Prompt de Arquitecto de Lógica de Física para Juegos

Implementación de mecánica de gancho de agarre con tensión elástica y fuerza centrífuga. **1. Fórmulas matemáticas (LaTeX) para física:** - Posición del jugador: `\vec{p}(t)` - Punto de anclaje del gancho: `\vec{a}` - Vector de cuerda: `\vec{r}(t) = \vec{p}(t) - \vec{a}` - Longitud natural de la cuerda: `L_0` - Constante elástica: `k` - Longitud actual: `L(t) = |\vec{r}(t)|` - Tensión elástica (fuerza restauradora): `\vec{F}_{tension} = -k \cdot (L(t) - L_0) \cdot \hat{r}(t)` donde `\hat{r}(t) = \frac{\vec{r}(t)}{L(t)}` - Fuerza centrífuga (componente perpendicular): `\vec{F}_{cent} = m \cdot \frac{|\vec{v}_{tang}|^2}{L(t)} \cdot \hat{n}(t)` donde `\vec{v}_{tang} = \vec{v} - (\vec{v} \cdot \hat{r})\hat{r}` y `\hat{n}(t)` es el vector unitario perpendicular a `\hat{r}` en el plano de oscilación. - Aceleración total: `\vec{a}(t) = \frac{\vec{F}_{tension} + \vec{F}_{cent} + \vec{F}_{gravity} + \vec{F}_{input}}{m}` - Amortiguación: `\vec{F}_{damp} = -c \cdot \vec{v}_{tang}` (constante `c` para disipación de energía). - Integración numérica (semi-implícita Euler): `\vec{v}(t+\Delta t) = \vec{v}(t) + \vec{a}(t) \cdot \Delta t`, luego `\vec{p}(t+\Delta t) = \vec{p}(t) + \vec{v}(t+\Delta t) \cdot \Delta t`. - Corrección de restricción de longitud (proyección): Si `L(t+\Delta t) > L_{max}`, proyectar `\vec{p}` de vuelta a la esfera de radio `L_{max}` centrada en `\vec{a}`. **2. Diagrama de transición de estados (Markdown):** ```mermaid stateDiagram-v2 [*] --> Idle: No input Idle --> Aiming: Press Fire1 (hold) Aiming --> Grappling: Release Fire1 (raycast hit) Aiming --> Idle: Release Fire1 (miss) / Cancel Grappling --> Grappling: Rope attached (elastic force active) Grappling --> Swinging: Player velocity tangential > threshold Swinging --> Grappling: Tangential velocity < threshold (damping) Grappling --> Released: Press Fire2 / Press Fire1 again Swinging --> Released: Press Fire2 / Press Fire1 again Released --> Idle: Rope detached, no collision Released --> Grappling: New anchor (cooldown period, min 0.2s) Grappling --> Idle: Anchor destroyed / Rope length > max (break) Swinging --> Idle: Player hits ground (collision with floor) ``` **3. Código de producción (C# para Unity):** ```csharp using UnityEngine; public class GrappleHookController : MonoBehaviour { [Header("Rope Physics")] [SerializeField] private float ropeNaturalLength = 5f; [SerializeField] private float maxRopeLength = 20f; [SerializeField] private float springConstant = 50f; [SerializeField] private float dampingCoeff = 2f; [SerializeField] private float gravityScale = 1f; [Header("Input")] [SerializeField] private KeyCode fireKey = KeyCode.Mouse0; [SerializeField] private KeyCode releaseKey = KeyCode.Mouse1; [SerializeField] private float inputCooldown = 0.2f; [Header("Player")] [SerializeField] private Rigidbody playerRigidbody; [SerializeField] private float playerMass = 1f; private Vector3 anchorPoint; private bool isGrappling = false; private float cooldownTimer = 0f; private RaycastHit hitInfo; private void Update() { cooldownTimer -= Time.deltaTime; if (Input.GetKeyDown(fireKey) && cooldownTimer <= 0f) { TryFireGrapple(); } if (Input.GetKeyDown(releaseKey) && isGrappling) { ReleaseGrapple(); } } private void FixedUpdate() { if (isGrappling) { ApplyRopePhysics(); } } private void TryFireGrapple() { Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition); if (Physics.Raycast(ray, out hitInfo, maxRopeLength)) { anchorPoint = hitInfo.point; isGrappling = true; cooldownTimer = inputCooldown; } } private void ReleaseGrapple() { isGrappling = false; cooldownTimer = inputCooldown; } private void ApplyRopePhysics() { Vector3 position = playerRigidbody.position; Vector3 velocity = playerRigidbody.velocity; Vector3 r = position - anchorPoint; float currentLength = r.magnitude; if (currentLength > maxRopeLength) { // Break rope isGrappling = false; return; } Vector3 rNormalized = r / currentLength; Vector3 gravityForce = Physics.gravity * playerMass * gravityScale; // Elastic tension float stretch = currentLength - ropeNaturalLength; Vector3 tensionForce = -springConstant * stretch * rNormalized; // Clamp to avoid infinite stretch tensionForce = Vector3.ClampMagnitude(tensionForce, 1000f); // Tangential velocity (for centrifugal) Vector3 tangentialVelocity = velocity - Vector3.Dot(velocity, rNormalized) * rNormalized; float tangentialSpeed = tangentialVelocity.magnitude; // Centrifugal force (outward from anchor, perpendicular to rope) Vector3 centrifugalForce = playerMass * (tangentialSpeed * tangentialSpeed / currentLength) * rNormalized; // Damping (linear and tangential) Vector3 dampingForce = -dampingCoeff * tangentialVelocity; // Input force (optional: player can add radial or tangential input) Vector3 inputForce = Vector3.zero; float verticalInput = Input.GetAxis("Vertical"); float horizontalInput = Input.GetAxis("Horizontal"); Vector3 cameraForward = Camera.main.transform.forward; Vector3 cameraRight = Camera.main.transform.right; Vector3 tangentialDir = Vector3.Cross(rNormalized, Vector3.up).normalized; // Convert input to tangential plane Vector3 inputVec = (cameraForward * verticalInput + cameraRight * horizontalInput); float dotR = Vector3.Dot(inputVec, rNormalized); Vector3 inputTangential = inputVec - dotR * rNormalized; inputForce = inputTangential * 10f * playerMass; // Net acceleration Vector3 acceleration = (tensionForce + centrifugalForce + gravityForce + dampingForce + inputForce) / playerMass; // Semi-implicit Euler integration velocity += acceleration * Time.fixedDeltaTime; position += velocity * Time.fixedDeltaTime; // Position constraint (project back to rope length) Vector3 newR = position - anchorPoint; float newLength = newR.magnitude; if (newLength > maxRopeLength) { position = anchorPoint + (newR / newLength) * maxRopeLength; // Reflect velocity component along rope to avoid compression Vector3 rNewNormal = (position - anchorPoint).normalized; float radialVelocity = Vector3.Dot(velocity, rNewNormal); if (radialVelocity < 0f) { velocity -= radialVelocity * rNewNormal; } } playerRigidbody.position = position; playerRigidbody.velocity = velocity; } private void OnDrawGizmos() { if (isGrappling) { Gizmos.color = Color.green; Gizmos.DrawLine(playerRigidbody.position, anchorPoint); } } } ```