Free-Form Geometric Modeling by Integrating Parametric and Implicit PDEs

• Published in: IEEE transactions on visualization and computer graphics Vol. 13; no. 3; pp. 549 - 561
• Main Authors: Du, Haixia, Qin, Hong
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.05.2007; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Blending; Boundary conditions; Computational modeling; Computer Graphics; Computer Simulation; Deformable models; Deformation; Design engineering; free-form deformation; Geometric modeling; Geometry; Imaging, Three-Dimensional; implicit models; Mathematics; Partial differential equations; PDE techniques; Scalars; Shape; shape blending; Software; Solid modeling; solid models; Solids; Three dimensional; Topology; Two dimensional; Visualization
• ISSN: 1077-2626; 1941-0506
• DOI: 10.1109/TVCG.2007.1004

Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit trivariate PDEs to define geometric solid models containing both geometric information and intensity distribution subject to flexible boundary conditions. The integrated formulation of second-order or fourth-order elliptic PDEs permits designers to manipulate PDE objects of complex geometry and/or arbitrary topology through direct sculpting and free-form modeling. We developed a PDEbased geometric modeling system for shape design and manipulation of PDE objects. The integration of implicit PDEs with parametric geometry offers more general and arbitrary shape blending and free-form modeling for objects with intensity attributes than pure geometric models.