/**
 * Returns the result, `[x,y]`, of evaluating the 2nd derivative of a linear,
 * quadratic or cubic bezier curve's power basis at `t === 0`.
 * 
 * * uses double precision calculations internally
 * 
 * @param ps An order 0,1,2 or 3 bezier, e.g. `[[0,0],[1,1],[2,1],[2,0]]`
 * 
 * @doc
 */
function evaluate2ndDerivativeAt0(ps: number[][]): number[] {
	// Bitlength: If the coordinates of the control points are bit-aligned then the
	// * max bitlength (incl bit shift) increase === 5 (for cubics)
	// * max bitlength (incl bit shift) increase === 3 (for quadratics)
	// * max bitlength (incl bit shift) increase === 0 (for lines)
	if (ps.length === 4) {
		const [[x0,y0], [x1,y1], [x2,y2]] = ps;
		return [
			6*((x2 + x0) - 2*x1),
			6*((y2 + y0) - 2*y1)
		]; // max bitlength increase 5
	} 
	
	if (ps.length === 3) {
		const [[x0,y0], [x1,y1], [x2,y2]] = ps;
		return [
			2*((x2 + x0) - 2*x1),
			2*((y2 + y0) - 2*y1) 
		]; // max bitlength increase 3
	} 
	
	if (ps.length <= 2) {
		return [0, 0];
	}

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


export { evaluate2ndDerivativeAt0 }