3D Modelling with C 2 Continuous PDE Surface Patches

Haibin Fu, Shaojun Bian, Ouwen Li, Jon Macey, Andres Iglesias, Ehtzaz Chaudhry, Lihua You and Jian Jun Zhang
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Haibin Fu: The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UK
Shaojun Bian: The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UK
Ouwen Li: The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UK
Jon Macey: The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UK
Andres Iglesias: Department of Applied Mathematics and Computational Sciences, University of Cantabria, 39005 Santander, Spain
Ehtzaz Chaudhry: The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UK
Lihua You: The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UK
Jian Jun Zhang: The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UK

Mathematics, 2022, vol. 10, issue 3, 1-20

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, C 2 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; C 2 continuity; PDE-based surface generation; sixth-order PDE; analytical mathematical expressions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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