import { squaredDistanceBetween } from 'flo-vector2d';
import { isQuadObtuse } from "./is-quad-obtuse.js";
import { evalDeCasteljau } from '../../local-properties-at-t/evaluate/double/eval-de-casteljau.js';

const { max, abs } = Math;


/**
 * Returns `true` if the given quadratic bezier curve is acute (see `isQuadObtuse`) 
 * and can be approximated with a line segment with maximum Hausdorff distance 
 * <= the given tolerance, `false` otherwise.
 * 
 * @param ps a quadratic bezier curve given as an array of its control
 * points, e.g. `[[1,2],[3,4],[5,6]]`
 * @param tolerance a maximum Hausdorff distance tolerance; defaults to `2**-10`
 * of the maximum coordinate of the given bezier curve
 * 
 * @internal
 */
function isQuadFlat(
        ps: number[][],
        tolerance?: number | undefined) {

    if (isQuadObtuse(ps)) { 
        return false; 
    }

    const [p0,p1,p2] = ps;
    const [x0,y0] = p0;
    const [x2,y2] = p2;

    if (tolerance === undefined) {
        const [x1,y1] = p1;
        const maxCoordinate = max(abs(x0),abs(y0),abs(x1),abs(y1),abs(x2),abs(y2));
        tolerance = maxCoordinate * 2**-10;
    }

    if (x0 === x2 && y0 === y2) { 
        const d = squaredDistanceBetween(p0,p1)/4;
        return d <= tolerance**2;
    }

    const [x,y] = evalDeCasteljau(ps, 0.5);

    const numerator = ((y2-y0)*x - (x2-x0)*y + x2*y0 - y2*x0)**2;
    const denominator = squaredDistanceBetween(p0, p2);

    const dSquared = numerator / denominator;

    return dSquared <= tolerance**2;
}


export { isQuadFlat }