Intersections between two circles

vector.utils.ts

export type Vec2 = { x: number; y: number };

export const vecAdd = (...vs: readonly Readonly<Vec2>[]): Vec2 =>
	vs.reduce(
		(acc, v) => ({
			x: acc.x + v.x,
			y: acc.y + v.y,
		}),
		{ x: 0, y: 0 }
	);

export const vecSub = (v1: Readonly<Vec2>, v2: Readonly<Vec2>): Vec2 => ({ x: v1.x - v2.x, y: v1.y - v2.y });
export const vecMult = (v: Readonly<Vec2>, s: number): Vec2 => ({ x: s * v.x, y: s * v.y });
export const vecLength = (v: Readonly<Vec2>): number => Math.sqrt(Math.pow(v.x, 2) + Math.pow(v.y, 2));
export const vecDist = (v1: Readonly<Vec2>, v2: Readonly<Vec2>): number => vecLength(vecSub(v1, v2));

// https://math.stackexchange.com/questions/256100#answer-1367732
export const circleIntersections = (
	c1: Readonly<Vec2>,
	r1: number,
	c2: Readonly<Vec2>,
	r2: number
): [pos: Vec2, neg: Vec2] => {
	const d = vecDist(c1, c2);

	const v1 = vecAdd(
		vecMult(vecAdd(c1, c2), 0.5),
		vecMult(vecSub(c2, c1), (Math.pow(r1, 2) - Math.pow(r2, 2)) / (2 * Math.pow(d, 2)))
	);

	const v2 = vecMult(
		{ x: c2.y - c1.y, y: c1.x - c2.x },
		Math.sqrt(
			2 * ((Math.pow(r1, 2) + Math.pow(r2, 2)) / Math.pow(d, 2)) -
				Math.pow(Math.pow(r1, 2) - Math.pow(r2, 2), 2) / Math.pow(d, 4) -
				1
		) / 2
	);

	return [vecAdd(v1, v2), vecSub(v1, v2)];
};