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import type { Point, SplinePoint } from '../types/geometric.js';
/**
 * @private
 */
export declare function _pointInLine(p1: Point, p2: Point, t: number, mode?: any): {
    x: number;
    y: number;
};
/**
 * @private
 */
export declare function _steppedInterpolation(p1: Point, p2: Point, t: number, mode: 'middle' | 'after' | unknown): {
    x: number;
    y: number;
};
/**
 * @private
 */
export declare function _bezierInterpolation(p1: SplinePoint, p2: SplinePoint, t: number, mode?: any): {
    x: number;
    y: number;
};