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.
Highlights
IntroductionWe present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves
In this paper, we present a new modelling method to create 3D models
Since all the undetermined constants in the closed form solution are determined by the design variables involved in the analytical mathematical expression of generalized elliptic curves, the proposed partial differential equation (PDE)-based modelling method has the advantage of few design variables
Summary
We present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Models has the advantages of representing complicated polygon models with fewer design variables and automatically achieving required continuity to avoid manual operations to stitch two adjacent surface patches together. Owing to their analytical mathematical expressions, this approach can facilitate other applications such as levels of detail for multi-resolution models and deep learning-based tasks for reducing processing time. Since all the undetermined constants in the closed form solution are determined by the design variables involved in the analytical mathematical expression of generalized elliptic curves, the proposed PDE-based modelling method has the advantage of few design variables. Mathematics 2022, 10, 319 form solution are determined by the design variables involved in the analytical mathematical expression of generalized elliptic curves, the proposed PDE-based modelling method has the advantage of few design variables
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