physics-rendering-expert

Name: physics-rendering-expert
Rating: 5 (20 reviews)
Author: erichowens

by @erichowens in AI & LLM

# Install this skill:

npx skills add erichowens/some_claude_skills --skill "physics-rendering-expert"

Install specific skill from multi-skill repository

# 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).

# SKILL.md

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
category: AI & Machine Learning
tags:
- physics
- pbd
- verlet
- simulation
- constraints
pairs-with:
- skill: metal-shader-expert
reason: GPU-accelerated physics rendering
- skill: native-app-designer
reason: Physics in app animations

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.

# Supported AI Coding Agents

This skill is compatible with the SKILL.md standard and works with all major AI coding agents:

⚡ Amp 🚀 Antigravity 🤖 Claude Code 🦀 Clawdbot 📝 Codex ▶️ Cursor 🤖 Droid 💎 Gemini CLI 🐙 GitHub Copilot 🪿 Goose 📊 Kilo Code 🔧 Kiro CLI 💻 OpenCode 🦘 Roo Code 🌲 Trae 🏄 Windsurf

Learn more about the SKILL.md standard and how to use these skills with your preferred AI coding agent.