Invite d'architecture logique de physique de jeu

[Game Physics Logic Architect Mode] **1. Mathematical Formulas (LaTeX)** Let `P` be the player position, `A` the anchor point, `L0` the rope's rest length, `k` the spring constant, `b` the damping coefficient, and `v` the player's velocity. Rope vector: `r = P - A` Current length: `L = |r|` Unit direction: `r̂ = r / L` Elastic tension force (Hooke's Law with damping): `F_spring = -k * (L - L0) * r̂ - b * (v · r̂) * r̂` Total force on player: `F_total = F_spring + F_gravity + F_input` Acceleration: `a = F_total / m` Velocity update (semi-implicit Euler): `v_new = v + a * dt` Position update: `P_new = P + v_new * dt` For rope length constraint (if `L > L_max`), project player back: `P_corrected = A + r̂ * L_max` Momentum conservation: `m * v_before = m * v_after` (if no external impulse). For elastic collision with anchor, reflect velocity component along `r̂`: `v_reflected = v - 2 * (v · r̂) * r̂` (only if `v · r̂ > 0`). Input-to-response latency: use fixed timestep `dt = 1/60` and buffer input for 1 frame (`input_buffer = 0.016s`). --- **State Machine Transition Diagram (Markdown)** ```mermaid stateDiagram-v2 [*] --> Idle Idle --> Aiming: PressAndHold (Input) Aiming --> Grappling: Release (Input) && RaycastHit Aiming --> Idle: Release (Input) && NoHit Grappling --> Swinging: RopeAttached Swinging --> Reeling: PressReel (Input) Swinging --> Detached: PressJump (Input) || RopeBreak Reeling --> Swinging: ReleaseReel (Input) Reeling --> Detached: RopeLength < Min Detached --> Idle: PlayerGrounded Swinging --> Idle: PlayerGrounded && RopeDetached ``` --- Production-Ready C# Code (Unity): ```csharp using UnityEngine; public class GrappleHook : MonoBehaviour { [Header("Physics")] public float springConstant = 100f; public float damping = 5f; public float maxRopeLength = 20f; public float minRopeLength = 2f; public float playerMass = 1f; [Header("Input")] public KeyCode grappleKey = KeyCode.Mouse0; public KeyCode reelKey = KeyCode.Mouse1; public KeyCode jumpKey = KeyCode.Space; private Vector3 anchorPoint; private Rigidbody rb; private bool isGrappling = false; private bool isReeling = false; private float currentRopeLength; void Start() { rb = GetComponent<Rigidbody>(); } void Update() { if (Input.GetKeyDown(grappleKey)) { TryAttachRope(); } if (Input.GetKeyUp(grappleKey)) { DetachRope(); } if (Input.GetKeyDown(reelKey)) { isReeling = true; } if (Input.GetKeyUp(reelKey)) { isReeling = false; } if (Input.GetKeyDown(jumpKey)) { DetachRope(); } } void FixedUpdate() { if (isGrappling) { ApplyRopePhysics(); } } void TryAttachRope() { Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition); if (Physics.Raycast(ray, out RaycastHit hit, Mathf.Infinity)) { anchorPoint = hit.point; currentRopeLength = Vector3.Distance(transform.position, anchorPoint); isGrappling = true; } } void ApplyRopePhysics() { Vector3 r = transform.position - anchorPoint; float L = r.magnitude; Vector3 rHat = r / L; // Elastic tension force Vector3 springForce = -springConstant * (L - currentRopeLength) * rHat; Vector3 dampingForce = -damping * Vector3.Dot(rb.linearVelocity, rHat) * rHat; Vector3 totalForce = springForce + dampingForce + Physics.gravity * rb.mass; rb.AddForce(totalForce, ForceMode.Force); // Rope length limit if (L > currentRopeLength) { rb.linearVelocity -= Vector3.Dot(rb.linearVelocity, rHat) * rHat; transform.position = anchorPoint + rHat * currentRopeLength; } // Reeling logic if (isReeling) { currentRopeLength = Mathf.Max(minRopeLength, currentRopeLength - 2f * Time.fixedDeltaTime); } } void DetachRope() { isGrappling = false; isReeling = false; } } ``` Note: The code uses `rb.linearVelocity` (Unity 6+). For older versions, use `rb.velocity`. The `ForceMode.5` is a placeholder - replace with `ForceMode.Force` or `ForceMode.Acceleration` as needed.