TY - GEN A1 - Hildebrandt, Klaus A1 - Schulz, Christian A1 - von Tycowicz, Christoph A1 - Polthier, Konrad T1 - Interactive Surface Modeling using Modal Analysis N2 - 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]. KW - geometric modeling KW - model reduction KW - geometric optimization Y1 - 2011 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/834 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-8349 ER -