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More intersection detection functions

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Mark Tolmacs 2024-09-30 15:31:02 +02:00
parent b7f504796b
commit 6e67aa3a3c
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4 changed files with 75 additions and 12 deletions
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38
packages/math/ellipse.ts
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@ -1,5 +1,5 @@
import { point, pointDistance, pointFromVector } from "./point";
import type { Ellipse, GenericPoint, Segment } from "./types";
import { point, pointDistance, pointFromVector, pointsEqual } from "./point";
import type { Ellipse, GenericPoint, Line, Segment } from "./types";
import { PRECISION } from "./utils";
import {
vector,
@ -180,3 +180,37 @@ export function ellipseSegmentInterceptPoints<Point extends GenericPoint>(
return intersections;
}
export function ellipseIntersectsLine<Point extends GenericPoint>(
{ center, halfWidth, halfHeight }: Ellipse<Point>,
[g, h]: Line<Point>,
): Point[] {
const [cx, cy] = center;
const x1 = g[0] - cx;
const y1 = g[1] - cy;
const x2 = h[0] - cx;
const y2 = h[1] - cy;
const a =
Math.pow(x2 - x1, 2) / Math.pow(halfWidth, 2) +
Math.pow(y2 - y1, 2) / Math.pow(halfHeight, 2);
const b =
2 *
((x1 * (x2 - x1)) / Math.pow(halfWidth, 2) +
(y1 * (y2 - y1)) / Math.pow(halfHeight, 2));
const c =
Math.pow(x1, 2) / Math.pow(halfWidth, 2) +
Math.pow(y1, 2) / Math.pow(halfHeight, 2) -
1;
const t1 = (-b + Math.sqrt(Math.pow(b, 2) - 4 * a * c)) / (2 * a);
const t2 = (-b - Math.sqrt(Math.pow(b, 2) - 4 * a * c)) / (2 * a);
const candidates = [
point<Point>(x1 + t1 * (x2 - x1) + cx, y1 + t1 * (y2 - y1) + cy),
point<Point>(x1 + t2 * (x2 - x1) + cx, y1 + t2 * (y2 - y1) + cy),
].filter((p) => !isNaN(p[0]) && !isNaN(p[1]));
if (candidates.length === 2 && pointsEqual(candidates[0], candidates[1])) {
return [candidates[0]];
}
return candidates;
}