import { allRootsCertifiedSimplified } from 'flo-poly';
import { toPowerBasis_1stDerivative } from '../../to-power-basis/to-power-basis-1st-derivative/double/to-power-basis-1st-derivative.js'
import { XBounds } from "./bounds.js";
import { getIntervalBox } from './get-interval-box/get-interval-box.js';


/**
 * Returns tight x-coordinate bounds of the given bezier curve.
 * 
 * @param ps an order 1, 2 or 3 bezier curve given as an array of control 
 * points, e.g. `[[0,0], [1,1], [2,1], [2,0]]`
 * 
 * @doc mdx
 */
 function getXBoundsTight(ps: number[][]): XBounds {
	const pS = ps[0];
	const pE = ps[ps.length-1];

	let minX: { ts: number[]; box: number[][]; };
	let maxX: { ts: number[]; box: number[][]; };
	if (pS[0] < pE[0]) {
		minX = { ts: [0,0], box: [pS,pS] };
		maxX = { ts: [1,1], box: [pE,pE] };
	} else {
		minX = { ts: [1,1], box: [pE,pE] };
		maxX = { ts: [0,0], box: [pS,pS] };
	}

	if (ps.length === 2) { 
		return { minX, maxX }; 
	}

	const [dx,] = toPowerBasis_1stDerivative(ps);

	const rootsX = allRootsCertifiedSimplified(dx,0,1);
		
	// Test points
	for (let i=0; i<rootsX.length; i++) {
		const r = rootsX[i];
		const ts = [r.tS, r.tE];
		const box = getIntervalBox(ps, ts);

		if (box[0][0] < minX.box[0][0]) { 
			minX = { ts, box } 
		}
		if (box[1][0] > maxX.box[0][0]) { 
			maxX = { ts, box } 
		}
	}

	return { minX, maxX };
}


export { getXBoundsTight }