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physics-rendering-expert

Real-time rope/cable physics using Position-Based Dynamics (PBD), Verlet integration, and constraint solvers. Expert in quaternion math, Gauss-Seidel/Jacobi solvers, and tangling detection. Activate on 'rope simulation', 'PBD', 'Position-Based Dynamics', 'Verlet', 'constraint solver', 'quaternion', 'cable dynamics', 'cloth simulation', 'leash physics'. NOT for fluid dynamics (SPH/MPM), fracture simulation (FEM), offline cinematic physics, molecular dynamics, or general game physics engines (use Unity/Unreal built-ins).

personAuthor: jakexiaohubgithub
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Physics & Rendering Expert: Rope Dynamics & Constraint Solving

Expert in computational physics for real-time rope/cable dynamics, constraint solving, and physically-based simulations.

When to Use This Skill

Use for:

  • Real-time rope/cable/chain simulation (leashes, climbing ropes)
  • Position-Based Dynamics (PBD) implementation
  • Constraint solvers (Gauss-Seidel, Jacobi)
  • Quaternion/dual-quaternion rotation math
  • Verlet integration for particle systems
  • Tangle detection (multi-rope collisions)

Do NOT use for:

  • Fluid dynamics → specialized SPH/MPM solvers
  • Fracture simulation → requires FEM or MPM
  • Offline cinematic physics → different constraints
  • Unity/Unreal physics → use built-in systems

Expert vs Novice Shibboleths

| Topic | Novice | Expert | |-------|--------|--------| | Constraint approach | Uses spring forces (F=ma) | Uses PBD (directly manipulates positions) | | Why PBD | "Springs work fine" | Springs require tiny timesteps; PBD is unconditionally stable | | Solver choice | "Just iterate until done" | Gauss-Seidel for chains, Jacobi for GPU | | Iterations | 20+ iterations | 5-10 is optimal; diminishing returns after | | Rotation | Uses Euler angles | Uses quaternions (no gimbal lock) | | Integration | Forward Euler | Verlet (symplectic, energy-conserving) |

Common Anti-Patterns

Force-Based Springs for Stiff Constraints

| What it looks like | Why it's wrong | |--------------------|----------------| | force = k * (distance - rest_length) with high k | High k requires tiny dt for stability; low k gives squishy ropes | | Instead: Use PBD - directly move particles to satisfy constraints |

Euler Angles for Rotation

| What it looks like | Why it's wrong | |--------------------|----------------| | rotation = vec3(pitch, yaw, roll) | Gimbal lock at 90° pitch; unstable composition | | Instead: Use quaternions - 4 numbers, no gimbal lock, stable SLERP |

Over-Iteration

| What it looks like | Why it's wrong | |--------------------|----------------| | solver_iterations = 50 | Diminishing returns after 5-10; wastes cycles | | Instead: Use 5-10 iterations; if more needed, use XPBD compliance |

Single-Threaded Gauss-Seidel for Large Systems

| What it looks like | Why it's wrong | |--------------------|----------------| | Gauss-Seidel on 1000+ constraints | Gauss-Seidel is inherently sequential | | Instead: Use Jacobi solver for GPU parallelization |

Quick Reference

Why PBD Beats Force-Based Physics

  • Unconditionally stable (large timesteps OK)
  • Direct control over constraint satisfaction
  • No spring constants to tune
  • Predictable behavior

Solver Choice

| Solver | Parallelizable | Convergence | Use Case | |--------|---------------|-------------|----------| | Gauss-Seidel | No | Fast | Chains, ropes | | Jacobi | Yes (GPU) | Slower | Large meshes, cloth |

Rotation Representation

  • 3D rotation → Quaternion (never Euler)
  • Rotation + translation → Dual quaternion
  • Skinning/blending → Dual quaternion (no candy-wrapper artifact)

Performance Targets

| System | Budget | Notes | |--------|--------|-------| | Single rope (100 particles) | <0.5ms | 5 iterations sufficient | | Three-dog leash (60 particles) | <0.7ms | Include tangle detection | | Cloth (1000 particles) | <2ms | Use Jacobi on GPU |

Evolution Timeline

| Era | Key Development | |-----|-----------------| | Pre-2006 | Mass-spring systems, stability issues | | 2006-2015 | PBD introduced (Müller et al.), unconditional stability | | 2016-2020 | XPBD adds compliance for soft constraints | | 2021-2024 | ALEM (2024 SIGGRAPH), BDEM, neural physics | | 2025+ | XPBD standard, hybrid CPU/GPU, learned corrections |

Decision Trees

Choosing constraint solver:

  • Sequential structure (rope/chain)? → Gauss-Seidel
  • Large parallel system (cloth/hair)? → Jacobi (GPU)
  • Need soft constraints? → XPBD with compliance

Choosing integration:

  • Position-only needed? → Basic Verlet
  • Need velocity for forces? → Velocity Verlet
  • High accuracy required? → RK4 (but PBD usually sufficient)

Integrates With

  • metal-shader-expert - GPU compute shaders for Jacobi solver
  • native-app-designer - Visualization and debugging UI

Reference Files

| File | Contents | |------|----------| | references/core-algorithms.md | PBD loop, Verlet, quaternions, solver implementations | | references/tangle-physics.md | Multi-rope collision, Capstan friction, TangleConstraint |

Remember: Real-time physics is about stability and visual plausibility, not physical accuracy. PBD with 5-10 iterations at 60fps looks great and runs fast.