Interactive Surface Modeling using Modal Analysis
Please always quote using this URN:urn:nbn:de:0296-matheon-8349
- We propose a framework for deformation-based surface modeling that is interactive, robust and intuitive to use. The deformations are described by a non-linear optimization problem that models static states of elastic shapes under external forces which implement the user input. Interactive response is achieved by a combination of model reduction, a robust energy approximation, and an efficient quasi-Newton solver. Motivated by the observation that a typical modeling session requires only a fraction of the full shape space of the underlying model, we use second and third derivatives of a deformation energy to construct a low-dimensional shape space that forms the feasible set for the optimization. Based on mesh coarsening, we propose an energy approximation scheme with adjustable approximation quality. The quasi-Newton solver guarantees superlinear convergence without the need of costly Hessian evaluations during modeling. We demonstrate the effectiveness of the approach on different examples including the test suite introduced in [Botsch and Sorkine 2008].
Author: | Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier |
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URN: | urn:nbn:de:0296-matheon-8349 |
Referee: | John M. Sullivan |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2011/12/11 |
Release Date: | 2011/12/11 |
Tag: | |
Institute: | Freie Universität Berlin |
MSC-Classification: | 68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section {04 in that areag 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) / 68Uxx Computing methodologies and applications / 68U05 Computer graphics; computational geometry [See also 65D18] |
Preprint Number: | 828 |