---
name: physics-rendering-expert
description: 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).
allowed-tools: Read,Write,Edit,Bash,mcp__firecrawl__firecrawl_search,WebFetch
metadata:
  category: AI & Machine Learning
  pairs-with:
  - skill: metal-shader-expert
    reason: GPU-accelerated physics rendering
  - skill: native-app-designer
    reason: Physics in app animations
  tags:
  - physics
  - pbd
  - verlet
  - simulation
  - constraints
---

# 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.


---
Source attribution: curiositech
Original project: https://github.com/curiositech/some_claude_skills/blob/f49825290077e5fb46bb3e867dfa8a5b0161152b/.claude/skills/physics-rendering-expert/SKILL.md
License: MIT
License information: https://opensource.org/license/mit
Original upstream instructions; downloaded from Mega AI Hub.

## Upstream license notice

MIT License

Copyright (c) 2025 Erich Owens

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.



# Mega AI Hub resource metadata

Creator / publisher: curiositech
Original project: https://github.com/curiositech/some_claude_skills/blob/f49825290077e5fb46bb3e867dfa8a5b0161152b/.claude/skills/physics-rendering-expert/SKILL.md
Attribution basis: Source repository record

Fields of work: Development & Engineering
Roles: Backend Developer, Game Developer, ML / AI Engineer
Specialties: Backend
Tools: Firecrawl
Country applicability: Country not specified
Classification basis: Source catalog labels
Instruction SHA-256: 6d922e793f16372cbab620ad9e739f1f1bca15600f2d5dd147fa234e3a7e5c87