import { getInterfaceRotation } from '../simultaneous-properties/get-interface-rotation.js';
import { fromTo2InclErrorBound } from "../transformation/split/from-to/from-to-2-incl-error-bound.js";
import { fromTo3InclErrorBound } from "../transformation/split/from-to/from-to-3-incl-error-bound.js";
import { classify } from './classification/classify.js';
import { getInflections } from "./get-inflections.js";

const { abs, PI: 𝜋 } = Math;


/**
 * Returns the total absolute curvature of the given bezier curve over the
 * given interval
 * 
 * * the result is given in radians. 
 * 
 * @param ps an order 0,1,2 or 3 bezier curve given as an array of its control
 * points, e.g. `[[1,2],[3,4],[5,6],[7,8]]`
 * @param interval
 * 
 * @doc mdx
 */
function totalAbsoluteCurvature(
		ps: number[][], 
		interval = [0,1]): number {
	
	if (ps.length <= 3) { 
		return abs(totalCurvature(ps, interval));
	}

	if (ps.length === 4) {
		const [tS,tE] = interval;
		if (tS === tE) { return 0; }
		const ps_ = fromTo3InclErrorBound(ps, tS, tE).ps;

		const ts = [0, ...getInflections(ps_), 1];

		let total = 0;
		for (let i=0; i<ts.length-1; i++) {
			total += abs(totalCurvature(ps_, [ts[i], ts[i+1]]));
		}

		return total;
	}

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


/**
 * Returns the total curvature of the bezier over the given interval.
 * 
 * * the result is given in radians. 
 * 
 * @param ps a cubic bezier, e.g. [[0,0],[1,1],[2,1],[2,0]]
 * @param interval the interval of integration (often === [0,1])
 * 
 * @doc mdx
 */
function totalCurvature(
		ps: number[][], 
		interval = [0,1]): number {

	if (ps.length <= 2) { return 0; }

	const [tS,tE] = interval;

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

	if (ps.length === 3) {
		const ps_ = fromTo2InclErrorBound(ps, tS, tE).ps;
		const [[x0,y0],[x1,y1],[x2,y2]] = ps_;
		const tanS = [x1 - x0, y1 - y0];
		const tanE = [x2 - x1, y2 - y1];

		// guaranteed: |θ| <= 𝜋, curvature = θ
		return getInterfaceRotation(tanS, tanE);
	}


	if (ps.length === 4) {
		// guaranteed: curvature <= 2𝜋
		const ps_ = fromTo3InclErrorBound(ps, tS, tE).ps;

		const bezClass = classify(ps_);

		const [[x0,y0],[x1,y1],[x2,y2],[x3,y3]] = ps_;
		const tanS = [x1 - x0, y1 - y0];
		const tanM = [x2 - x1, y2 - y1];
		const tanE = [x3 - x2, y3 - y2];

		if ((tanM[0] === 0 && tanM[1] === 0) ||
			bezClass.realOrder <= 2) {

			return getInterfaceRotation(tanS, tanE);
		}

		const cpθ =
			getInterfaceRotation(tanS, tanM) + 
			getInterfaceRotation(tanM, tanE);

		if (bezClass.nodeType === 'acnode' || 
			bezClass.nodeType === 'cusp') {

			return cpθ <= -𝜋
				? cpθ + 2*𝜋 
				: cpθ >= +𝜋 
					? cpθ - 2*𝜋
					: cpθ;
		}

		return cpθ;
	}

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


export { totalCurvature, totalAbsoluteCurvature }