Curve

Overview

Contains these main types of interpolating spline:

• Cubic Spline
• Hermite Spline
• Bezier Spline
• B Spline

Common Props

• dataPoints - The data points of spline

Common Methods

• constructor(dataPoints: number[], config?: Partial<Config>, step?: number)
• getInterpolation(forceUpdate: boolean = true)
• setConfig(config: Object) & getConfig()
• setStep(step: number) & getStep()

Example

import { BezierSpline } from '@anntopia/geometry'
const dataPoints = [
  50, 250,
  200, 150,
  100, 50,
  250, 70,
  400, 50,
  450, 250,
]
const spline = new BezierSpline(dataPoints, { tension: 0.5 }, 0.01)
let points = spline.getInterpolation() // get interpolatin points
// spline.dataPoints: [50, 250, 200, 150, 100, 50, 250, 70, 400, 50, 450, 250]
// points: [50, 250, 52.67857360839844, 249.23570251464844, 55.333335876464844, 248.4666748046875, ...]
spline.setConfig({ tension: 0.7 }) // change config
spline.setStep(0.001) // change step
points = spline.getInterpolation() // get interpolating points with the new config and step
// points: [50, 250, 50.256561279296875, 249.97325134277344, 50.512908935546875, 249.94638061523438, ...]

Cubic Spline

Config

name	type	description
boundary	0 - natural; 1 - clamped; 2 - not-a-knot	Boundary type. Default is 0
derivatives	[number, number]	First derivatives of x in start and end points. Need to set this if the boundary type is 0(natural). Default is [0, 0]

Cubic Parameter Spline

Config

Same as the Config in CubicSpline

Hermite Spline

Config

name	type	description
derivatives	number[]	First derivatives of x and y in every data points.

Cardinal Spline

Config

name	type	description
vs	[number, number]	Virtual start point. Default position has the offset by [0.01,0.01] from the first data point.
ve	[number, number]	Virtual end point. Default position has the offset by [0.01,0.01] from the end data point.
tension	number	Tension value, range is [0,1]. Default is 0.1.

Bezier Spline

Config

name	type	description
tension	number	Tension value, range is [0,1]. Default is 0.5.
closed	boolean	Closed curve. Default is false.

CatmullRom Spline

B Spline

Config

name	type	description
k	number	Degree of spline. Default is 3
knots	number[]	Knot vectors. length = n + k + 1. Default is an array of quasiUniform knots.

Method

• insertKnot(t)

  Insert knot and add new data point automatically.

  • t number

    knot value, range is (0,1)

Knot Functions

Helper functions for creating knots of b-spline (includes NURBS)

type	function name	example
Uniform	createUniformKnots(param)	[0, 0.2, 0.4, 0.6, 0.8, 1]
QuasiUniform	createQuasiUniformKnots(param)	[0, 0, 0, 1/3, 2/3, 1, 1, 1]
PiceceWise	createPiceceWiseKnots(param)	[0, 0, 0, 1/2, 1/2, 1, 1, 1]
NonUniform	createNonUniformKnots(param)	[0, 0, 0, 0.34, 0.35, 0.66, 1, 1, 1]

param Object

• points - number[]

  Data points array

• k - number

  Degree of spline

knots length = n(points number) + k(degree of spline) + 1

NURBS

Config

name	type	description
k	number	Same as the Config in BSpine
knots	number[]	Same as the Config in BSpine
w	number[]	Weight values. The length is the same as data points. Default is all 1 element array.

Method

• insertKnot(t)

  Insert knot and add new data point and weight automatically.

  • t number

    knot value, range is (0,1)