import type { Circle } from '../geometry/circle.js';
import type { PrePointOnShape } from '../point-on-shape/point-on-shape.js';
import type { MatMeta } from '../mat/mat-meta.js';
/**
 * Adds a 2-prong to the MAT. The first point on the shape boundary is given and
 * the second one is found by the algorithm.
 *
 * A 2-prong is defined as a MAT circle that touches the shape at exactly 2
 * points.
 *
 * Before any 2-prongs are added the entire shape is our δΩ.
 *
 * As per the paper by Choi, Choi, Moon and Wee:
 *   "The starting point of this algorithm is a choice of a circle Br(x)
 *    centered at an interior point x which contains two boundary portions c and
 *    d of dΩ as in Fig. 19."
 * In fact, we (and they) start by fixing one point on the boundary beforehand.
 *
 * @param meta
 * @param isHoleClosing `true` if this is a hole-closing two-prong, `false` otherwise
 * @param for1Prong
 * @param angle
 * @param yPos the source point of the 2-prong to be found
 *
 * @internal
 */
declare function find2Prong(meta: MatMeta): (isHoleClosing: boolean, for1Prong: boolean, angle: number, yPos: PrePointOnShape) => {
    circle: Circle;
    z: PrePointOnShape;
} | undefined;
export { find2Prong };