3 research outputs found
Animation of deformable bodies with quadratic bézier finite elements
pre-printIn this article, we investigate the use of quadratic finite elements for graphical animation of deformable bodies.We consider both integrating quadratic elements with conventional linear elements to achieve a computationally efficient adaptive-degree simulation framework as well as wholly quadratic elements for the simulation of nonlinear rest shapes. In both cases, we adopt the B´ezier basis functions and employ a co-rotational linear strain formulation. As with linear elements, the co-rotational formulation allows us to precompute per-element stiffness matrices, resulting in substantial computational savings. We present several examples that demonstrate the advantages of quadratic elements in general and our adaptive-degree system in particular. Furthermore, we demonstrate, for the first time in computer graphics, animations of volumetric deformable bodies with nonlinear rest shapes
MINVO Basis: Finding Simplexes with Minimum Volume Enclosing Polynomial Curves
This paper studies the problem of finding the smallest -simplex enclosing
a given -degree polynomial curve. Although the Bernstein and
B-Spline polynomial bases provide feasible solutions to this problem, the
simplexes obtained by these bases are not the smallest possible, which leads to
undesirably conservative results in many applications. We first prove that the
polynomial basis that solves this problem (MINVO basis) also solves for the
-degree polynomial curve with largest convex hull enclosed in a
given -simplex. Then, we present a formulation that is \emph{independent} of
the -simplex or -degree polynomial curve given. By using
Sum-Of-Squares (SOS) programming, branch and bound, and moment relaxations, we
obtain high-quality feasible solutions for any and prove
numerical global optimality for . The results obtained for show
that, for any given -degree polynomial curve, the MINVO basis is
able to obtain an enclosing simplex whose volume is and times
smaller than the ones obtained by the Bernstein and B-Spline bases,
respectively. When , these ratios increase to and
, respectively.Comment: 25 pages, 16 figure