MetalAVBD: Augmented Vertex Block Descent in Metal

MetalAVBD is a GPU-accelerated implementation of the Augmented Vertex Block Descent (AVBD) solver in Metal 4.

This project is a Metal-based realization of the research project from the University of Utah:

Augmented Vertex Block Descent
Chris Giles, Elie Diaz, and Cem Yuksel
ACM Transactions on Graphics (Proceedings of SIGGRAPH 2025)

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📽 Demos & Research

• Official Project Page - Research details and comparisons.
• Research Paper (PDF) - Deep dive into the Augmented Lagrangian formulation.
• YouTube Video - Official demonstration of the solver from the research authors.

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🚀 Key Solver Features

Following the principles of the AVBD research, this implementation offers:

• Unconditional Stability: Converges toward the implicit Euler solution, ensuring physical correctness even with large timesteps.
• Augmented Lagrangian Formulation: Handles hard constraints with infinite stiffness without numerical instabilities or the "softness" common in traditional penalty methods.
• Convergence: Improved convergence rates in scenes with high stiffness ratios.
• GPU Pipeline:
  • Full GPU broadphase using spatial hashing.
  • Parallel Gauss-Seidel solver utilizing contact-aware body coloring for deterministic stability.
• Scale: Capable of simulating millions of interacting objects in real-time.

🛠 Metal 4 Technical Implementation

This project is optimized for modern Apple Silicon and Metal 4 features:

• GPU Task Scheduling: Leverages adjacency-based coloring to orchestrate constraint solving with minimal contention.
• Descriptor Management: Uses Argument Tables and Residency Sets for efficient resource access.
• Atomic Memory Management: Optimized compute shaders using atomic batching to manage dynamic contact manifolds and allocations on the GPU.
• Diverse Primitive Manifolds:
  • Box (SAT): Accurate face/edge/vertex collision.
  • Sphere: Analytical geometry checks.
  • Torus: Advanced collision manifold generation via approximate sphere decomposition.
  • SDF (Signed Distance Field): High-performance collision against complex mesh geometry using pre-generated 3D volumes.
• SDF Visualization: Real-time raymarching visualizer for debugging and inspecting SDF volume alignment and quality.

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🚧 Limitations

• SDF-to-SDF Collision: Currently, collision detection between two SDF-based objects is not implemented. Only Primitive-to-SDF collisions are supported.

📱 Requirements

• Device: Physical iOS device (A17 Pro / M1 or later) or Apple Silicon Mac.
• OS: iOS 18.0+ / macOS 15.0+ (Metal 4 support required).
• Tooling: Xcode 16.0+

Important

This project utilizes advanced Metal features and cannot be run on the iOS Simulator. Please use a physical device or the "macOS Designed for iPad" destination.

📜 License & Acknowledgments

This implementation is independent of the original authors' code but is built strictly according to the mathematical foundations laid out in their research.

• Original Research: University of Utah Graphics Lab
• License: This project is licensed under the MIT License - see the LICENSE file for details.