Imported from curiositech/some_claude_skills (.claude/skills/physics-rendering-expert/SKILL.md). Install upstream with npx skills add curiositech/some_claude_skills --skill physics-rendering-expert. Copyright stays with the author.

Physics & Rendering Expert: Rope Dynamics & Constraint Solving

Name: physics-rendering-expert
Author: curiositech

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.

{ "ocm": "1", "id": "curiositech-some-claude-skills-physics-rendering-expert", "kind": "skill", "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).", "publisher": "curiositech", "version": "1.0.0", "capabilities": { "domains": [ "general" ], "tags": [ "skill-md", "physics", "pbd", "verlet", "simulation", "constraints", "skills-sh" ], "languages": [ "en" ] }, "quality_prior": 0.6, "examples": [ "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)." ], "primary": false, "metadata": { "source": { "provider": "skills.sh", "repository": "https://github.com/curiositech/some_claude_skills", "path": ".claude/skills/physics-rendering-expert/SKILL.md", "ref": "HEAD", "url": "https://github.com/curiositech/some_claude_skills/blob/HEAD/.claude/skills/physics-rendering-expert/SKILL.md", "key": "curiositech/some_claude_skills/.claude/skills/physics-rendering-expert/SKILL.md" }, "allowed_tools": [ "Read,Write,Edit,Bash,mcp__firecrawl__firecrawl_search,WebFetch" ] }, "instructions": "# Physics & Rendering Expert: Rope Dynamics & Constraint Solving\n\nExpert in computational physics for real-time rope/cable dynamics, constraint solving, and physically-based simulations.\n\n## When to Use This Skill\n\n**Use for:**\n- Real-time rope/cable/chain simulation (leashes, climbing ropes)\n- Position-Based Dynamics (PBD) implementation\n- Constraint solvers (Gauss-Seidel, Jacobi)\n- Quaternion/dual-quaternion rotation math\n- Verlet integration for particle systems\n- Tangle detection (multi-rope collisions)\n\n**Do NOT use for:**\n- Fluid dynamics → specialized SPH/MPM solvers\n- Fracture simulati", "cost": { "context_tokens": 1174 } }

physics-rendering-expert

About