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Example‐Based Materials in Laplace–Beltrami Shape Space
Author(s) -
Zhu Fei,
Li Sheng,
Wang Guoping
Publication year - 2015
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12457
Subject(s) - eigenfunction , topology (electrical circuits) , invariant (physics) , computer science , energy minimization , metric (unit) , dimension (graph theory) , mathematics , geometry , pure mathematics , physics , economics , mathematical physics , eigenvalues and eigenvectors , operations management , quantum mechanics , combinatorics
We present a novel method for flexible and efficient simulation of example‐based elastic deformation. The geometry of all input shapes is projected into a common shape space spanned by the Laplace–Beltrami eigenfunctions. The eigenfunctions are coupled to be compatible across shapes. Shape representation in the common shape space is scale‐invariant and topology‐independent. The limitation of previous example‐based approaches is circumvented that all examples must have identical topology with the simulated object. Additionally, our method allows examples that are arbitrary in size, similar but not identical in shape with the object. We interpolate the examples via a weighted‐energy minimization to find the target configuration that guides the object to desired deformation. Large deformation between examples is handled by a physically plausible energy metric. This optimization is efficient as the eigenfunctions are pre‐computed and the problem dimension is small. We demonstrate the benefits of our approach with animation results and performance analysis.