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3D Modelling with C2 Continuous PDE Surface Patches

Authors: Haibin Fu; Shaojun Bian; Ouwen Li; Jon Macey; Andres Iglesias; Ehtzaz Chaudhry; Lihua You; +1 Authors

3D Modelling with C2 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.

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Spain
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Keywords

analytical mathematical expressions, Sixth-order PDE, Generalized elliptic curves, PDE-based surface generation, generalized elliptic curves, <i>C</i><sup>2</sup> continuity, Analytical mathematical expressions, 3D modelling, C2 continuity, QA1-939, sixth-order PDE, 3D modelling; generalized elliptic curves; <i>C</i><sup>2</sup> continuity; PDE-based surface generation; sixth-order PDE; analytical mathematical expressions, Mathematics

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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