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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,6 @@ | ||
| import test from 'ava' | ||
| import { rombergIntegral } from '../src' | ||
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| test('rombergIntegral', (t) => { | ||
| t.snapshot(rombergIntegral(0.8478111820247928, 2.90107925830033, t => Math.sqrt(10000 * Math.sin(t) ** 2 + 22500 * Math.cos(t) ** 2))) | ||
| }) |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,11 @@ | ||
| # Snapshot report for `spec/length.ts` | ||
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| The actual snapshot is saved in `length.ts.snap`. | ||
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| Generated by [AVA](https://avajs.dev). | ||
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| ## rombergIntegral | ||
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| > Snapshot 1 | ||
| 241.31511665318624 |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,84 @@ | ||
| import { Arc, Circle, Ellipse, EllipseArc, ellipseToEllipseArc, getFormattedEndAngle } from "./geometry" | ||
| import { BezierCurve, QuadraticCurve } from "./intersection" | ||
| import { angleToRadian } from "./radian" | ||
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| export function getCircleLength(circle: Circle) { | ||
| return 2 * Math.PI * circle.r | ||
| } | ||
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| export function getArcLength(arc: Arc) { | ||
| const endAngle = getFormattedEndAngle(arc) | ||
| return arc.r * angleToRadian(Math.abs(endAngle - arc.startAngle)) | ||
| } | ||
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| export function getEllipseLength(ellipse: Ellipse, delta?: number) { | ||
| return getEllipseArcLength(ellipseToEllipseArc(ellipse), delta) | ||
| } | ||
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| export function getEllipseArcLength(ellipse: EllipseArc, delta?: number) { | ||
| // let d1 = Math.sin(radian), d2 = Math.cos(radian) | ||
| // x = d2 rx cos(t) - d1 ry sin(t) + cx | ||
| // y = d1 rx cos(t) + d2 ry sin(t) + cy | ||
| // x' = -d2 rx sin(t) - d1 ry cos(t) = dx/dt | ||
| // y' = -d1 rx sin(t) + d2 ry cos(t) = dy/dt | ||
| // dz = sqrt(dx^2 + dy^2) | ||
| // dz/dt = sqrt(cos(t) cos(t) d1 d1 ry ry + cos(t) cos(t) d2 d2 ry ry + d1 d1 rx rx sin(t) sin(t) + d2 d2 rx rx sin(t) sin(t)) | ||
| // dz/dt = sqrt(cos(t) cos(t)ry ry + rx rx sin(t) sin(t)) | ||
| const e1 = ellipse.rx ** 2, e2 = ellipse.ry ** 2 | ||
| // dz/dt = sqrt(e1 sin(t) sin(t) + e2 cos(t) cos(t)) | ||
| const radian1 = angleToRadian(ellipse.startAngle), radian2 = angleToRadian(getFormattedEndAngle(ellipse)) | ||
| return rombergIntegral(Math.min(radian1, radian2), Math.max(radian1, radian2), t => Math.sqrt(e1 * Math.sin(t) ** 2 + e2 * Math.cos(t) ** 2), delta) | ||
| } | ||
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| export function getQuadraticCurveLength({ from: { x: a1, y: b1 }, cp: { x: a2, y: b2 }, to: { x: a3, y: b3 } }: QuadraticCurve, delta?: number) { | ||
| const c1 = a2 - a1, c2 = a3 - a2 - c1, c3 = b2 - b1, c4 = b3 - b2 - c3 | ||
| // x = c2 t t + 2 c1 t + a1 | ||
| // y = c4 t t + 2 c3 t + b1 | ||
| // x' = 2 c2 t + 2 c1 = dx/dt | ||
| // y' = 2 c4 t + 2 c3 = dy/dt | ||
| // dz = sqrt(dx^2 + dy^2) | ||
| // dz/dt = 2 sqrt((c2 t + c1)^2 + (c4 t + c3)^2) | ||
| // dz/dt = 2 sqrt((c2 c2 + c4 c4) t t + (2 c1 c2 + 2 c3 c4) t + c1 c1 + c3 c3) | ||
| const e1 = c2 * c2 + c4 * c4, e2 = 2 * c1 * c2 + 2 * c3 * c4, e3 = c1 * c1 + c3 * c3 | ||
| // dz/dt = 2 sqrt(e1 t t + e2 t + e3) | ||
| return rombergIntegral(0, 1, t => 2 * Math.sqrt(e1 * t * t + e2 * t + e3), delta) | ||
| } | ||
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| export function getBezierCurveLength({ from: { x: a1, y: b1 }, cp1: { x: a2, y: b2 }, cp2: { x: a3, y: b3 }, to: { x: a4, y: b4 } }: BezierCurve) { | ||
| const c1 = -a1 + 3 * a2 + -3 * a3 + a4, c2 = 3 * (a1 - 2 * a2 + a3), c3 = 3 * (a2 - a1) | ||
| const d1 = -b1 + 3 * b2 + -3 * b3 + b4, d2 = 3 * (b1 - 2 * b2 + b3), d3 = 3 * (b2 - b1) | ||
| // x = c1 t t t + c2 t t + c3 t + a1 | ||
| // y = d1 t t t + d2 t t + d3 t + b1 | ||
| // x' = 3 c1 t t + 2 c2 t + c3 = dx/dt | ||
| // y' = 3 d1 t t + 2 d2 t + d3 = dy/dt | ||
| // dz = sqrt(dx^2 + dy^2) | ||
| // dz/dt = sqrt((3 c1 t t + 2 c2 t + c3)^2 + (3 d1 t t + 2 d2 t + d3)^2) | ||
| // dz/dt = sqrt((9 c1 c1 + 9 d1 d1) t t t t + (12 c1 c2 + 12 d1 d2) t t t + (4 c2 c2 + 6 c1 c3 + 4 d2 d2 + 6 d1 d3) t t + (4 c2 c3 + 4 d2 d3) t + c3 c3 + d3 d3) | ||
| const e1 = 9 * c1 * c1 + 9 * d1 * d1, e2 = 12 * c1 * c2 + 12 * d1 * d2, e3 = 4 * c2 * c2 + 6 * c1 * c3 + 4 * d2 * d2 + 6 * d1 * d3, e4 = 4 * c2 * c3 + 4 * d2 * d3, e5 = c3 * c3 + d3 * d3 | ||
| // dz/dt = sqrt(e1 t t t t + e2 t t t + e3 t t + e4 t + e5) | ||
| return rombergIntegral(0, 1, t => Math.sqrt(e1 * t * t * t * t + e2 * t * t * t + e3 * t * t + e4 * t + e5)) | ||
| } | ||
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| export function cotesIntegral(a: number, b: number, f: (t: number) => number, count?: number): number { | ||
| if (count && Number.isInteger(count) && count > 1) { | ||
| let result = 0 | ||
| const d = (b - a) / count | ||
| for (let i = 0; i < count; i++) { | ||
| result += cotesIntegral(a + i * d, a + (i + 1) * d, f) | ||
| } | ||
| return result | ||
| } | ||
| const h = (b - a) / 4 | ||
| return (b - a) * (7 * f(a) + 32 * f(a + h) + 12 * f(a + 2 * h) + 32 * f(a + 3 * h) + 7 * f(b)) / 90 | ||
| } | ||
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| export function rombergIntegral(a: number, b: number, f: (t: number) => number, delta = 1e-2): number { | ||
| let p: number | undefined | ||
| for (let count = 1; ; count *= 2) { | ||
| const c = cotesIntegral(a, b, f, count) | ||
| if (p && Math.abs(p - c) < delta) { | ||
| return c | ||
| } | ||
| p = c | ||
| } | ||
| } |