Class NumericalCurveMapper

This curve mapper implementation uses a numerical integration method (Gauss Legendre) in order to approximate curve segment lengths. For re-parameterization of the curve function in terms of arc length, a number of precalculated lengths (samples) is used to fit a monotone piecewise cubic function using the approach suggested here: https://stackoverflow.com/questions/35275073/uniform-discretization-of-bezier-curve

Hierarchy

AbstractCurveMapper
- NumericalCurveMapper

Index

Constructors

constructor

new NumericalCurveMapper(nQuadraturePoints?: number, nInverseSamples?: number, onInvalidateCache?: (() => void)): NumericalCurveMapper
Parameters
- nQuadraturePoints: number = 24
  
  the number of Gauss-Legendre Quadrature points to use for arc length approximation
- nInverseSamples: number = 21
  
  the number of arc length samples to use to fit an inverse function for calculating t from arc length
- Optional onInvalidateCache: (() => void)
  
  callback function to be invoked when cache is invalidated
  - - (): void
    - Returns void
Returns NumericalCurveMapper
Overrides AbstractCurveMapper.constructor
- Defined in curve-mappers/numerical-curve-mapper.ts:34

Properties

_alpha

_alpha: number = 0.0

_cache

_cache: object

_closed

_closed: boolean = false

_gauss

_gauss: number[][]

_nSamples

_nSamples: number = 21

_onInvalidateCache

_onInvalidateCache: (() => void) = null

Type declaration

- (): void
- Returns void

_points

_points: Vector[]

_subDivisions

_subDivisions: number

_tension

_tension: number = 0.5

Accessors

alpha

get alpha(): number
Curve alpha parameter (0=uniform, 0.5=centripetal, 1=chordal)

Returns number
Inherited from AbstractCurveMapper.alpha
- Defined in curve-mappers/abstract-curve-mapper.ts:61
set alpha(alpha: number): void
Parameters
- alpha: number
Returns void
Inherited from AbstractCurveMapper.alpha
- Defined in curve-mappers/abstract-curve-mapper.ts:62

arcLengths

get arcLengths(): any
Returns any
- Defined in curve-mappers/numerical-curve-mapper.ts:49

closed

get closed(): boolean
Determines whether the curve should be a closed curve or not

Returns boolean
Inherited from AbstractCurveMapper.closed
- Defined in curve-mappers/abstract-curve-mapper.ts:93
set closed(closed: boolean): void
Parameters
- closed: boolean
Returns void
Inherited from AbstractCurveMapper.closed
- Defined in curve-mappers/abstract-curve-mapper.ts:94

points

get points(): Vector[]
Control points for curve

Returns Vector[]
Inherited from AbstractCurveMapper.points
- Defined in curve-mappers/abstract-curve-mapper.ts:83
set points(points: Vector[]): void
Parameters
- points: Vector[]
Returns void
Inherited from AbstractCurveMapper.points
- Defined in curve-mappers/abstract-curve-mapper.ts:84

tension

get tension(): number
Curve tension (0=Catmull-rom, 1=linear)

Returns number
Inherited from AbstractCurveMapper.tension
- Defined in curve-mappers/abstract-curve-mapper.ts:72
set tension(tension: number): void
Parameters
- tension: number
Returns void
Inherited from AbstractCurveMapper.tension
- Defined in curve-mappers/abstract-curve-mapper.ts:73

Methods

_invalidateCache

_invalidateCache(): void
Clear cache

Returns void
Overrides AbstractCurveMapper._invalidateCache
- Defined in curve-mappers/numerical-curve-mapper.ts:43

computeArcLength

computeArcLength(index: number, t0?: number, t1?: number): number
Computes the arc length of a curve segment

Returns
arc length between t0 and t1
Parameters
- index: number
  
  index of curve segment
- t0: number = 0.0
  
  calculate length from t
- t1: number = 1.0
  
  calculate length to t
Returns number
- Defined in curve-mappers/numerical-curve-mapper.ts:117

computeArcLengths

computeArcLengths(): number[]
Calculate a running sum of arc length for mapping a position on the curve (u) to the position at the corresponding curve segment (t).

Returns
array with accumulated curve segment arc lengths

Returns number[]
- Defined in curve-mappers/numerical-curve-mapper.ts:138

evaluateForT

evaluateForT(func: SegmentFunction, t: number, target?: Vector): Vector
Evaluate curve segment function at t

Returns
vector
Parameters
- func: SegmentFunction
- t: number
  
  time along full curve (encodes segment index and segment t)
- Optional target: Vector
  
  optional target vector
Returns Vector
Inherited from AbstractCurveMapper.evaluateForT
- Defined in curve-mappers/abstract-curve-mapper.ts:112

getCoefficients

getCoefficients(idx: number): any
Get the curve function coefficients at the given segment index. The coefficients are calculated once per segment and put in cache until it is invalidated.

Returns
coefficients for the curve function at the given segment index
Parameters
- idx: number
  
  segment index
Returns any
Inherited from AbstractCurveMapper.getCoefficients
- Defined in curve-mappers/abstract-curve-mapper.ts:124

getSamples

getSamples(idx: number): [number[], number[], number[], number[]]
Get samples for inverse function from cache if present, otherwise calculate and put in cache for re-use.

Returns
Lengths, slopes and coefficients for inverse function
Parameters
- idx: number
  
  curve segment index
Returns [number[], number[], number[], number[]]
- Defined in curve-mappers/numerical-curve-mapper.ts:62

getT

getT(u: number): number
Maps a uniform time along the curve to non-uniform time (t)

Returns
t encoding segment index and local time along curve
Parameters
- u: number
  
  normalized uniform position along the spline curve
Returns number
Overrides AbstractCurveMapper.getT
- Defined in curve-mappers/numerical-curve-mapper.ts:201

getU

getU(t: number): number
Maps a non-uniform time along the curve to uniform time (u)

Returns
uniform time along curve
Parameters
- t: number
  
  non-uniform time along curve
Returns number
Overrides AbstractCurveMapper.getU
- Defined in curve-mappers/numerical-curve-mapper.ts:222

inverse

inverse(idx: number, len: number): number
Calculate t from arc length for a curve segment

Returns
time (t) along curve segment matching the input length
Parameters
- idx: number
  
  segment index
- len: number
  
  length
Returns number
- Defined in curve-mappers/numerical-curve-mapper.ts:159

lengthAt

lengthAt(u: number): number
Get curve length at u

Returns
length in point coordinates
Parameters
- u: number
  
  normalized uniform position along the spline curve
Returns number
Overrides AbstractCurveMapper.lengthAt
- Defined in curve-mappers/numerical-curve-mapper.ts:192

reset

reset(): void
Returns void
Inherited from AbstractCurveMapper.reset
- Defined in curve-mappers/abstract-curve-mapper.ts:102

Class NumericalCurveMapper

Hierarchy

Index

Constructors

Properties

Accessors

Methods

Constructors

constructor

Parameters

nQuadraturePoints: number = 24

nInverseSamples: number = 21

Optional onInvalidateCache: (() => void)

Returns void

Returns NumericalCurveMapper

Properties

_alpha

_cache

_closed

_gauss

_nSamples

_onInvalidateCache

Type declaration

Returns void

_points

_subDivisions

_tension

Accessors

alpha

Returns number

Parameters

alpha: number

Returns void

arcLengths

Returns any

closed

Returns boolean

Parameters

closed: boolean

Returns void

points

Returns Vector[]

Parameters

points: Vector[]

Returns void

tension

Returns number

Parameters

tension: number

Returns void

Methods

_invalidateCache

Returns void

computeArcLength

Returns

Parameters

index: number

t0: number = 0.0

t1: number = 1.0

Returns number

computeArcLengths

Returns

Returns number[]

evaluateForT

Returns

Parameters

func: SegmentFunction

t: number

Optional target: Vector

Returns Vector

getCoefficients

Returns

Parameters

idx: number

Returns any

getSamples

Returns

Parameters

idx: number

Returns [number[], number[], number[], number[]]

`Optional` onInvalidateCache: (() => void)

`Optional` target: Vector