/**
 * Returns a hybrid quadratic bezier curve with error bounds (with the first
 * and last control points omitted).
 * 
 * * **the returned error bounds have counters of <8> and <12> respectively for
 * the 1st and 2nd control points (i.e. for the hybrid control points)**
 * * specifically modified for use in the geometric interval bezier-bezier 
 * intersection algorithm, e.g. for efficiency the first and last points are 
 * not returned
 * * **precondition:** coordinate-wise error bound 'Wilson counters' on the
 * cubic bezier control points of 
 * `[[<6>,<6>], [<6>,<6>], [<10>,<10>], [<11>,<11>]]` are assumed (due to other
 * parts of the algorithm)
 * 
 * @param G a cubic bezier curve - coordinate error bounds are assumed to have 
 * counters of `[[<6>,<6>], [<6>,<6>], [<10>,<10>], [<11>,<11>]]`
 * 
 * @internal
 */
function toHybridQuadratic(
		G: { ps: number[][], _ps: number[][] }): { hq: number[][], _hq: number[][] } {

	// the below is too slow
	//const [[x0, y0], [x1, y1], [x2, y2], [x3, y3]] = ps; 

	const Gps = G.ps;    // the cubic bezier curve
	const G_ps = G._ps;  // and its error bound coordinates

	const p0 = Gps[0];
	const p1 = Gps[1];
	const p2 = Gps[2];
	const p3 = Gps[3];

	const x0 = p0[0];  // <6>x0
	const y0 = p0[1];  // <6>y0
	const x1 = p1[0];  // <6>x1
	const y1 = p1[1];  // <6>y1
	const x2 = p2[0];  // <10>x2
	const y2 = p2[1];  // <10>y2
	const x3 = p3[0];  // <11>x3
	const y3 = p3[1];  // <11>y3

	const _p0 = G_ps[0];
	const _p1 = G_ps[1];
	const _p2 = G_ps[2];
	const _p3 = G_ps[3];

	const _x0 = _p0[0];
	const _y0 = _p0[1];
	const _x1 = _p1[0];
	const _y1 = _p1[1];
	const _x2 = _p2[0];
	const _y2 = _p2[1];
	const _x3 = _p3[0];
	const _y3 = _p3[1];

	// <8> <= <8>(<7>(<0>3*<6>x1) + <6>x0)
	const _hq1 = [(3*_x1 + _x0)/2, (3*_y1 + _y0)/2];
	// <12> <= <12>(<11>(<0>3*<10>x2) + <11>x3)
	const _hq2 = [(3*_x2 + _x3)/2, (3*_y2 + _y3)/2];

	return { 
		hq: [[(3*x1 - x0)/2, (3*y1 - y0)/2],   // evaluated at (1-t)
			 [(3*x2 - x3)/2, (3*y2 - y3)/2]],  // evaluated at t
		// error bounds (still need to be multiplied by 4*u and 6*u)
		_hq: [_hq1, _hq2]  
	};
}


export { toHybridQuadratic }