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Stable Inverse Dynamic Curves

Alexandre Derouet-Jourdan 1, 2, * Florence Bertails-Descoubes 1, * Joëlle Thollot 2
* Corresponding author
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
2 ARTIS - Acquisition, representation and transformations for image synthesis
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : 2d animation is a traditional but fascinating domain that has recently regained popularity both in animated movies and video games. This paper introduces a method for automatically converting a smooth sketched curve into a 2d dynamic curve at stable equilibrium under gravity. The curve can then be physically animated to produce secondary motions in 2d animations or simple video games. Our approach proceeds in two steps. We first present a new technique to fit a smooth piecewise circular arcs curve to a sketched curve. Then we show how to compute the physical parameters of a dynamic rod model (super-circle) so that its stable rest shape under gravity exactly matches the fitted circular arcs curve. We demonstrate the interactivity and controllability of our approach on various examples where a user can intuitively setup efficient and precise 2d animations by specifying the input geometry.
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Alexandre Derouet-Jourdan, Florence Bertails-Descoubes, Joëlle Thollot. Stable Inverse Dynamic Curves. ACM Transactions on Graphics, Association for Computing Machinery, 2010, 29 (6), pp.137-137:9. ⟨10.1145/1866158.1866159⟩. ⟨inria-00518204⟩

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