Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

SIGGRAPH: G: Improved Projective Dynamics Global Using Snapshots-based Reduced Bases

Shaimaa Monem, Peter Benner, Christian Lessig

TL;DR

This work tackles real-time simulation of deformable objects by addressing the insufficiency of rest-state–based reduction subspaces to capture large deformations and rotations. It introduces a snapshots-based approach to build rotation-inclusive reduced bases, combining mass-weighted localized PCA and SPLOCS within the projective dynamics framework, and avoiding pre-alignment of rotations. The key contributions are a practical pipeline for constructing $U$ from time-varying snapshots, improved numerical stability and computational efficiency, and demonstrated realism gains over state-of-the-art methods such as linear blend skinning subspaces. This approach enables faster, more physically faithful interactive simulations in graphics applications, with implementations available on GitHub for real-time use and further exploration.

Abstract

We propose a snapshots-based method to compute reduction subspaces for physics-based simulations. Our method is applicable to any mesh with some artistic prior knowledge of the solution and only requires a record of existing solutions during, for instance, the range-of-motion test that is required before approving a mesh character for an application. Our subspaces span a wider range of motion, especially large deformations, and rotations by default. Compared to the state-of-the-art, we achieve improved numerical stability, computational efficiency, and more realistic simulations with a smaller sub-space.

SIGGRAPH: G: Improved Projective Dynamics Global Using Snapshots-based Reduced Bases

TL;DR

This work tackles real-time simulation of deformable objects by addressing the insufficiency of rest-state–based reduction subspaces to capture large deformations and rotations. It introduces a snapshots-based approach to build rotation-inclusive reduced bases, combining mass-weighted localized PCA and SPLOCS within the projective dynamics framework, and avoiding pre-alignment of rotations. The key contributions are a practical pipeline for constructing from time-varying snapshots, improved numerical stability and computational efficiency, and demonstrated realism gains over state-of-the-art methods such as linear blend skinning subspaces. This approach enables faster, more physically faithful interactive simulations in graphics applications, with implementations available on GitHub for real-time use and further exploration.

Abstract

We propose a snapshots-based method to compute reduction subspaces for physics-based simulations. Our method is applicable to any mesh with some artistic prior knowledge of the solution and only requires a record of existing solutions during, for instance, the range-of-motion test that is required before approving a mesh character for an application. Our subspaces span a wider range of motion, especially large deformations, and rotations by default. Compared to the state-of-the-art, we achieve improved numerical stability, computational efficiency, and more realistic simulations with a smaller sub-space.

Paper Structure

This paper contains 9 sections, 5 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Modal Analysis Bases
  4. Sparse and Local Bases
  5. Linear Blend Skinning Bases
  6. Localized Bases
  7. Approach
  8. Method and Implementations
  9. Conclusion

Figures (4)

  • Figure 1: Graphical comparison showcase of full simulations (displayed in green) alongside with reduced models, localized PCA (in blue), SPLOCS (in orange), and LBS (in red). The series includes centered frames from a simulation rendering a "falling bunny."
  • Figure 2: Few local components for a bunny deformed under gravitational forces: POD (blue) and SPLOCS (orange).
  • Figure 3: Comparing relative time required for the global linear system solve at different bases types.
  • Figure 4: Visual and numerical stability comparison between full model and different reduced simulations, at 200 bases.