3D Modelling with <i>C</i>² Continuous PDE Surface Patches

Abstract

In this paper, we present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Then, a vector-valued sixth-order partial differential equation is proposed, and its closed form solution is derived to create PDE surface patches from cross section curves where two adjacent PDE-surface patches are automatically stitched together. With the approach presented in this paper, C2 continuity between adjacent surface patches is well-maintained. Since surface creation of the model is transformed into the generation of cross sectional curves and few undetermined constants are required to describe cross sectional curves accurately, the proposed approach can save manual operations, reduce information storage, and generate 3D models quickly.

Keywords

• 3D modelling
• generalized elliptic curves
• <i>C</i>² continuity
• PDE-based surface generation
• sixth-order PDE
• analytical mathematical expressions