/**
 * Frame-rate-independent exponential approach toward a target.
 * factor = 1 - e^(-rate*dt) so that two dt/2 steps equal one dt step exactly.
 * Higher `rate` = snappier; lower = smoother.
 */
export declare function approachExponential(current: number, target: number, rate: number, dt: number): number;
/**
 * Eases a continuous heading scalar (e.g. -1..1 direction factor) toward a
 * target. Uses the same exponential approach so direction flips ramp smoothly
 * through zero instead of snapping.
 */
export declare function easeHeading(current: number, target: number, rate: number, dt: number): number;
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