Add basic functions for BBox and CubicBezier

jest.test.ts

@@ -0,0 +1,14 @@
+import {expect} from '@jest/globals'
+
+beforeEach(() => {
+	const EPSILON = 1e-6
+
+	function nearlyEqual(a: number, b: number) {
+		return (
+			Math.abs(a - b) <= EPSILON * Math.max(1, Math.abs(a), Math.abs(b)) ||
+			undefined
+		)
+	}
+
+	expect.addEqualityTesters([nearlyEqual])
+})

package.json

@@ -38,6 +38,7 @@
 	"homepage": "https://baku89.github.io/pathed",
 	"devDependencies": {
 		"@types/jest": "^29.5.4",
+		"@types/lodash": "^4.14.202",
 		"@typescript-eslint/eslint-plugin": "^6.7.0",
 		"@typescript-eslint/parser": "^6.7.0",
 		"eslint": "^8.49.0",
@@ -47,6 +48,7 @@
 		"eslint-plugin-unused-imports": "^3.0.0",
 		"jest": "^29.7.0",
 		"jest-runner-eslint": "^2.1.1",
+		"lodash": "^4.17.21",
 		"prettier": "^3.0.3",
 		"ts-jest": "^29.1.1",
 		"ts-node": "^10.9.1",
@@ -55,6 +57,8 @@
 		"typescript": "^5.2.2"
 	},
 	"dependencies": {
+		"@types/bezier-js": "^4.1.3",
+		"bezier-js": "^6.1.4",
 		"linearly": "^0.21.0"
 	}
 }

src/BBox.test.ts

@@ -0,0 +1,25 @@
+import '../jest.config'
+
+import {BBox, unite} from './BBox'
+
+describe('unite', () => {
+	it('should unite multiple bounding boxes correctly', () => {
+		const bbox1: BBox = [
+			[0, 0],
+			[2, 2],
+		]
+		const bbox2: BBox = [
+			[1, 1],
+			[3, 3],
+		]
+		const bbox3: BBox = [
+			[-1, -1],
+			[1, 1],
+		]
+		const result = unite(bbox1, bbox2, bbox3)
+		expect(result).toEqual([
+			[-1, -1],
+			[3, 3],
+		])
+	})
+})

src/BBox.ts

@@ -0,0 +1,22 @@
+import {vec2} from 'linearly'
+
+export type BBox = readonly [min: vec2, max: vec2]
+
+export function unite(...bboxes: BBox[]): BBox {
+	let minX = Infinity,
+		minY = Infinity,
+		maxX = -Infinity,
+		maxY = -Infinity
+
+	for (const [min, max] of bboxes) {
+		minX = Math.min(minX, min[0])
+		minY = Math.min(minY, min[1])
+		maxX = Math.max(maxX, max[0])
+		maxY = Math.max(maxY, max[1])
+	}
+
+	return [
+		[minX, minY],
+		[maxX, maxY],
+	]
+}

src/CubicBezier.test.ts

@@ -0,0 +1,44 @@
+import '../jest.config'
+
+import {atT, bound, CubicBezier, length, normal} from './CubicBezier'
+
+describe('CubicBezier', () => {
+	const a: CubicBezier = [
+		[0, 0],
+		[0, 1],
+		[1, 1],
+		[1, 0],
+	]
+	const b: CubicBezier = [
+		[0, 0],
+		[2, 0],
+		[1, 1],
+		[1, 0],
+	]
+
+	it('should compute the `length` correctly', () => {
+		expect(length(a)).toBeCloseTo(2, 10)
+		expect(length(b)).toBeCloseTo(2, 10)
+	})
+
+	it('should compute the `bound` correctly', () => {
+		expect(bound(a)).toEqual([
+			[0, 0],
+			[1, 0.75],
+		])
+		expect(bound(b)).toEqual([
+			[0, 0],
+			[1.25, 0.444444],
+		])
+	})
+
+	it('should compute the `atT` correctly', () => {
+		expect(atT(a, 0)).toEqual([0, 0])
+		expect(atT(a, 0.5)).toEqual([0.5, 0.75])
+		expect(atT(a, 1)).toEqual([1, 0])
+	})
+
+	it('should compute the `normal` correctly', () => {
+		expect(normal(a, 0.5)).toEqual([0, 1])
+	})
+})

src/CubicBezier.ts

@@ -1,8 +1,135 @@
+import {Bezier as BezierJS, Point} from 'bezier-js'
 import {vec2} from 'linearly'
 
-export type CubicBezier = [
+export type CubicBezier = readonly [
 	start: vec2,
 	control1: vec2,
 	control2: vec2,
 	end: vec2,
 ]
+
+export const toBezierJS = memoizeCubicBezierFunction(
+	(bezier: CubicBezier): BezierJS => {
+		const [start, control1, control2, end] = bezier
+		return new BezierJS(
+			start[0],
+			start[1],
+			control1[0],
+			control1[1],
+			control2[0],
+			control2[1],
+			end[0],
+			end[1]
+		)
+	}
+)
+
+function toPoint([x, y]: vec2): Point {
+	return {x, y}
+}
+
+/**
+ * Calculates the length of the Bezier curve. Length is calculated using numerical approximation, specifically the Legendre-Gauss quadrature algorithm.
+ */
+export const length = memoizeCubicBezierFunction(
+	(bezier: CubicBezier): number => {
+		const bezierJS = toBezierJS(bezier)
+		return bezierJS.length()
+	}
+)
+
+/**
+ * Calculates the bounding box of this Bezier curve.
+ */
+export const bound = memoizeCubicBezierFunction(
+	(bezier: CubicBezier): [vec2, vec2] => {
+		const bezierJS = toBezierJS(bezier)
+		const {x, y} = bezierJS.bbox()
+
+		return [
+			[x.min, y.min],
+			[x.max, y.max],
+		]
+	}
+)
+
+/**
+ * Calculates the point on the curve at the specified `t` value.
+ */
+export function atT(bezier: CubicBezier, t: number): vec2 {
+	const bezierJS = toBezierJS(bezier)
+	const {x, y} = bezierJS.get(t)
+	return [x, y]
+}
+
+/**
+ * Calculates the curve tangent at the specified `t` value. Note that this yields a not-normalized vector.
+ */
+export function derivative(bezier: CubicBezier, t: number): vec2 {
+	const bezierJS = toBezierJS(bezier)
+	const {x, y} = bezierJS.derivative(t)
+	return [x, y]
+}
+
+/**
+ * Calculates the curve tangent at the specified `t` value. Unlike {@link derivative}, this yields a normalized vector.
+ */
+export function tangent(bezier: CubicBezier, t: number): vec2 {
+	return vec2.normalize(derivative(bezier, t))
+}
+
+/**
+ * Calculates the curve normal at the specified `t` value. Note that this yields a normalized vector.
+ */
+export function normal(bezier: CubicBezier, t: number): vec2 {
+	const bezierJS = toBezierJS(bezier)
+	const {x, y} = bezierJS.normal(t)
+	return [x, y]
+}
+
+/**
+ * Finds the on-curve point closest to the specific off-curve point
+ */
+export function project(
+	bezier: CubicBezier,
+	origin: vec2
+): {position: vec2; t?: number; distance?: number} {
+	const bezierJS = toBezierJS(bezier)
+	const {x, y, t, d} = bezierJS.project(toPoint(origin))
+	return {position: [x, y], t, distance: d}
+}
+
+function memoizeCubicBezierFunction<T>(f: (bezier: CubicBezier) => T) {
+	const cache = new WeakMap<
+		vec2,
+		WeakMap<vec2, WeakMap<vec2, WeakMap<vec2, T>>>
+	>()
+
+	return (bezier: CubicBezier): T => {
+		const [start, control1, control2, end] = bezier
+
+		if (!cache.has(start)) {
+			cache.set(start, new WeakMap())
+		}
+
+		const cache1 = cache.get(start)!
+
+		if (!cache1.has(control1)) {
+			cache1.set(control1, new WeakMap())
+		}
+
+		const cache2 = cache1.get(control1)!
+
+		if (!cache2.has(control2)) {
+			cache2.set(control2, new WeakMap())
+		}
+
+		const cache3 = cache2.get(control2)!
+
+		if (!cache3.has(end)) {
+			cache3.set(end, f(bezier))
+		}
+
+		return cache3.get(end)!
+	}
+}

src/index.ts

@@ -1,2 +1,4 @@
-export * from './CubicBezier'
-export * from './Path'
+export type * from './CubicBezier'
+export * as CubicBezier from './CubicBezier'
+export type * from './Path'
+export * as Path from './Path'

yarn.lock

@@ -701,6 +701,11 @@
   dependencies:
     "@babel/types" "^7.20.7"
 
+"@types/bezier-js@^4.1.3":
+  version "4.1.3"
+  resolved "https://registry.yarnpkg.com/@types/bezier-js/-/bezier-js-4.1.3.tgz#237d4fe7e9aae7edd0c27a71f9f236f4ddc1c562"
+  integrity sha512-FNVVCu5mx/rJCWBxLTcL7oOajmGtWtBTDjq6DSUWUI12GeePivrZZXz+UgE0D6VYsLEjvExRO03z4hVtu3pTEQ==
+
 "@types/graceful-fs@^4.1.3":
   version "4.1.6"
   resolved "https://registry.yarnpkg.com/@types/graceful-fs/-/graceful-fs-4.1.6.tgz#e14b2576a1c25026b7f02ede1de3b84c3a1efeae"
@@ -740,6 +745,11 @@
   resolved "https://registry.yarnpkg.com/@types/json-schema/-/json-schema-7.0.12.tgz#d70faba7039d5fca54c83c7dbab41051d2b6f6cb"
   integrity sha512-Hr5Jfhc9eYOQNPYO5WLDq/n4jqijdHNlDXjuAQkkt+mWdQR+XJToOHrsD4cPaMXpn6KO7y2+wM8AZEs8VpBLVA==
 
+"@types/lodash@^4.14.202":
+  version "4.14.202"
+  resolved "https://registry.yarnpkg.com/@types/lodash/-/lodash-4.14.202.tgz#f09dbd2fb082d507178b2f2a5c7e74bd72ff98f8"
+  integrity sha512-OvlIYQK9tNneDlS0VN54LLd5uiPCBOp7gS5Z0f1mjoJYBrtStzgmJBxONW3U6OZqdtNzZPmn9BS/7WI7BFFcFQ==
+
 "@types/node@*":
   version "20.6.0"
   resolved "https://registry.yarnpkg.com/@types/node/-/node-20.6.0.tgz#9d7daa855d33d4efec8aea88cd66db1c2f0ebe16"
@@ -1061,6 +1071,11 @@ balanced-match@^1.0.0:
   resolved "https://registry.yarnpkg.com/balanced-match/-/balanced-match-1.0.2.tgz#e83e3a7e3f300b34cb9d87f615fa0cbf357690ee"
   integrity sha512-3oSeUO0TMV67hN1AmbXsK4yaqU7tjiHlbxRDZOpH0KW9+CeX4bRAaX0Anxt0tx2MrpRpWwQaPwIlISEJhYU5Pw==
 
+bezier-js@^6.1.4:
+  version "6.1.4"
+  resolved "https://registry.yarnpkg.com/bezier-js/-/bezier-js-6.1.4.tgz#c7828f6c8900562b69d5040afb881bcbdad82001"
+  integrity sha512-PA0FW9ZpcHbojUCMu28z9Vg/fNkwTj5YhusSAjHHDfHDGLxJ6YUKrAN2vk1fP2MMOxVw4Oko16FMlRGVBGqLKg==
+
 brace-expansion@^1.1.7:
   version "1.1.11"
   resolved "https://registry.yarnpkg.com/brace-expansion/-/brace-expansion-1.1.11.tgz#3c7fcbf529d87226f3d2f52b966ff5271eb441dd"
@@ -2396,6 +2411,11 @@ lodash.merge@^4.6.2:
   resolved "https://registry.yarnpkg.com/lodash.merge/-/lodash.merge-4.6.2.tgz#558aa53b43b661e1925a0afdfa36a9a1085fe57a"
   integrity sha512-0KpjqXRVvrYyCsX1swR/XTK0va6VQkQM6MNo7PqW77ByjAhoARA8EfrP1N4+KlKj8YS0ZUCtRT/YUuhyYDujIQ==
 
+lodash@^4.17.21:
+  version "4.17.21"
+  resolved "https://registry.yarnpkg.com/lodash/-/lodash-4.17.21.tgz#679591c564c3bffaae8454cf0b3df370c3d6911c"
+  integrity sha512-v2kDEe57lecTulaDIuNTPy3Ry4gLGJ6Z1O3vE1krgXZNrsQ+LFTGHVxVjcXPs17LhbZVGedAJv8XZ1tvj5FvSg==
+
 lru-cache@^5.1.1:
   version "5.1.1"
   resolved "https://registry.yarnpkg.com/lru-cache/-/lru-cache-5.1.1.tgz#1da27e6710271947695daf6848e847f01d84b920"