3D Modelling with <i>C</i><sup>2</sup> Continuous PDE Surface Patches
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 crea...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/3/319 |
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| author | Haibin Fu Shaojun Bian Ouwen Li Jon Macey Andres Iglesias Ehtzaz Chaudhry Lihua You Jian Jun Zhang |
| author_facet | Haibin Fu Shaojun Bian Ouwen Li Jon Macey Andres Iglesias Ehtzaz Chaudhry Lihua You Jian Jun Zhang |
| author_sort | Haibin Fu |
| collection | DOAJ |
| description | 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, <i>C</i><sup>2</sup> 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. |
| first_indexed | 2024-03-09T23:32:45Z |
| format | Article |
| id | doaj.art-04dca7eb8a9a4d2ab75a2c1e1c000f48 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:32:45Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-04dca7eb8a9a4d2ab75a2c1e1c000f482023-11-23T17:05:35ZengMDPI AGMathematics2227-73902022-01-0110331910.3390/math100303193D Modelling with <i>C</i><sup>2</sup> Continuous PDE Surface PatchesHaibin Fu0Shaojun Bian1Ouwen Li2Jon Macey3Andres Iglesias4Ehtzaz Chaudhry5Lihua You6Jian Jun Zhang7The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UKThe National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UKThe National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UKThe National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UKDepartment of Applied Mathematics and Computational Sciences, University of Cantabria, 39005 Santander, SpainThe National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UKThe National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UKThe National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UKIn 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, <i>C</i><sup>2</sup> 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.https://www.mdpi.com/2227-7390/10/3/3193D modellinggeneralized elliptic curves<i>C</i><sup>2</sup> continuityPDE-based surface generationsixth-order PDEanalytical mathematical expressions |
| spellingShingle | Haibin Fu Shaojun Bian Ouwen Li Jon Macey Andres Iglesias Ehtzaz Chaudhry Lihua You Jian Jun Zhang 3D Modelling with <i>C</i><sup>2</sup> Continuous PDE Surface Patches Mathematics 3D modelling generalized elliptic curves <i>C</i><sup>2</sup> continuity PDE-based surface generation sixth-order PDE analytical mathematical expressions |
| title | 3D Modelling with <i>C</i><sup>2</sup> Continuous PDE Surface Patches |
| title_full | 3D Modelling with <i>C</i><sup>2</sup> Continuous PDE Surface Patches |
| title_fullStr | 3D Modelling with <i>C</i><sup>2</sup> Continuous PDE Surface Patches |
| title_full_unstemmed | 3D Modelling with <i>C</i><sup>2</sup> Continuous PDE Surface Patches |
| title_short | 3D Modelling with <i>C</i><sup>2</sup> Continuous PDE Surface Patches |
| title_sort | 3d modelling with i c i sup 2 sup continuous pde surface patches |
| topic | 3D modelling generalized elliptic curves <i>C</i><sup>2</sup> continuity PDE-based surface generation sixth-order PDE analytical mathematical expressions |
| url | https://www.mdpi.com/2227-7390/10/3/319 |
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