/**
 * Returns the 2nd derivative of the power basis representation of a 
 * bezier curve of order cubic or less (with intermediate calculations done in 
 * double precision).
 * 
 * * 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]]`
 * 
 * @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_2ndDerivative(ps: number[][]): number[][] {
	if (ps.length === 4) {
		const [[x0,y0], [x1,y1], [x2,y2], [x3,y3]] = ps;
		return [[
			6*((x3 - x0) + 3*(x1 - x2)),
			6*((x2 + x0) - 2*x1)
		], [
			6*((y3 - y0) + 3*(y1 - y2)),
			6*((y2 + y0) - 2*y1)
		]]
	} 
	
	if (ps.length === 3) {
		const [[x0,y0], [x1,y1], [x2,y2]] = ps;
		return [[
			2*(x2 - 2*x1 + x0)
		], [
			2*(y2 - 2*y1 + y0)
		]];
	}
	
	if (ps.length <= 2) {
		return [[0],[0]];
	}

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


export { toPowerBasis_2ndDerivative }