physics-rendering-expert

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

| 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) |

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 |

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 |

| 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 |

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)

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

| 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.