@baku89/pave v1.0.1

@baku89/pave / CubicBezier

CubicBezier

A collection of functions to handle a cubic Bézier segment represented as BareSegmentC.

The projection strategy follows bezier-js (MIT, https://github.com/Pomax/bezierjs).

Functions

bounds()

bounds(arg): [vec2, vec2]

Defined in: CubicBezier.ts:46

Calculates the rect of this Bezier curve.

Parameters

Returns

[vec2, vec2]

curvature()

curvature(bezier, loc): number

Defined in: CubicBezier.ts:121

Signed curvature κ = (B′ × B″) / ‖B′‖³ at the specified location. Positive when the curve turns towards its normal side. Returns 0 where the speed vanishes.

Parameters

Returns

number

cuspTimes()

cuspTimes(bezier): number[]

Defined in: CubicBezier.ts:198

The t values in (0, 1) where the speed vanishes, so that the curve turns back on itself. A cubic has at most one unless it is degenerate to a line.

Parameters

Returns

number[]

derivative()

derivative(bezier, loc): vec2

Defined in: CubicBezier.ts:88

Calculates the curve tangent at the specified t value. Note that this yields a not-normalized vector.

Parameters

Returns

vec2

divideAtTimes()

divideAtTimes(segment, times): VertexC[]

Defined in: CubicBezier.ts:370

Parameters

Returns

VertexC[]

extremaTimes()

extremaTimes(bezier): number[]

Defined in: CubicBezier.ts:135

Sorted, unique t values in (0, 1) where x(t) or y(t) has an extremum. Splitting at these times yields pieces that are monotone along both axes.

Parameters

Returns

number[]

fromQuadraticBezier()

fromQuadraticBezier(start, control, point): SegmentC

Defined in: CubicBezier.ts:25

Parameters

Returns

SegmentC

inflectionTimes()

inflectionTimes(bezier): number[]

Defined in: CubicBezier.ts:148

Sorted t values in (0, 1) where the curvature changes sign (B′ × B″ = 0).

Parameters

Returns

number[]

isStraight()

isStraight(bezier, tolerance): boolean

Defined in: CubicBezier.ts:400

Parameters

Returns

boolean

isZero()

isZero(bezier): boolean

Defined in: CubicBezier.ts:387

Parameters

Returns

boolean

length()

length(bezier): number

Defined in: CubicBezier.ts:39

Calculates the length of the Bezier curve. Length is calculated using numerical approximation, specifically the Legendre-Gauss quadrature algorithm.

Parameters

Returns

number

normal()

normal(bezier, loc): vec2

Defined in: CubicBezier.ts:114

Calculates the curve normal at the specified t value. Note that this yields a normalized vector.

Parameters

Returns

vec2

of()

of(start, control1, control2, point): SegmentC

Defined in: CubicBezier.ts:16

Parameters

Returns

SegmentC

offset()

offset(bezier, distance, tolerance): Path

Defined in: CubicBezier.ts:483

Returns the raw parallel curve of the Bézier at the given signed distance along its normal, as an open path of cubic Béziers fitted within tolerance. Where the distance exceeds the radius of curvature the result folds back on itself; use Path.offset for a trimmed result.

Parameters

Returns

Path

point()

point(bezier, loc): vec2

Defined in: CubicBezier.ts:80

Calculates the point on the curve at the specified t value.

Parameters

Returns

vec2

project()

project(bezier, origin): object

Defined in: CubicBezier.ts:290

Finds the on-curve point closest to the specific off-curve point

Parameters

Returns

object

secondDerivative()

secondDerivative(bezier, loc): vec2

Defined in: CubicBezier.ts:96

Calculates the second derivative d²B/dt² at the specified t value.

Parameters

Returns

vec2

selfIntersectionTimes()

selfIntersectionTimes(bezier): null | [number, number]

Defined in: CubicBezier.ts:171

The two t values at which the curve passes through the same point, or null if it has no loop. Solved in closed form: with B(t) = at³ + bt² + ct + d, dividing B(s) - B(t) by s - t leaves an equation in s + t and st.

Parameters

Returns

null | [number, number]

tangent()

tangent(bezier, loc): vec2

Defined in: CubicBezier.ts:107

Calculates the curve tangent at the specified t value. Unlike derivative, this yields a normalized vector.

Parameters

Returns

vec2

tangentTimes()

tangentTimes(bezier, direction): number[]

Defined in: CubicBezier.ts:220

Sorted t values in (0, 1) where the tangent is parallel to direction. These are the points where a line along direction touches the curve, and where the curve is farthest along the perpendicular of direction.

Parameters

Returns

number[]

tangentTimesFrom()

tangentTimesFrom(bezier, origin): number[]

Defined in: CubicBezier.ts:236

Sorted t values in (0, 1) where the line from origin to the curve is tangent to it. The condition (B(t) − origin) × B′(t) = 0 is a quintic, so the roots are found by bracketing sign changes and bisecting.

Parameters

Returns

number[]

toTime()

toTime(bezier, loc): number

Defined in: CubicBezier.ts:59

Parameters

Returns

number

trim()

trim(bezier, start, end): SegmentC

Defined in: CubicBezier.ts:330

Parameters

Returns

SegmentC