Arc

A collection of functions to handle arcs represented with SegmentA.

Utilities

toCenterParameterization()

toCenterParameterization(arg): object

Converts the Arc command to a center parameterization that can be used in Context2D.ellipse(). https://observablehq.com/@awhitty/svg-2-elliptical-arc-to-canvas-path2d

Parameters

Parameter	Type
`arg`	`BareSegmentA`

Returns

object

Name	Type	Default value
`angles`	`AngleRange`	-
`center`	`vec2`	-
`radii`	`vec2`	-
`sweep`	`boolean`	true
`xAxisRotation`	`number`	-

Other

approximateByCubicBeziers()

approximateByCubicBeziers(arc, tolerance): VertexC[]

Defined in: Arc.ts:151

Approximates the arc by cubic Béziers so that the deviation from the true arc stays within tolerance. The sweep is split into equal steps of at most 90°, whose size is solved from the sixth-power error law of the cubic arc approximation. For elliptic arcs the larger radius is used, which is conservative.

Parameters

Parameter	Type	Default value	Description
`arc`	`BareSegmentA`	`undefined`	The arc to approximate
`tolerance`	`number`	`0.05`	The maximum deviation allowed, in the same unit as the coordinates

Returns

VertexC[]

The vertices of the approximating cubics, excluding the start point

bounds()

bounds(arg): Rect

Defined in: Arc.ts:239

Calculates the bound of given arc.

Parameters

Parameter	Type	Description
`arg`	`BareSegmentA`	The arc segment to calculate

Returns

Rect

The bound of the arc

Example

curvature()

curvature(arc, loc): number

Defined in: Arc.ts:624

Returns the signed curvature at the given location. Positive when the arc turns towards its normal side.

Parameters

Parameter	Type
`arc`	`BareSegmentA`
`loc`	`SegmentLocation`

Returns

number

derivative()

derivative(arc, loc): vec2

Defined in: Arc.ts:403

Parameters

Parameter	Type
`arc`	`BareSegmentA`
`loc`	`SegmentLocation`

Returns

vec2

divideAtTimes()

divideAtTimes(arc, times): VertexA[]

Defined in: Arc.ts:457

Parameters

Parameter	Type
`arc`	`BareSegmentA`
`times`	`Iterable`<`number`>

Returns

VertexA[]

ellipticArcLength()

ellipticArcLength(radii, angles): number

Defined in: Arc.ts:534

Computes the arc length of an ellipse over a range of centric angles.

The integrand |d/dt (rx cos t, ry sin t)| is smooth but has sharp dips near the minor axis of an eccentric ellipse, so a single fixed-order quadrature over a wide span loses accuracy. The span is therefore cut at quadrant boundaries and Gauss–Legendre quadrature is applied to each piece (see ellipticArcLengthRad for the accuracy this achieves).

Parameters

Parameter	Type
`radii`	`vec2`
`angles`	`AngleRange`

Returns

number

isCircular()

isCircular(arc): boolean

Defined in: Arc.ts:555

Returns true if the arc lies on a circle (equal radii).

Parameters

Parameter	Type
`arc`	`BareSegmentA`

Returns

boolean

isStraight()

isStraight(arc, tolerance): boolean

Defined in: Arc.ts:496

Parameters

Parameter	Type	Default value
`arc`	`BareSegmentA`	`undefined`
`tolerance`	`number`	`0`

Returns

boolean

isZero()

isZero(arg): boolean

Defined in: Arc.ts:491

Returns true if the length of arc segment is zero.

Parameters

Parameter	Type
`arg`	`BareSegmentA`

Returns

boolean

length()

length(arg): number

Defined in: Arc.ts:370

Parameters

Parameter	Type
`arg`	`BareSegmentA`

Returns

number

normal()

normal(arc, loc): vec2

Defined in: Arc.ts:422

Parameters

Parameter	Type
`arc`	`BareSegmentA`
`loc`	`SegmentLocation`

Returns

vec2

of()

of(start, radii, xAxisRotation, largeArcFlag, sweepFlag, point): SegmentA

Defined in: Arc.ts:34

Parameters

Parameter	Type
`start`	`vec2`
`radii`	`vec2`
`xAxisRotation`	`number`
`largeArcFlag`	`boolean`
`sweepFlag`	`boolean`
`point`	`vec2`

Returns

SegmentA

offset()

offset(arc, distance, tolerance): Path

Defined in: Arc.ts:652

Returns the raw parallel curve of the arc at the given signed distance along its normal, as an open path. Circular arcs stay circular arcs (A); elliptic arcs are approximated by cubic Béziers within tolerance.

Parameters

Parameter	Type	Default value
`arc`	`BareSegmentA`	`undefined`
`distance`	`number`	`undefined`
`tolerance`	`number`	`0.05`

Returns

Path

point()

point(arc, loc): vec2

Defined in: Arc.ts:394

Parameters

Parameter	Type
`arc`	`BareSegmentA`
`loc`	`SegmentLocation`

Returns

vec2

tangent()

tangent(arc, loc): vec2

Defined in: Arc.ts:418

Parameters

Parameter	Type
`arc`	`BareSegmentA`
`loc`	`SegmentLocation`

Returns

vec2

tangentTimes()

tangentTimes(arc, direction): number[]

Defined in: Arc.ts:579

Sorted t values in (0, 1) where the tangent of the arc is parallel to direction.

Parameters

Parameter	Type	Description
`arc`	`BareSegmentA`	-
`direction`	`vec2`	The direction to compare the tangent with. Its length does not matter.

Returns

number[]

tangentTimesFrom()

tangentTimesFrom(arc, origin): number[]

Defined in: Arc.ts:599

Sorted t values in (0, 1) where the line from origin to the arc is tangent to it. There are none when origin lies inside the ellipse.

Parameters

Parameter	Type	Description
`arc`	`BareSegmentA`	-
`origin`	`vec2`	The point the tangents pass through

Returns

number[]

toTime()

toTime(arc, loc): number

Defined in: Arc.ts:375

Parameters

Parameter	Type
`arc`	`BareSegmentA`
`loc`	`SegmentLocation`

Returns

number

transform()

transform(arc, matrix): SegmentA

Defined in: Arc.ts:284

Transforms the given arc segment with the given matrix.

Parameters

Parameter	Type
`arc`	`BareSegmentA`
`matrix`	`mat2d`

trim(arc, start, end): SegmentA

Defined in: Arc.ts:426

Parameters

Parameter	Type
`arc`	`BareSegmentA`
`start`	`SegmentLocation`
`end`	`SegmentLocation`

Returns

SegmentA