/** @internal */
export declare function divide_curve(x1: number, y1: number, sx1: number, sy1: number, x2: number, y2: number, curve: [number, number][]): {
    index: number;
    off: [number[], number[]];
};
/** @internal */
export declare function find_offcurve(curve: [number, number][], sx: number, sy: number): number[];
/** @internal */
export declare function generateFattenCurve(x1: number, y1: number, sx1: number, sy1: number, sx2: number, sy2: number, x2: number, y2: number, kRate: number, widthFunc: (t: number) => number): {
    left: [number, number][];
    right: [number, number][];
};