import type { Vec2 } from './Vec2';
export interface CubicBezierCurve {
    p0: Vec2;
    p1: Vec2;
    p2: Vec2;
    p3: Vec2;
}
export interface PointOnCurve {
    x: number;
    y: number;
    /** tangent angle in radians */
    angle: number;
}
export declare class BezierPath {
    readonly curve: CubicBezierCurve;
    /** Total arc length of this curve in logical pixels */
    readonly totalLength: number;
    /**
     * Flat LUT with LUT_SIZE+1 entries.
     * lut[i*3]   = x position at sample i
     * lut[i*3+1] = y position at sample i
     * lut[i*3+2] = tangent angle at sample i
     */
    readonly lut: Float64Array;
    /**
     * arcLen[i] = cumulative arc length from p0 to sample i.
     * Used by binary search in getPointAtLength().
     */
    private readonly arcLen;
    /** SVG path data string — used by canvas Path2D for edge tube drawing */
    readonly svgD: string;
    constructor(curve: CubicBezierCurve);
    /**
     * Returns the point at arc-length `distance` along the curve.
     * Clamps to [0, totalLength]. O(log n) via binary search.
     */
    getPointAtLength(distance: number): PointOnCurve;
    /**
     * Returns the unit tangent vector at arc-length `distance`.
     */
    getTangentAtLength(distance: number): Vec2;
    /**
     * Find the closest point on the curve to a given point.
     * Uses LUT scan — O(LUT_SIZE). Returns arc-length distance and position.
     * Used by InteractionSystem for edge hit testing.
     */
    closestPoint(px: number, py: number): {
        distance: number;
        point: PointOnCurve;
        distSq: number;
    };
    /** Binary search: returns largest i such that arcLen[i] <= target */
    private binarySearchArc;
    /**
     * Build a bezier from source boundary point to target boundary point.
     * Control points are derived from the center-to-center perpendicular,
     * preserving smooth curvature regardless of where the boundary points land.
     *
     * @param source   Start point (source node boundary)
     * @param target   End point (target node boundary)
     * @param srcCenter  Source node center (for control point calculation)
     * @param tgtCenter  Target node center (for control point calculation)
     * @param curvature  Perpendicular offset scale (signed, default 0.3)
     * @param offset     Additional offset for the mid control point
     */
    /**
     * Build an arc-length-parameterized cubic bezier.
     *
     * `curvature`  controls the perpendicular offset at the source-side control
     * point (p1, placed at ~1/3 of the chord).
     *
     * `curvature2` controls the perpendicular offset at the target-side control
     * point (p2, placed at ~2/3 of the chord).  When omitted it equals
     * `curvature` → symmetric arc.  When different it produces asymmetric arcs
     * or S-curves (opposite signs), giving organic / freeform paths.
     */
    static fromBoundaryPoints(source: Vec2, target: Vec2, srcCenter: Vec2, tgtCenter: Vec2, curvature?: number, curvature2?: number, offset?: Vec2): BezierPath;
    /**
     * Simple center-to-center bezier (backward-compat helper).
     */
    static fromCenters(source: Vec2, target: Vec2, curvature?: number, curvature2?: number, offset?: Vec2): BezierPath;
}
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