import { gaussQuadrature } from "flo-gauss-quadrature";
import { ds } from "../../local-properties-at-t/ds.js";
import { splitByCurvature } from "../../transformation/split/split-by-curvature.js";
import { fromTo3InclErrorBound } from "../../transformation/split/from-to/from-to-3-incl-error-bound.js";


/**
 * Returns the curve length of the given cubic bezier curve within the 
 * specified parameter interval.
 * 
 * @param interval the paramter interval over which the length is 
 * to be calculated (often `[0,1]`)
 * @param ps a cubic bezier curve given by an ordered array of its control
 * points, e.g. `[[0,0],[1,1],[2,1],[3,3]]`
 * @param maxCurviness optional maximum 'curviness' (defined as the total angle
 * change between consecutive line segments between the curve control points)
 * before subdivision occurs; defaults to 0.4 radians
 * @param gaussOrder the optional order of the Gaussian Quadrature performed 
 * between curve segments; defaults to 16; can be 4,16 or 64
 * 
 * @internal
 */
 function lengthBez3(
	 	interval: number[], 
		ps: number[][],
		maxCurviness = 0.4,
		gaussOrder: 4|16|64 = 16): number {

	const tS = interval[0];
	const tE = interval[1];

	if (tS === tE) { return 0; }

	const [[x0, y0], [x1, y1], [x2, y2], [x3, y3]] = ps;
	// Keep line below to ensure zero length curve returns zero!
	if (x0 === x1 && x1 === x2 && x2 === x3 &&
		y0 === y1 && y1 === y2 && y2 === y3) {

		return 0;
	}

	const ps_ = fromTo3InclErrorBound(ps,tS,tE).ps;
	const ts = splitByCurvature(ps_, maxCurviness);

	let total = 0;
	for (let i=0; i<ts.length-1; i++) {
		const tS = ts[i];
		const tE = ts[i+1];

		total += gaussQuadrature(ds(ps_), [tS,tE], gaussOrder);
	}

	return total;
}


export { lengthBez3 }