@davepagurek/flo-mat/src/find-2-prong/find-equidistant-point-on-line.ts

Medial / Scale Axis Transform (MAT/SAT) Library.

/**
 * @internal
 * @param x
 * @param y
 * @param z
 * @returns The point on the line from y to x that is equidistant from y and z. 
 */
function findEquidistantPointOnLine(x: number[], y: number[], z: number[]) {
	// Some basic algebra (not shown) finds the required point.
	
	// Swap axes if x and y are more aligned to y-axis than to x-axis.
	const swapAxes = Math.abs((x[1] - y[1]) / (x[0] - y[0])) > 1;
	
	// Cache
	let x1, x2, y1, y2, z1, z2;
	
	if (swapAxes) {
		x1 = x[1];	x2 = x[0];
		y1 = y[1];	y2 = y[0];
		z1 = z[1];	z2 = z[0];	
	} else {
		x1 = x[0];	x2 = x[1];
		y1 = y[0];	y2 = y[1];
		z1 = z[0];	z2 = z[1];
	}
	
	// a <= 1 (due to swapped axes)
	const a = (x2 - y2) / (x1 - y1); 
	const b = y2 - a*y1;
	const c = (y1*y1 + y2*y2 - z1*z1 - z2*z2) + 2*b*(z2 - y2);
	const d = y1 - z1 + a*(y2 - z2);
	const t1 = c/(2*d);
	const t2 = a*t1 + b;
	
	return swapAxes ? [t2,t1] : [t1,t2];
}


export { findEquidistantPointOnLine }