Solid modelling based on sixth order partial differential equations
Although solid modelling based on partial differential equations (PDEs) has many advantages, such existing methods can either only deal with simple cases or incur expensive computational overheads. To overcome these shortcomings, in this paper we present an efficient PDE based approach to creating a...
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| Published in | Computer aided design Vol. 43; no. 6; pp. 720 - 729 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.06.2011
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0010-4485 1879-2685 |
| DOI | 10.1016/j.cad.2011.01.021 |
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| Abstract | Although solid modelling based on partial differential equations (PDEs) has many advantages, such existing methods can either only deal with simple cases or incur expensive computational overheads. To overcome these shortcomings, in this paper we present an efficient PDE based approach to creating and manipulating solid models. With trivariate partial differential equations, the idea is to formulate an accurate closed form solution to the PDEs subject to various complex boundary constraints. The analytical nature of this solution ensures both high computational efficiency and modelling flexibility. In addition, we will also discuss how different geometric shapes can be produced by making use of controls incorporated in the PDEs and the boundary constraint equations, including the surface functions, tangents and curvature in the boundary constraints, the shape control parameters and the sculpting forces. Two examples are included to demonstrate the applications of the proposed approach and solutions.
► This paper presents a solid modelling method based on sixth order partial differential equations. ► Closed form solution is developed to raise modelling efficiency. ► General boundary constraints and sculpting forces are considered to improve modelling capacity. ► Complicated solid models are created from solid chunks based on partial differential equation. ► The created solid models are effectively manipulated by changing design parameters in partial differential equations and boundary constraints. |
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| AbstractList | Although solid modelling based on partial differential equations (PDEs) has many advantages, such existing methods can either only deal with simple cases or incur expensive computational overheads. To overcome these shortcomings, in this paper we present an efficient PDE based approach to creating and manipulating solid models. With trivariate partial differential equations, the idea is to formulate an accurate closed form solution to the PDEs subject to various complex boundary constraints. The analytical nature of this solution ensures both high computational efficiency and modelling flexibility. In addition, we will also discuss how different geometric shapes can be produced by making use of controls incorporated in the PDEs and the boundary constraint equations, including the surface functions, tangents and curvature in the boundary constraints, the shape control parameters and the sculpting forces. Two examples are included to demonstrate the applications of the proposed approach and solutions.
► This paper presents a solid modelling method based on sixth order partial differential equations. ► Closed form solution is developed to raise modelling efficiency. ► General boundary constraints and sculpting forces are considered to improve modelling capacity. ► Complicated solid models are created from solid chunks based on partial differential equation. ► The created solid models are effectively manipulated by changing design parameters in partial differential equations and boundary constraints. |
| Author | Zhang, Jian J. Chang, J. You, L.H. Yang, X.S. |
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| CitedBy_id | crossref_primary_10_1007_s11042_022_13297_x crossref_primary_10_1016_j_cam_2021_113680 crossref_primary_10_1007_s00371_012_0693_0 crossref_primary_10_1007_s00371_014_0950_5 crossref_primary_10_29121_shodhkosh_v2_i2_2021_3654 crossref_primary_10_1016_j_gmod_2015_05_002 crossref_primary_10_1016_j_jmaa_2024_129163 crossref_primary_10_1016_j_enganabound_2023_04_012 crossref_primary_10_1007_s11042_020_09060_9 |
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| Keywords | Shape manipulation Solid modelling Closed form solution Sixth order partial differential equations |
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| Title | Solid modelling based on sixth order partial differential equations |
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