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

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


/**
 * Returns the *exact* 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_1stDerivativeExact(
		ps: number[][]): number[][][] {

	if (ps.length === 4) {
		return toPowerBasis3_1stDerivativeExact(ps);
	} 
	
	if (ps.length === 3) {
		return toPowerBasis2_1stDerivativeExact(ps);
	} 
	
	if (ps.length === 2) {
		return toPowerBasis1_1stDerivativeExact(ps);
	}

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

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


/** @internal */ 
function toPowerBasis3_1stDerivativeExact(
	ps: number[][]): number[][][] {

	const [[x0,y0], [x1,y1], [x2,y2], [x3,y3]] = ps;

	return [[
		sce(3,eadd(td(x3,x0), sce(3,td(x1,x2)))),
		sce(6,ge(ts(x2,x0), -2*x1)),
		sce(3,td(x1,x0))
	], [
		sce(3,eadd(td(y3,y0), sce(3,td(y1,y2)))),
		sce(6,ge(ts(y2,y0), -2*y1)),
		sce(3,td(y1,y0))
	]];
} 


/** @internal */ 
function toPowerBasis2_1stDerivativeExact(
		ps: number[][]): number[][][] {

	const [[x0,y0], [x1,y1], [x2,y2]] = ps;

	return [[
		ge(ts(2*x2,2*x0), -4*x1),
		td(2*x1,2*x0),
	], [
		ge(ts(2*y2,2*y0), -4*y1),
		td(2*y1,2*y0),
	]];
}


/** @internal */ 
function toPowerBasis1_1stDerivativeExact(
		ps: number[][]): number[][][] {

	const [[x0,y0], [x1,y1]] = ps;

	return [[
		td(x1,x0),
	], [
		td(y1,y0),
	]];
}


export { toPowerBasis_1stDerivativeExact }