Physics MCP Server

Predicts whether two moving spheres will collide within a time window,
and if so, calculates when and where the collision occurs. Uses analytic
relative motion to find exact collision time (if any).

Args:
    body1_position: Position of first object [x, y, z] in meters
    body1_velocity: Velocity of first object [x, y, z] in m/s
    body1_radius: Radius of first object in meters (must be positive)
    body2_position: Position of second object [x, y, z] in meters
    body2_velocity: Velocity of second object [x, y, z] in m/s
    body2_radius: Radius of second object in meters (must be positive)
    max_time: Maximum time to check in seconds. Default 10.0.

Returns:
    CollisionCheckResponse containing:
        - will_collide: True if collision will occur
        - collision_time: Time until collision in seconds (if collision occurs)
        - collision_point: Approximate collision location [x, y, z] (if collision occurs)
        - impact_speed: Relative velocity at impact in m/s (if collision occurs)
        - closest_approach_distance: Minimum distance between objects
        - closest_approach_time: Time of closest approach

Tips for LLMs:
    - Objects are modeled as spheres (point masses with radius)
    - Collision detection is exact for constant velocity motion
    - Returns earliest collision time if multiple intersections
    - If no collision, check closest_approach_distance to see how close they get
    - Use for: asteroid tracking, car crash prediction, sports ball interactions
    - For complex shapes or forces, use create_simulation instead

Example:
    # Check if two cars will collide
    result = await check_collision(
        body1_position=[0.0, 0.0, 0.0],
        body1_velocity=[10.0, 0.0, 0.0],
        body1_radius=2.0,
        body2_position=[50.0, 1.0, 0.0],
        body2_velocity=[-8.0, 0.0, 0.0],
        body2_radius=2.0
    )
    if result.will_collide:
        print(f"Collision in {result.collision_time:.2f} seconds at {result.impact_speed:.1f} m/s")