Geo

Returns a piecewise linear approximation of the given arcsegment, stepping by epsilon

arcSeg

The arc segment to approximate

ellipseStartPoint

The point to start the arc segment at

epsilon

The x distance between each point

戻り値: The list of points that approximate the arc segment

Returns a list of points that approximate bezier [p1-p4] with maximum error of epsilon

p1

Start point of the bezier curve

p2

First control point of the bezier curve

p3

Second control point of the bezier curve

p4

End point of the bezier curve

epsilon

The maximum amount of error

戻り値: A list of points that approximate the bezier curve

Elevate the given Bezier Curve up to degree [epsilon]

controlPoints

An array of control points that define a Bezier Curve

epsilon

The degree to raise the bezier to

戻り値: A list of points that define an elevated Bezier Curve

Determines using the Winding Number method whether [p1] is in the figure defined by [points]

p1

points

bounds

Returns the closest point to in .

points

The list of points checking for distance to source.

source

The point we want to be closest to.

戻り値: The closest point to .

Returns true if [p1] lies inside [geom], false otherwise

p1

geom

Count intersections on the ray from outside bounding box to p1. If odd, it's in, else it's out (Raycasting)

p1

geom

overrideNonZero

戻り値: True if p1 is in the geometry

Determines using raycasting whether or not [p1] lies inside [geom]

p1

geom

戻り値: True if p1 is in the geometry

Return the angle of the line going from the origin to a point.

x

y

戻り値: an angle in degrees, with 0 along the positive X axis, and with 90.0 along the positive Y axis.

Gets the positive angle with repect to center's x axis of [point]

point

center

Gets the cubed root of [x]

x

Calculates all intersections between infinite line [p1,p2] and the cubic bezier curve [s,c1,c2,e]

p1

First point on the infinite line

p2

Second point on the infinite line

s

The start point of the Bezier Curve

c1

The first control point of the Bezier Curve

c2

The second control point of the Bezier Curve

e

The end of the Bezier Curve

intersections

The list of intersections

戻り値: True if there are any intersections; false otherwise

Returns all intersections between infinite line [p1-p2] and [geom] and puts them in [result]

geom

The geometry to find intersections with

p1

First point on the infinite line

p2

Second point on the infinite line

result

The list of intersections

戻り値: True if intersections are found; false otherwise

Returns all intersections between infinite line [p1-p2] and [geom] and puts them in [result]

geom

The geometry to find intersections with

p1

First point on the infinite line

p2

Second point on the infinite line

result

The list of intersections

mustBeFilled

True if each figure must be filled to be included

戻り値: True if intersections are found; false otherwise

Returns a point on [path] that is the closest intersection of the path and the line formed by p1/p2

path

The Path Geometry to find intersections with

p1

First point on the infinite line

p2

Second point on the infinite line

result

The list of intersection points

mustBeFilled

True if each figure must be filled to be included

戻り値: True if intersections are found; false otherwise

Returns all intersections between infinite line [p1-p2] and [rect] and puts them in [result]

rect

The Rect to check for intersections

p1

First point on the infinite line

p2

Second point on the infinite line

result

The list of intersections

戻り値: True if intersections are found; false otherwise

Returns a list of points that approximate the pathgeometry [pg]

pg

The path geometry to approximate

戻り値: A list of points that approximate the path geometry

Returns all intersections between infinite line [line1-line2] and the ArcSegment and puts them in [result]

line1

First point on the infinite line

line2

Second point on the infinite line

ellipseStartPoint

The start point of the arc segment

arcSeg

The arc segment to find intersections with

intersection

The list to return the intersections with

戻り値: Returns true if their are any intersections; false otherwise

Returns all intersections between infinite line [line1-line2] and [ellipse] and returns them

line1

First point on the infinite line

line2

Second point on the infinite line

ellipse

The ellipse we are checking for intersections with

戻り値: A list of intersection points

Find the closest point of a rectangle to a given point that is on a line from that point.

rect

p1

the point we are looking to be closest to, on the line formed with

p2

forms a line with

result

the point of this object that is closest to and that is on the infinite line from to

戻り値: true if the infinite line does intersect with the rectangle; false otherwise

Returns all intersections between infinite line [line1-line2] and the PolyBezier and puts them in [result]

line1

First point of the infinite line

line2

Second point of the infinite line

start

First point of the PolyBezier

points

List of points in the PolyBezier

epsilon

Accuracy tolerance

result

The list of intersections

戻り値: True if intersections are found; false otherwise

Returns all intersections of infinite line [line1-line2] and the polyline defined by [start] and [points]

line1

First point of the infinite line

line2

Second point of the infinite line

start

First point of the polyline

points

List of line segments

result

The list of intersections

戻り値: True if intersections are found; false otherwise

Returns all intersections between infinite line [line1-line2] and the PolyBezier and puts them in [result]

line1

First point of the infinite line

line2

Second point of the infinite line

start

First point of the PolyQuadBezier

points

List of points in the PolyQuadBezier

epsilon

Accuracy tolerance

result

The list of intersections

戻り値: True if intersections are found; false otherwise

Returns all intersections between infinite line [l1-l2] and the QuadBezier and puts them in [result]

s

Start point of the bezier curve

c1

First control point of the bezier curve

e

End point of the bezier curve

l1

First point of the infinite line

l2

Second point of the infinite line

epsilon

Accuracy tolerance

result

List of the intersections

戻り値: True if intersections are found; false otherwise

Returns a list of the 3 roots of a cubic equation of the form at^3 + bt^2 + ct + d

a

b

c

d

戻り値: A list of the roots

Returns true if [point] is within [fuzz] pixels of the infinite line passing through [p1] and [p2]

p1

Point 1 on the infinite line

p2

Point 2 on the infinite line

point

The point we're checking to be on the line

fuzz

The number of pixels away [point] can be from the line

戻り値: True if [point] is on or within [fuzz] pixels of the line, false otherwise

Inverts the square Matrix [matrix]

matrix

The matrix to invert

Compute a Size that fits in while maintaining the aspect ratio given by .

target

aspect

if both width and height are zero or negative, assume 1x1

Returns true if line(line1, line2) intersects with line segment(seg1, seg2) and sets [intersection] to the point

line1

line2

seg1

seg2

intersection

Find the intersection point of the elliptical path defined by rectangle rect and an infinite line p1-p2 that is closest to point p1 within the area from startAngle through the sweepAngle.

rect

p1

p2

result

startAngle

sweepAngle

Find the intersection point of the elliptical path defined by rectangle rect and an infinite line p1-p2 that is closest to point p1.

rect

p1

p2

result

Find the intersection point of the finite line segment A-B and the infinite line P-Q that is closest to point P.

a

b

p

q

result

Return a point on a straight line segment that is closest to a given point.

a

One end of the line.

b

The other end of the line.

p

The point to be closest to.

result

A Point that is on the finite length straight line segment from to

戻り値: true if the point is on a perpendicular line to the line segment; false if the point is beyond either end of the line segment. When this returns false, the will be either or .

Returns true if [fe] contains [p]. [fe] must be onscreen.

p

Point in [fe]'s coordinates

fe

The framework element to test

戻り値: True if [fe] contains [p] else false

Rotates the point [p] about (0,0)

p

The point to be rotated

angle

The angle to rotate the point in degrees (Counter-Clockwise is positive)

Scales the given point by scaleX, scaleY

pt

The point to be scaled

scaleX

The amount to scale the point in the x direction

scaleY

The amount to scale the point in the y direction

戻り値: The scaled point

Breaks the bezier up into line segments that are a maximum of sqrt(epsilon) away from the original curve

p1

Start point of the bezier curve

p2

First control point of the bezier curve

p3

Second control point of the bezier curve

p4

End point of the bezier curve

result

The list of line segments

epsilon

The square of the maximum amount of deviation from the original curve

Translates the point by transX, transY

pt

The point to be translated

transX

The amount to translate in the x direction

transY

The amount to translate in the y direction

戻り値: The translated point

Translates a collection of points by transX, transY

pts

The collection to be translated

transX

The amount to translate in the x direction

transY

The amount to translate in the y direction

戻り値: The translated collection