import { allRoots } from "flo-poly";


/** 
 * Returns the given order 1,2 or 3 bezier curve's inflection point `t` 
 * parameter values in ascending order.
 * 
 * * see [Caffeine Owl](http://www.caffeineowl.com/graphics/2d/vectorial/cubic-inflexion.html)
 * 
 * @param ps an order 0,1,2 or 3 bezier curve given as an array of its control
 * points, e.g. `[[1,2],[3,4],[5,6],[7,8]]`
 * 
 * @doc mdx
 */
function getInflections(ps: number[][]): number[] {
	if (ps.length < 4) {
		// Neither lines, nor parabolas have inflection points
		return [];
	}

	const [[x0, y0], [x1, y1], [x2, y2], [x3, y3]] = ps;
	
	// From http://www.caffeineowl.com/graphics/2d/vectorial/cubic-inflexion.html eq. 4
	const ax = x1 - x0;
	const ay = y1 - y0;
	const bx = x2 - x1 - ax;
	const by = y2 - y1 - ay;
	const cx = x3 - x2 - ax - (2*bx);
	const cy = y3 - y2 - ay - (2*by);
	
	// From http://www.caffeineowl.com/graphics/2d/vectorial/cubic-inflexion.html eq. 6:
	//   infl(t) := ax*by - ay*bx + t*(ax*cy - ay*cx) + t^2*(bx*cy - by*cx);
	// We find the roots of the quadratic - a,b,c are the quadratic coefficients
	const a = bx*cy - by*cx;
	const b = ax*cy - ay*cx;
	const c = ax*by - ay*bx;
	
	return allRoots([a,b,c], 0, 1);
}


export { getInflections }