/**
 * Returns the tangent vector (not necessarily of unit length) of an 
 * order 0,1,2 or 3 bezier curve at `t === 1`, i.e.
 * Returns the result, `[x,y]`, of evaluating the derivative of a linear, 
 * quadratic or cubic bezier curve's power basis at `t === 1`. 
 * 
 * * uses double precision calculations internally
 * 
 * @param ps An order 1,2 or 3 bezier, e.g. `[[0,0],[1,1],[2,1],[2,0]]`
 * 
 * @doc
 */
function tangentAt1(ps: number[][]): number[] {
	// Bitlength: If the coordinates of the control points are grid-aligned then
	// * max bitlength (incl bit shift) increase === 3 (for cubics)
	// * max bitlength (incl bit shift) increase === 2 (for quadratics)
	// * max bitlength (incl bit shift) increase === 1 (for lines)
	if (ps.length === 4) {
		const [x2,y2] = ps[2];
		const [x3,y3] = ps[3];
		return [
			3*(x3 - x2),
			3*(y3 - y2),
		]; // max bitlength increase 3
	} 
	
	if (ps.length === 3) {
		const [x1,y1] = ps[1];
		const [x2,y2] = ps[2];
		return [
			2*(x2 - x1),
			2*(y2 - y1),
		]; // max bitlength increase 2
	} 
	
	if (ps.length === 2) {
		const [[x0,y0], [x1,y1]] = ps;
		return [
			x1 - x0,
			y1 - y0
		]; // max bitlength increase 1
	}

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

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


export { tangentAt1 }