Method of trimming PDE surfaces
A method for trimming surfaces generated as solutions to partial differential equations (PDEs) is presented. The work we present here utilises the 2D parameter space on which the trim curves are defined whose projection on the parametrically represented PDE surface is then trimmed out. To do this we...
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| Vydané v: | Computers & graphics Ročník 30; číslo 2; s. 225 - 232 |
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| Jazyk: | English |
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01.04.2006
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| ISSN: | 0097-8493, 1873-7684 |
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| Abstract | A method for trimming surfaces generated as solutions to partial differential equations (PDEs) is presented. The work we present here utilises the 2D parameter space on which the trim curves are defined whose projection on the parametrically represented PDE surface is then trimmed out. To do this we define the trim curves to be a set of boundary conditions which enable us to solve a low order elliptic PDE on the parameter space. The chosen elliptic PDE is solved analytically, even in the case of a very general complex trim, allowing the design process to be carried out interactively in real time. To demonstrate the capability for this technique we discuss a series of examples where trimmed PDE surfaces may be applicable. |
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| AbstractList | A method for trimming surfaces generated as solutions to partial differential equations (PDEs) is presented. The work we present here utilises the 2D parameter space on which the trim curves are defined whose projection on the parametrically represented PDE surface is then trimmed out. To do this we define the trim curves to be a set of boundary conditions which enable us to solve a low order elliptic PDE on the parameter space. The chosen elliptic PDE is solved analytically, even in the case of a very general complex trim, allowing the design process to be carried out interactively in real time. To demonstrate the capability for this technique we discuss a series of examples where trimmed PDE surfaces may be applicable. |
| Author | Ugail, Hassan |
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| CitedBy_id | crossref_primary_10_1016_j_amc_2019_06_025 crossref_primary_10_1111_j_1467_8659_2007_01053_x crossref_primary_10_1517_17425247_2011_633506 |
| Cites_doi | 10.1145/280814.280826 10.1109/MCG.1987.277025 10.1016/0010-4485(90)90043-C 10.1016/0010-4485(95)00060-7 10.1007/BF01840357 10.1016/0010-4485(90)90049-I 10.1016/0167-8396(87)90024-0 10.1145/237748.237751 10.1016/S0167-8396(01)00042-5 10.1016/S0167-8396(99)00033-3 10.1016/S0045-7949(03)00321-3 10.1145/258734.258865 10.1016/j.cad.2004.01.009 10.1016/0167-8396(88)90017-9 10.1145/318009.318078 |
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| Keywords | Numerical algorithms and problems PDE surfaces Laplace equation Modeling Boundary representations Trimming Curve and surface representations |
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| Title | Method of trimming PDE surfaces |
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