Dynamic modeling of butterfly subdivision surfaces

摘要

The authors develop integrated techniques that unify physics basednmodeling with geometric subdivision methodology and present a scheme forndynamic manipulation of the smooth limit surface generated by then(modified) butterfly scheme using physics based “force”ntools. This procedure based surface model obtained through butterflynsubdivision does not have a closed form analytic formulation (unlikenother well known spline based models), and hence poses challengingnproblems to incorporate mass and damping distributions, internalndeformation energy, forces, and other physical quantities required tondevelop a physics based model. Our primary contributions to computerngraphics and geometric modeling include: (1) a new hierarchicalnformulation for locally parameterizing the butterfly subdivision surfacenover its initial control polyhedron, (2) formulation of dynamicnbutterfly subdivision surface as a set of novel finite elements, and (3)napproximation of this new type of finite elements by a collection ofnexisting finite elements subject to implicit geometric constraints. Ournnew physics based model can be sculpted directly by applying synthesizednforces and its equilibrium is characterized by the minimum of andeformation energy subject to the imposed constraints. We demonstratenthat this novel dynamic framework not only provides a direct and naturalnmeans of manipulating geometric shapes, but also facilitatesnhierarchical shape and nonrigid motion estimation from large range andnvolumetric data sets using very few degrees of freedom (control verticesnthat define the initial polyhedron)