3D circle-circle intersection in Javascript. Intersection of two circles that share the same plane (in 3D). Convenient use with three.js vectors

geometry.js

function IntersectTHREE() {};

// intersection of two 3d circles
// c1,n1,c2,n2 are the center points and normal directions as 3d vectors (ex: {x: 1, y: 2, z: 3} )
IntersectTHREE.circleCircle = function(c1, n1, r1, c2, n2, r2) 
{
	let r = Intersect.circleCircle(
	c1.x, c1.y, c1.z, n1.x, n1.y, n1.z, r1, 
	c2.x, c2.y, c2.z, n2.x, n2.y, n2.z, r2);

	return r;
}

function Intersect() {};

// intersection of two 3d circles that lie in the same plane.
// x1,y1,z1: center point of circle 1
// nx,ny,nz: normal of circle 1 (axis)
// r1: radius  1
//
// returns an object { coincident: true [if the circles are identical], points: [isect0, isect1] }
//
// basic algorithm from: http://stackoverflow.com/questions/35748840/circle-circle-intersection-in-3d#35751516
// 
Intersect.circleCircle = function(x1, y1, z1, nx1, ny1, nz1, r1,  x2, y2, z2, nx2, ny2, nz2, r2) 
{
	let eps = 1e-5;

	// sum of components of n1 x n2;
	para = ny2*nz1-nz2*ny1 + nz2*nx1-nx2*nz1 + nx2*ny1-ny2*nx1;
	if (Math.abs(para) > eps) 
	{
		// TODO: non-parallel circle intersection
		// if there are any intersections they are on a line width direction: n1 x n2 (intersection line of both planes)
		return null;
	}

	let diffx, diffy, diffz;
	diffx = x2-x1; diffy = y2-y1; diffz = z2-y1;


	if (Math.abs(diffx * nx2 + diffy * ny2 + diffz * nz2) > eps)
	{
		// planes are parallel offset 
		return null;
	}


	let dist = Math.sqrt(diffx*diffx + diffy*diffy + diffz*diffz);

	if (dist < eps && Math.abs(r1 - r2) < eps)
	{
		// circles are identical
		return { coincident: true, points: null };
	}


	if (dist > (r1 + r2))
		return null;

	if (Math.abs(dist - (r1 + r2)) < eps) 
	{
		// circles intersect in one point (tangent)
		let p = [];
		p[0] = (x1 * r2 + x2 * r1) / (r1+r2);
		p[1] = (y1 * r2 + y2 * r1) / (r1+r2);
		p[2] = (z1 * r2 + z2 * r1) / (r1+r2);

		return {coincident: false, points: [p]}; 
	}

	if (dist < Math.abs(r2 - r1))
		return null;

	if (Math.abs(dist - (r2 - r1)) < eps)
	{
		// circles intersect in one point (tangent)
		let p = [];
		p[0] = (x1 - x2) * r2 / (r2 - r1);
		p[0] = (y1 - y2) * r2 / (r2 - r1);
		p[0] = (z1 - z2) * r2 / (r2 - r1);

		return {coincident: false, points: [p]};
	}

	// circles intersect in two points
	// find intersections using quadratic formula
	
	//normalize diff
	diffx /= dist; diffy /= dist; diffz /= dist;

	let perpx, perpy, perpz;
	perpx = diffy*nz1-diffz*ny1; 
	perpy = diffz*nx1-diffx*nz1;
	perpz = diffx*ny1-diffy*nx1;

	let q = dist*dist + r2*r2 - r1*r1;
	let dx = 0.5 * q / dist;
	let dy = 0.5 * Math.sqrt(4 * dist*dist * r2*r2 - q*q) / dist;

	let p0 = [
		x1 + diffx * dx + perpx * dy,
		y1 + diffy * dx + perpy * dy,
		z1 + diffz * dx + perpz * dy];

	let p1 = [
		x1 + diffx * dx - perpx * dy,
		y1 + diffy * dx - perpy * dy,
		z1 + diffz * dx - perpz * dy];

	return {coincident: false, points: [p0, p1]};
}