import { type Vector2Like } from "three";
import type { TriangleCache } from "./math";
/**
 * A triangle in 2D space with precomputed geometric properties.
 * Extends the base TriangleCache with the actual vertex coordinates.
 *
 * @template T - Type of vertices that must be Vector2Like objects
 */
export interface Triangle<T extends Vector2Like> extends TriangleCache {
    /** First vertex of the triangle (Vector2Like coordinates) */
    readonly a: T;
    /** Second vertex of the triangle (Vector2Like coordinates) */
    readonly b: T;
    /** Third vertex of the triangle (Vector2Like coordinates) */
    readonly c: T;
}
/**
 * Result of Delaunay triangulation containing triangles and boundary information.
 *
 * @template T - Type of vertices that must be Vector2Like objects
 */
export interface TriangulationResult<T extends Vector2Like> {
    /** Array of triangles forming the Delaunay triangulation */
    readonly triangles: Triangle<T>[];
    /** Map from boundary vertices to their adjacent boundary vertices [prev, next] */
    readonly boundaryEdgeMap: Map<T, [T, T]>;
}
/**
 * Implements Bowyer-Watson algorithm for Delaunay triangulation in 2D space.
 * Generates a triangulation where no point lies inside the circumcircle of any triangle.
 */
export declare class DelaunayTriangulator {
    /**
     * Performs Delaunay triangulation on a set of 2D points using the Bowyer-Watson algorithm.
     * The resulting triangulation satisfies the Delaunay condition: no point lies inside
     * the circumcircle of any triangle.
     *
     * @template T - Type of vertices that must be Vector2Like objects
     * @param points - Array of points to triangulate (minimum 3 points required)
     * @returns Triangulation result containing triangles and boundary edge information
     * @throws {Error} When fewer than 3 points provided, points contain invalid coordinates,
     *                 duplicate points exist, or all points are collinear
     * @see {@link TriangulationResult} for result structure details
     * @see {@link Triangle} for triangle structure details
     */
    static triangulate<T extends Vector2Like>(points: T[]): TriangulationResult<T>;
    /**
     * Identifies and removes triangles whose circumcircles contain the given point.
     * Such triangles violate the Delaunay condition and must be removed.
     * Modifies the input triangles array in-place for efficiency.
     *
     * @template T - Type of vertices that must be Vector2Like objects
     * @param triangles - Array of triangles to filter (modified in-place)
     * @param point - Point to test against triangle circumcircles (Vector2Like coordinates)
     * @returns Array of triangles that contain the point in their circumcircles
     * @see {@link isPointInsideCircle} for circumcircle containment test
     */
    private static filterBadTriangles;
    /**
     * Constructs the polygon boundary formed by removing bad triangles.
     * Finds edges that belong to only one triangle (outer edges of the cavity).
     * These edges will form the boundary of the polygon hole left by removed triangles.
     *
     * @template T - Type of vertices that must be Vector2Like objects
     * @param triangles - Array of triangles forming the cavity (finite array)
     * @returns Array of edges [vertex1, vertex2] that form the polygon boundary
     */
    private static buildPolygon;
    /**
     * Removes triangles containing super triangle vertices and builds boundary edge map.
     * Filters out triangles that include any vertex from the initial super triangle,
     * keeping only triangles formed entirely from input points. Also constructs
     * a map of boundary vertices to their adjacent boundary vertices.
     *
     * @template T - Type of vertices that must be Vector2Like objects
     * @param triangles - Array of triangles to filter (modified in-place)
     * @param superTriangle - The super triangle used to initialize triangulation
     * @returns Map from boundary vertices to arrays of their adjacent boundary vertices
     * @throws {Error} When boundary vertex connectivity invariants are violated
     */
    private static filterSuperTriangleVertices;
    /**
     * Constructs a large triangle that encompasses all input points.
     * The super triangle provides an initial triangulation that contains all points,
     * allowing the incremental algorithm to proceed. Vertices are positioned far
     * outside the bounding box of input points.
     *
     * @template T - Type of vertices that must be Vector2Like objects
     * @param points - Array of input points to encompass (finite coordinates)
     * @returns Triangle that contains all input points with precomputed properties
     * @see {@link precomputeTriangle} for triangle property computation
     */
    private static buildSuperTriangle;
    /**
     * Tests whether a vertex belongs to a specific triangle.
     * Uses reference equality to determine if the vertex is one of the triangle's vertices.
     *
     * @template T - Type of vertices that must be Vector2Like objects
     * @param vertex - Vertex to test for membership (Vector2Like coordinates)
     * @param triangle - Triangle to test against
     * @returns True if the vertex is one of the triangle's vertices, false otherwise
     */
    private static isVertexFromTriangle;
}