import { isCollinear } from "./is-collinear.js";


/**
 * Returns `true` if the given bezier has all control points collinear and 
 * it is self-overlapping, i.e. if it intersects itself at an infinite number 
 * of points.
 * 
 * * a bezier curve can only intersect itself at an infinite number of 
 * points if its locus is a 'self-overlapping line'.
 * 
 * @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]]`
 * 
 * @doc mdx
 */
function isSelfOverlapping(ps: number[][]) {
    if (!isCollinear(ps)) { return false; }

    // Check if control points are non-strict monotone
    const xs = ps.map(p => p[0]);
    const ys = ps.map(p => p[1]);
    return !(isMonotone(xs) && isMonotone(ys));
}


/**
 * Returns true if the given array of numbers are non-strict monotone increasing.
 * @param xs an array of numbers
 * 
 * @internal
 */
function isMonotoneIncreasing(xs: number[]) {
    for (let i=1; i<xs.length; i++) {
        if (xs[i-1] > xs[i]) {
            return false;
        }
    }
    return true;
}


/**
 * Returns true if the given array of numbers are non-strict monotone decreasing.
 * @param xs an array of numbers
 * 
 * @internal
 */
function isMonotoneDecreasing(xs: number[]) {
    for (let i=1; i<xs.length; i++) {
        if (xs[i-1] < xs[i]) {
            return false;
        }
    }
    return true;
}


/**
 * @param xs 
 * 
 * @internal
 */
function isMonotone(xs: number[]) {
    return isMonotoneIncreasing(xs) || isMonotoneDecreasing(xs);
}


export { isSelfOverlapping }