Stable Inverse Dynamic Curves

Alexandre Derouet-Jourdan, Florence Bertails-Descoubes, JoŽlle Thollot
ACM Transactions on Graphics, December 2010 (Proceedings of the ACM SIGGRAPH Asia 2010 Conference)

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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Artistic contribution: Gibule's character was created by Laurence Boissieux (INRIA).