/**
 * Yaw-frame steering math. The engine's heading convention is
 * `forward = (sin yaw, cos yaw)` on the XZ plane with +Y up, which makes a
 * positive yaw increment rotate counterclockwise seen from above — a turn to
 * the entity's LEFT on screen. Every hand-written `heading += steer * rate * dt`
 * therefore turns the wrong way; integrate steering through `steerYaw` instead.
 */
export type YawVectorXZ = readonly [number, number];
/** XZ forward direction of a yaw (`rotationY`): `(sin yaw, cos yaw)`. */
export declare function yawForward(yaw: number): YawVectorXZ;
/** XZ screen-right of a yaw — `forward × up` with up = +Y: `(-cos yaw, sin yaw)`. */
export declare function yawRight(yaw: number): YawVectorXZ;
/**
 * Integrate one steering step. `steerRight` is the signed steer input
 * (+1 = turn right, matching `DRIVE_AXIS_BINDINGS`' KeyD/ArrowRight),
 * `turnRatePerSecond` is radians per second at full lock. Steering right
 * decreases yaw in the engine frame; this helper owns that sign so game
 * code never re-derives it.
 */
export declare function steerYaw(yaw: number, steerRight: number, turnRatePerSecond: number, dt: number): number;
/**
 * Signed steer-right input that closes on `desiredYaw` when integrated
 * through `steerYaw` — the seek half every AI driver and homing script
 * needs. Magnitude is the wrapped radian error in (−π, π]; scale and clamp
 * it into [-1, 1] at the call site.
 */
export declare function steerToward(yaw: number, desiredYaw: number): number;
/**
 * @internal Rotate `yaw` toward `targetYaw` by at most `turnRatePerSecond * dt`
 * radians, always along the shortest arc, snapping exactly onto the target once
 * within a single step so it converges without overshoot or jitter — the
 * smoothing behind a rendered body-turn (`PlayerMovementConfig.turnSpeed`). A
 * large enough rate (or `dt`) reaches the target in one call, matching a snap.
 */
export declare function approachYaw(yaw: number, targetYaw: number, turnRatePerSecond: number, dt: number): number;