

◆ line_line_infinite_p() [1/2]

static double[] game2dai.maths.Geometry2D.line_line_infinite_p	(	double	x0,
		double	y0,
		double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x3,
		double	y3
	)

static

Find the point of intersection between two infinite lines that pass through the points ([x0,y0],[x1,y1]) and ([x2,y2],[x3,y3]).
An array is returned that contains the intersection points in x, y order. If the array is of length:
0 then there is no intersection
2 these are the x/y coordinates of the intersection point.

Returns: an array of coordinates for the intersection if any

◆ line_line_infinite_p() [2/2]

static Vector2D game2dai.maths.Geometry2D.line_line_infinite_p	(	Vector2D	v0,
		Vector2D	v1,
		Vector2D	v2,
		Vector2D	v3
	)

static

Find the intersection point between two infinite lines that pass through the points (v0,v1) and (v2,v3)

Returns: a Vector2D object of the intercept or null if parallel

◆ line_line_p() [1/2]

static double[] game2dai.maths.Geometry2D.line_line_p	(	double	x0,
		double	y0,
		double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x3,
		double	y3
	)

static

Find the point of intersection between two lines.
An array is returned that contains the intersection points in x, y order. If the array is of length:
0 then there is no intersection
2 these are the x/y coordinates of the intersection point.

Parameters

x0	start of line 1
y0	start of line 1
x1	end of line 1
y1	end of line 1
x2	start of line 2
y2	start of line 2
x3	end of line 2
y3	end of line 2

Returns: an array of coordinates for the intersection if any

◆ line_line_p() [2/2]

static Vector2D game2dai.maths.Geometry2D.line_line_p	(	Vector2D	v0,
		Vector2D	v1,
		Vector2D	v2,
		Vector2D	v3
	)

static

Find the point of intersection between two lines.
This method uses Vector2D objects to represent the line end points.

Parameters

v0	start of line 1
v1	end of line 1
v2	start of line 2
v3	end of line 2

Returns: a Vector2D object holding the intersection coordinates else null if no intersection

◆ line_lines_p()

static double[] game2dai.maths.Geometry2D.line_lines_p	(	double	x0,
		double	y0,
		double	x1,
		double	y1,
		double[]	xy,
		boolean	continuous
	)

static

Calculate the intersection points between a line and a collection of lines.
This will calculate all the intersection points between a given line and the lines formed from the points in the array xy.
If the parameter continuous = true the points form a continuous line so the

line 1 is from xy[0],xy[1] to xy[2],xy[3] and
line 2 is from xy[2],xy[3] to xy[4],xy[5] and so on

and if continuous is false then each set of four array elements form their own line

line 1 is from xy[0],xy[1] to xy[2],xy[3] and
line 2 is from xy[4],xy[5] to xy[6],xy[7] and so on

Parameters

x0	x position of the line start
y0	y position of the line start
x1	x position of the line end
y1	y position of the line end
xy	array of x/y coordinates
continuous	if true the points makes a continuous line

Returns: an array with all the intersection coordinates

◆ outcode()

static int game2dai.maths.Geometry2D.outcode	(	double	pX,
		double	pY,
		double	rectX,
		double	rectY,
		double	rectWidth,
		double	rectHeight
	)

staticprivate

Code copied from java.awt.geom.Rectangle2D#intersectsLine(double, double, double, double)

◆ point_nearest_infinite_line()

static Vector2D game2dai.maths.Geometry2D.point_nearest_infinite_line	(	Vector2D	v0,
		Vector2D	v1,
		Vector2D	p
	)

static

Given a point find the nearest position on an infinite line.

Parameters

v0	line start
v1	line end
p	point to consider

Returns: returns null if the line is undefined else the nearest position

◆ point_nearest_line()

static Vector2D game2dai.maths.Geometry2D.point_nearest_line	(	Vector2D	v0,
		Vector2D	v1,
		Vector2D	p
	)

static

Given a point find the nearest position on a finite line.

Parameters

v0	line start
v1	line end
p	point to consider

Returns: returns null if the line is undefined or if the nearest point is not on the line

◆ point_to_line_dist()

static void game2dai.maths.Geometry2D.point_to_line_dist ( double nearness )

static

This sets the distance used to decide whether a point is 'near, a line. This is initially set at 1.0

Parameters

nearness must be >0 otherwise it is unchanged

◆ tangents_between_circles()

static double[] game2dai.maths.Geometry2D.tangents_between_circles	(	double	cx0,
		double	cy0,
		double	r0,
		double	cx1,
		double	cy1,
		double	r1
	)

static

Will calculate the contact points for both outer and inner tangents.
There are no tangents if one circle is completely inside the other. If the circles interact only the outer tangents exist. When the circles do not intersect there will be 4 tangents (outer and inner), the array has the outer pair first.

Parameters

cx0	x position for the first circle
cy0	y position for the first circle
r0	radius of the first circle
cx1	x position for the second circle
cy1	y position for the second circle
r1	radius of the second circle

Returns: an array of tangent contact points

◆ tangents_to_circle()

static double[] game2dai.maths.Geometry2D.tangents_to_circle	(	double	x,
		double	y,
		double	cx,
		double	cy,
		double	r
	)

static

Calculate the tangents from a point.
If the array is of length:
0 then there is no tangent the point is inside the circle
2 there is just one intersection (the point is on the circumference)
4 there are two points.

Parameters

x	x position for point of interest
y	y position for point of interest
cx	centre of circle x position
cy	centre of circle y position
r	radius of circle

Returns: an array of the tangent point coordinates

◆ which_side_pn()

static int game2dai.maths.Geometry2D.which_side_pn	(	double	x0,
		double	y0,
		double	nx,
		double	ny,
		double	px,
		double	py
	)

static

Outside is in the same direction of the plane normal.
This version requires a single point on the plane and the normal direction. Useful for an infinite plane or for testing many points against a single plane when the plane normal does not have to be calculated each time.

Parameters

x0	x position point of a point on the plane
y0	y position point of a point on the plane
nx	x value of normal vector
ny	y value of normal vector
px	x position of the point to test
py	y position of the point to test

Returns: returns either PLANE_INSIDE, PLANE_OUTSIDE or ON_PLANE

◆ which_side_pp()

static int game2dai.maths.Geometry2D.which_side_pp	(	double	x0,
		double	y0,
		double	x1,
		double	y1,
		double	px,
		double	py
	)

static

Outside is in the same direction of the plane normal.
The first four parameters represent the start and end position for a line segment (finite plane).

Parameters

x0	x start of the line
y0	y start of the line
x1	x end of the line
y1	y end of the line
px	x position of the point to test
py	y position of the point to test

Returns: returns either PLANE_INSIDE, PLANE_OUTSIDE or ON_PLANE

The documentation for this class was generated from the following file:

/Users/peter/git/ai4games-repos/AI_4_2D_Games/src/game2dai/maths/Geometry2D.java

Static Public Member Functions

Static Public Attributes

Static Private Member Functions

Static Private Attributes

Member Function Documentation

◆ box_box()

◆ box_box_p()

◆ circle_circle()

◆ circle_circle_p()

◆ distance()

◆ distance_sq()

◆ is_point_near_infinite_line() [1/2]

◆ is_point_near_infinite_line() [2/2]

◆ is_point_near_line() [1/2]

◆ is_point_near_line() [2/2]

◆ isInsidePolygon()

◆ isInsideRectangle_xywh() [1/2]

◆ isInsideRectangle_xywh() [2/2]

◆ isInsideRectangle_xyxy() [1/2]

◆ isInsideRectangle_xyxy() [2/2]

◆ isInsideTriangle() [1/3]

◆ isInsideTriangle() [2/3]

◆ isInsideTriangle() [3/3]

◆ line_box_xywh()

◆ line_box_xyxy()

◆ line_circle()

◆ line_circle_p()

◆ line_line()

◆ line_line_infinite_p() [1/2]

◆ line_line_infinite_p() [2/2]

◆ line_line_p() [1/2]

◆ line_line_p() [2/2]

◆ line_lines_p()

◆ outcode()

◆ point_nearest_infinite_line()

◆ point_nearest_line()

◆ point_to_line_dist()

◆ tangents_between_circles()

◆ tangents_to_circle()

◆ which_side_pn()

◆ which_side_pp()