/**
 * Returns the 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_1stDerivative(ps: number[][]): number[][] {
	if (ps.length === 4) {
		return toPowerBasis3_1stDerivative(ps);
	} 
	
	if (ps.length === 3) {
		return toPowerBasis2_1stDerivative(ps);
	} 
	
	if (ps.length === 2) {
		return toPowerBasis1_1stDerivative(ps);
	}

	if (ps.length === 1) {
		return [[0], [0]];
	}

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


/** @internal */
function toPowerBasis3_1stDerivative(ps: number[][]): number[][] {
	const [[x0,y0], [x1,y1], [x2,y2], [x3,y3]] = ps;

	return [[
		3*((x3 - x0) + 3*(x1 - x2)),
		6*((x2 + x0) - 2*x1),
		3*(x1 - x0)
	], [
		3*((y3 - y0) + 3*(y1 - y2)),
		6*((y2 + y0) - 2*y1),
		3*(y1 - y0)
	]];
}


/** @internal */
function toPowerBasis2_1stDerivative(ps: number[][]): number[][] {
	const [[x0,y0], [x1,y1], [x2,y2]] = ps;

	return [[
		2*((x2 + x0) - 2*x1),
		2*(x1 - x0)
	], [
		2*((y2 + y0) - 2*y1),
		2*(y1 - y0)
	]];
}


/** @internal */
function toPowerBasis1_1stDerivative(ps: number[][]): number[][] {
	const [[x0,y0], [x1,y1]] = ps;

	return [[
		x1 - x0
	], [
		y1 - y0
	]];
}


export { toPowerBasis_1stDerivative }