import { twoDiff, scaleExpansion2, eAdd, growExpansion } from 'big-float-ts';

const td = twoDiff;
const sce = scaleExpansion2;
const eadd = eAdd;
const ge = growExpansion;


/**
 * Returns the *exact* 2nd derivative of the power basis representation of a 
 * bezier curve of order cubic or less.
 * 
 * * returns the resulting power basis x and y coordinate polynomials from 
 * highest power to lowest, e.g. if `x(t) = at^2 + bt + c` 
 * and `y(t) = dt^2 + et + f` then  the result is returned 
 * as `[[a,b,c],[d,e,f]]`, where the `a,b,c,...` are [Shewchuk](https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf) floating point
 * expansions
 * 
 * @param ps an order 0,1,2 or 3 bezier curve given by an ordered array of its
 * control points, e.g. `[[0,0],[1,1],[2,1],[2,0]]`
 * 
 * @doc
 */
function toPowerBasis_2ndDerivativeExact(ps: number[][]): number[][][] {
	if (ps.length === 4) {
		const [[x0,y0], [x1,y1], [x2,y2], [x3,y3]] = ps;
		return [[
			sce(6,(eadd(td(x3,x0), sce(3,(td(x1,x2)))))),
			sce(6,(ge(td(x2,2*x1),x0)))
		], [
			sce(6,(eadd(td(y3,y0), sce(3,(td(y1,y2)))))),
			sce(6,(ge(td(y2,2*y1),y0)))
		]]
	} 
	
	if (ps.length === 3) {
		const [[x0,y0], [x1,y1], [x2,y2]] = ps;
		return [[
			ge(td(2*x2,4*x1),2*x0)
		], [
			ge(td(2*y2,4*y1),2*y0)
		]];
	} 
	
	if (ps.length <= 2) {
		return [[[0]],[[0]]];
	}

	throw new Error('The given bezier curve must be of order <= 3.');	
}


export { toPowerBasis_2ndDerivativeExact }