On the Approximation Theory of Linear Variational Subspace Design

TL;DR

This paper introduces a method for automatically designing linear variational subspaces for large-scale constrained quadratic programming, enabling scalable and automated model reduction in real-time graphics applications.

Contribution

It proposes a novel automatic subspace design technique with theoretical error bounds, eliminating the need for manual handcrafted subspaces.

Findings

Effective in interactive deformable modeling

Provides meaningful approximation error bounds

Demonstrates empirical success in real-time applications

Abstract

Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often requires a handcrafted subspace that spans a domain that hypothetically embodies desirable solutions. For many applications, obtaining such subspaces case-by-case either is impossible or requires extensive human labors, hence does not readily have a scalable solution for growing number of tasks. We propose linear variational subspace design for large-scale constrained quadratic programming, which can be computed automatically without any human interventions. We provide meaningful approximation error bound that substantiates the quality of calculated subspace, and demonstrate its empirical success in interactive deformable modeling for triangular and tetrahedral meshes.