@tldraw/editor/src/lib/primitives/geometry/CubicBezier2d.ts

tldraw infinite canvas SDK (editor).

import { Vec, VecLike } from '../Vec'
import { Geometry2dFilters, Geometry2dOptions } from './Geometry2d'
import { Polyline2d } from './Polyline2d'

/** @public */
export class CubicBezier2d extends Polyline2d {
	private _a: Vec
	private _b: Vec
	private _c: Vec
	private _d: Vec
	private _resolution: number

	constructor(
		config: Omit<Geometry2dOptions, 'isFilled' | 'isClosed'> & {
			start: Vec
			cp1: Vec
			cp2: Vec
			end: Vec
			resolution?: number
		}
	) {
		const { start: a, cp1: b, cp2: c, end: d } = config
		super({ ...config, points: [a, d] })

		this._a = a
		this._b = b
		this._c = c
		this._d = d
		this._resolution = config.resolution ?? 10
	}

	override getVertices() {
		const vertices = [] as Vec[]
		const { _a: a, _b: b, _c: c, _d: d } = this
		// we'll always use ten vertices for each bezier curve
		for (let i = 0, n = this._resolution; i <= n; i++) {
			const t = i / n
			vertices.push(
				new Vec(
					(1 - t) * (1 - t) * (1 - t) * a.x +
						3 * ((1 - t) * (1 - t)) * t * b.x +
						3 * (1 - t) * (t * t) * c.x +
						t * t * t * d.x,
					(1 - t) * (1 - t) * (1 - t) * a.y +
						3 * ((1 - t) * (1 - t)) * t * b.y +
						3 * (1 - t) * (t * t) * c.y +
						t * t * t * d.y
				)
			)
		}
		return vertices
	}

	nearestPoint(A: VecLike): Vec {
		let nearest: Vec | undefined
		let dist = Infinity
		let d: number
		let p: Vec
		for (const edge of this.segments) {
			p = edge.nearestPoint(A)
			d = Vec.Dist2(p, A)
			if (d < dist) {
				nearest = p
				dist = d
			}
		}

		if (!nearest) throw Error('nearest point not found')
		return nearest
	}

	getSvgPathData(first = true) {
		const { _a: a, _b: b, _c: c, _d: d } = this
		return `${first ? `M ${a.toFixed()} ` : ``} C${b.toFixed()} ${c.toFixed()} ${d.toFixed()}`
	}

	static GetAtT(segment: CubicBezier2d, t: number) {
		const { _a: a, _b: b, _c: c, _d: d } = segment
		return new Vec(
			(1 - t) * (1 - t) * (1 - t) * a.x +
				3 * ((1 - t) * (1 - t)) * t * b.x +
				3 * (1 - t) * (t * t) * c.x +
				t * t * t * d.x,
			(1 - t) * (1 - t) * (1 - t) * a.y +
				3 * ((1 - t) * (1 - t)) * t * b.y +
				3 * (1 - t) * (t * t) * c.y +
				t * t * t * d.y
		)
	}

	override getLength(_filters?: Geometry2dFilters, precision = 32) {
		let n1: Vec,
			p1 = this._a,
			length = 0
		for (let i = 1; i <= precision; i++) {
			n1 = CubicBezier2d.GetAtT(this, i / precision)
			length += Vec.Dist(p1, n1)
			p1 = n1
		}
		return length
	}
}