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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].

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Metadaten
Author:Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier
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
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