CAN: A Curvature-Aware Nesterov Optimizer for Fast Elastic Simulation With Topological Changes

Area of Science:

• Computer Graphics
• Physics Simulation
• Computational Science

Background:

• Fast simulation of elastic bodies is crucial for computer graphics.
• Current methods are limited by requiring fixed mesh connectivity, failing during topological changes like cutting or fracturing.

Purpose of the Study:

• To develop a novel optimizer that decouples simulation acceleration from mesh topology.
• To enable robust and efficient physics-based animation for dynamic-topology scenarios.

Main Methods:

• Introduced CAN, a topology-agnostic optimizer.
• Developed Curvature-Aware Momentum (CAM) to prevent overshooting.
• Developed Curvature-Aware Line Search (CALS) for high-quality step sizes.

Main Results:

• CAN achieves superior convergence compared to prior works.
• Demonstrated effectiveness across a wide range of dynamic-topology scenarios.
• The method is inherently parallel and requires no precomputation tied to connectivity.

Conclusions:

• CAN establishes a new paradigm for robust and efficient physics-based animation.
• The optimizer's topology-agnostic nature overcomes limitations of existing methods.
• Enables advanced simulations involving cutting, fracturing, and merging without performance degradation.