PDE-based Geometric Modeling and Interactive Sculpting for Graphics

Date: June 04, 2004 Time: (All day)
Event Type: Lecture

Partial differential equations (PDEs) are widely used in Computer Graphics fields to model geometric objects, simulate natural phenomena, formulate physical laws, etc. To make full use of the advantages of PDE techniques for geometric modeling, we present a PDE-based modeling system for geometric and physics-based modeling including shape design and direct sculpting, object reconstruction, shape blending, data recovery, free-form deformation, and medial axis or skeleton extraction and manipulation. The PDE modeling system employs two types of PDEs, elliptic PDEs defining static geometric objects through boundary constraints, and parabolic PDEs modeling dynamic objects via initial value conditions. The functionalities of the elliptic PDE model include 2D and 3D physics-based parametric shape design and sculpting, interactive modeling for arbitrary polygonal meshes, object reconstruction from arbitrary sketches or unorganized scattered data, shape blending and direct manipulation of implicit PDE objects of arbitrary topology, and free-form solid modeling and deformation with intensity and physical properties. The parabolic PDEs are used for diffusion-based medial axis extraction of geometric objects bounded by arbitrary polygonal meshes, skeleton-based shape sculpting and recovery through front propagation. We provide a set of comprehensive shape modeling functionalities such as design, reconstruction, manipulation, blending, deformation, as well as simplification in a single PDE framework towards realizing the full potential of PDE techniques as modeling and simulating tools in computer graphics.