Incremental Deformation Subspace Reconstruction. (27th October 2016)

• Record Type: Journal Article
• Authors: Mukherjee, R.; Wu, X.; Wang, H.
• Is Part Of: Computer graphics forum. Volume 35:Number 7(2016)
• Page Start: 169
• Page End: 178
• Publication Date: 2016-10-27
• Subjects: Categories and Subject Descriptors (according to ACM CCS) -- I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism—Animation; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.13014
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract: Recalculating the subspace basis of a deformable body is a mandatory procedure for subspace simulation, after the body gets modified by interactive applications. However, using linear modal analysis to calculate the basis from scratch is known to be computationally expensive. In the paper, we show that the subspace of a modified body can be efficiently obtained from the subspace of its original version, if mesh changes are small. Our basic idea is to approximate the stiffness matrix by its low‐frequency component, so we can calculate new linear deformation modes by solving an incremental eigenvalue decomposition problem. To further handle nonlinear deformations in the subspace, we present a hybrid approach to calculate modal derivatives from both new and original linear modes. Finally, we demonstrate that the cubature samples trained for the original mesh can be reused in fast reduced force and stiffness matrix evaluation, and we explore the use of our techniques in various simulation problems. Our experiment shows that the updated subspace basis still allows a simulator to generate visual plausible deformation effects. The whole system is efficient and it is compatible with other subspace construction approaches.