Conic

class Conic

Describes a conic section or any quadric curve

A quadric curve can be represented in the form k² - lm, where, k, l, m are linear functionals. l and m are two lines tangent to the curve, while k is the line connecting the two points of tangency.

Summary

Properties from Conic

number	_dirtyID = 0 Flags changes in the shape data
	controlPoints
	k The chord connecting the points of tangency on l and m.
	l A line tangent to the curve.
	m A line tangent to the curve.

Methods from Conic

Conic	static createCircle(radius: number)
Conic	static createEllipse(a: number, b: number)
Conic	static createHyperbola(a: number, b: number)
Conic	static createParabola(a: number)
void	setControlPoints(c0: PIXI.Point, c1: PIXI.Point, c2: PIXI.Point)
this	setk(a: number, b: number, c: number) Sets the equation of the "k" line to ax + by + c = 0.
this	setl(a: number, b: number, c: number) Sets the equation of the "l" line to ax + by + c = 0.
this	setm(a: number, b: number, c: number) Sets the equation of the line "m" to ax + by + c = 0.
this	update() Flag the shape as dirty after you have modified the data directly.

Public Properties

_dirtyID Conic.ts:60

_dirtyID: number = 0

Flags changes in the shape data

controlPoints Conic.ts:48

controlPoints

The control points in design space. The control points allow you to map design space points to the local space points when creating a graphic.

By default, the conic is a quadratic bezier curve.

k Conic.ts:33

The chord connecting the points of tangency on l and m.

l Conic.ts:38

A line tangent to the curve.

m Conic.ts:43

A line tangent to the curve.

Public Methods

createCircle Conic.ts:143

static createCircle(radius: number) → {Conic}

Creates a circular conic of the given radius that is in the bounding box (0,0,2_r_,2_r_).

Implicit form: (x/√2 + y/√2 - r/√2)² - xy = 0

Simplified form: (x - r)² - (y - r)² - r² = 0

Parameters:
Name	Type	Description
radius	number	the radius of the circle

Returns:
Type	Description
Conic	the conic shape

createEllipse Conic.ts:167

static createEllipse(a: number, b: number) → {Conic}

Creates an ellipse with the given major & minor semi-axes that is located in the bounding box (0,0,2_a_,2_b_).

Implicit form: (x/a + y/b - 1)² - 2_xy_/ab = 0

Simplified form: (x/a - 1)² + (y/b - 1)² - 1 = 0

Parameters:
Name	Type	Description
a	number	major semi-axis length
b	number	minor semi-axis length

Returns:
Type	Description
Conic

createHyperbola Conic.ts:214

static createHyperbola(a: number, b: number) → {Conic}

Creates a hyperbola that opens up and down; since hyperbolas are not closed curves, they do not have a bounding box.

Implicit form: 1² - (y/b - x/a)(y/b + x/a) = 0

Simplified form: (y/b)² - (x/a)² = 1

Parameters:
Name	Type	Description
a	number	major semi-axis
b	number	minor semi-axis

Returns:
Type	Description
Conic

createParabola Conic.ts:191

static createParabola(a: number) → {Conic}

Creates a parabola that opens upward (for a > 0); since parabolas are not closed curves, they do not have a bounding box.

The standard bezier curve is the parabola x² - y, with the control points (0,0), (1/2,0), (1,1).

Equation: x^{2 - 4_ay_ = 0}

Parameters:
Name	Type	Description
a	number	distance of directrix, focus from the vertex of the parabola (0,0)

Returns:
Type	Description
Conic

setControlPoints Conic.ts:120

setControlPoints(c0: PIXI.Point, c1: PIXI.Point, c2: PIXI.Point) → {void}

Set control points in texture space

Parameters:
Name	Type	Description
c0	PIXI.Point
c1	PIXI.Point
c2	PIXI.Point

Returns:
Type	Description
void

setk Conic.ts:66

setk(a: number, b: number, c: number) → {this}

Sets the equation of the "k" line to ax + by + c = 0.

Parameters:
Name	Type	Description
a	number
b	number
c	number

Returns:
Type	Description
this

setl Conic.ts:84

setl(a: number, b: number, c: number) → {this}

Sets the equation of the "l" line to ax + by + c = 0.

Parameters:
Name	Type	Description
a	number
b	number
c	number

Returns:
Type	Description
this

setm Conic.ts:102

setm(a: number, b: number, c: number) → {this}

Sets the equation of the line "m" to ax + by + c = 0.

Parameters:
Name	Type	Description
a	number
b	number
c	number

Returns:
Type	Description
this

update Conic.ts:133

update() → {this}

Flag the shape as dirty after you have modified the data directly.

Returns:
Type	Description
this