Proofs of two Theorems concerning Sparse Spacetime Constraints

TL;DR

This paper provides formal proofs for two theorems related to the use of sparse spacetime constraints in animating deformable objects, enhancing the theoretical foundation of the approach introduced in a prior SIGGRAPH publication.

Contribution

It offers rigorous mathematical proofs for key theorems underpinning sparse spacetime constraints in deformable object animation, strengthening the theoretical basis of the original method.

Findings

Theorems are formally proven, validating the approach.

Mathematical foundation for sparse spacetime constraints is established.

Supports the original method with rigorous proofs.

Abstract

In the SIGGRAPH 2014 paper [SvTSH14] an approach for animating deformable objects using sparse spacetime constraints is introduced. This report contains the proofs of two theorems presented in the paper.