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fix(geom-closest-point): use alt algorithm closestPointEllipse()
- new approach has no weird edge cases as previous
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,60 +1,44 @@ | ||
| import { SQRT3, THIRD } from "@thi.ng/math"; | ||
| import { clamp01, SQRT2_2 } from "@thi.ng/math"; | ||
| import { ReadonlyVec } from "@thi.ng/vectors"; | ||
|
|
||
| /** | ||
| * Based on: https://www.iquilezles.org/www/articles/ellipsedist/ellipsedist.htm | ||
| * | ||
| * @remarks | ||
| * Updated to avoid `NaN` if `px == eo.x` or `py == eo.y` | ||
| * Based on iterative solution by Luc Maisonobe: | ||
| * | ||
| * - https://www.spaceroots.org/documents/distance/distance-to-ellipse.pdf | ||
| * - https://gist.github.com/JohannesMP/777bdc8e84df6ddfeaa4f0ddb1c7adb3 | ||
| * | ||
| * Further optimizations: constant folding, avoiding duplicate calculations in | ||
| * loop | ||
| * | ||
| * @param p - query point | ||
| * @param eo - ellipse center/origin | ||
| * @param er - ellipse radii | ||
| * @param n - number of iterations | ||
| */ | ||
| export const closestPointEllipse = ( | ||
| [px, py]: ReadonlyVec, | ||
| [ex, ey]: ReadonlyVec, | ||
| [rx, ry]: ReadonlyVec | ||
| [rx, ry]: ReadonlyVec, | ||
| n = 3 | ||
| ) => { | ||
| px = Math.abs(px - ex); | ||
| py = Math.abs(py - ey); | ||
| const flip = rx > ry; | ||
| if (flip) { | ||
| let t = px; | ||
| px = py; | ||
| py = t; | ||
| t = rx; | ||
| rx = ry; | ||
| ry = t; | ||
| } | ||
| const l = ry * ry - rx * rx; | ||
| const m = (rx * px) / l; | ||
| const m2 = m * m; | ||
| const n = (ry * py) / l; | ||
| const n2 = n * n; | ||
| const c = (m2 + n2 - 1) / 3; | ||
| const c3 = c * c * c; | ||
| const q = c3 + m2 * n2 * 2; | ||
| const d = c3 + m2 * n2; | ||
| const g = m + m * n2; | ||
| let co: number; | ||
| if (d < 0) { | ||
| const h = Math.acos(q / c3) / 3; | ||
| const s = Math.cos(h); | ||
| const t = Math.sin(h) * SQRT3; | ||
| const a = Math.sqrt(-c * (s + t + 2) + m2); | ||
| const b = Math.sqrt(-c * (s - t + 2) + m2); | ||
| co = (b + Math.sign(l) * a + Math.abs(g) / (a * b) - m) / 2; | ||
| } else { | ||
| const h = 2 * m * n * Math.sqrt(d); | ||
| const s = Math.sign(q + h) * Math.pow(Math.abs(q + h), THIRD); | ||
| const u = Math.sign(q - h) * Math.pow(Math.abs(q - h), THIRD); | ||
| const a = -s - u - 4 * c + 2 * m2; | ||
| const b = (s - u) * SQRT3; | ||
| const rm = Math.sqrt(a * a + b * b); | ||
| const p = Math.max(rm - a, 0); | ||
| co = p > 0 ? (b / p + (2 * g) / rm - m) / 2 : 1; | ||
| const apx = Math.abs(px - ex); | ||
| const apy = Math.abs(py - ey); | ||
| const ab = (rx * rx - ry * ry) / rx; | ||
| const ba = (ry * ry - rx * rx) / ry; | ||
| let tx = SQRT2_2; | ||
| let ty = tx; | ||
| for (; --n >= 0; ) { | ||
| const _ex = ab * (tx * tx * tx); | ||
| const _ey = ba * (ty * ty * ty); | ||
| const qx = apx - _ex; | ||
| const qy = apy - _ey; | ||
| const q = Math.hypot(rx * tx - _ex, ry * ty - _ey) / Math.hypot(qx, qy); | ||
| tx = clamp01((qx * q + _ex) / rx); | ||
| ty = clamp01((qy * q + _ey) / ry); | ||
| const t = Math.hypot(tx, ty); | ||
| tx /= t; | ||
| ty /= t; | ||
| } | ||
| const si = Math.sqrt(Math.max(1 - co * co, 0)); | ||
| return flip ? [ry * si + ex, rx * co + ey] : [rx * co + ex, ry * si + ey]; | ||
| return [rx * (px < ex ? -tx : tx) + ex, ry * (py < ey ? -ty : ty) + ey]; | ||
| }; |