/**
 * Geometry helpers for professional connector paths.
 * Orthogonal polylines get filleted corners; mind-map branches use quadratic curves.
 */
/** Sample a quadratic Bézier into polyline points (flat [x,y,...]). */
export declare function quadraticToPoints(x0: number, y0: number, cx: number, cy: number, x1: number, y1: number, steps?: number): number[];
/** SVG path `d` for a quadratic mind-map branch. */
export declare function quadraticPathD(x0: number, y0: number, cx: number, cy: number, x1: number, y1: number): string;
/**
 * Replace sharp orthogonal corners with arc fillets approximated as polylines.
 * Keeps endpoints exact; skips fillets when a segment is too short.
 */
export declare function roundOrthogonalCorners(points: number[], radius?: number, segments?: number): number[];
/** Sample a cubic Bézier into polyline points (flat [x,y,...]). */
export declare function cubicToPoints(x0: number, y0: number, x1: number, y1: number, x2: number, y2: number, x3: number, y3: number, steps?: number): number[];
/**
 * Mermaid-style horizontal link: exits source horizontally, enters target horizontally.
 * Smooth cubic when y differs (flowchart LR / mindmap look).
 */
export declare function mermaidHorizontalLink(x1: number, y1: number, x2: number, y2: number, steps?: number): number[];
/**
 * L-bend as a single cubic — exits along the first leg, enters along the second
 * (string / cable elbow, not a sharp corner).
 */
export declare function stringLCurve(x0: number, y0: number, x1: number, y1: number, x2: number, y2: number, tension?: number, steps?: number): number[];
/**
 * U-bend as a single cubic — vertical exit, horizontal span, vertical entry.
 * Control points sit on the rail so the wire bows like a flexible string.
 */
export declare function stringUCurve(x0: number, y0: number, railY: number, x3: number, y3: number, steps?: number): number[];
/**
 * Horizontal U (C-bend): leave left/right, span vertically, enter left/right.
 */
export declare function stringCCurve(x0: number, y0: number, railX: number, x3: number, y3: number, steps?: number): number[];
/**
 * Convert an orthogonal polyline skeleton into string-like U / L / S curves.
 * Keeps endpoints exact so arrows stay glued to connection ports.
 */
export declare function stringCurveFromOrthogonal(points: number[], steps?: number): number[];
/**
 * Smooth path through free waypoints (string through beads).
 * Uses Catmull-Rom → cubic segments so bends feel continuous while dragging.
 */
export declare function pathThroughWaypoints(x1: number, y1: number, waypoints: Array<{
    x: number;
    y: number;
}>, x2: number, y2: number, stepsPerSeg?: number): number[];
/** Uniform Catmull-Rom spline sampled as a flat polyline. */
export declare function catmullRomToPoints(points: number[], stepsPerSeg?: number): number[];
/**
 * Nearest point on a polyline to (x,y), plus insertion index for a new vertex
 * after the segment that contains the projection (1-based vertex index).
 */
export declare function nearestPointOnPolyline(points: number[], x: number, y: number): {
    x: number;
    y: number;
    segIndex: number;
    dist: number;
    t: number;
};
/**
 * Mermaid flowchart TB bus geometry for parent → children.
 * Multi-child: shared stem + rail + drops; each drop path is also available
 * as a rounded elbow for professional T-junctions.
 */
export declare function mermaidOrgBusPaths(parentX: number, parentBottomY: number, children: Array<{
    x: number;
    topY: number;
}>, _cornerRadius?: number): {
    stem: number[];
    bus: number[];
    drops: number[][];
    elbows: number[][];
};