Shape Morphing of Complex Geometries Using Partial Differential Equations
Shape Morphing of Complex Geometries Using Partial Differential Equations
复制标题
使用偏微分方程的复杂几何形状变形
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
H. Ugail
中科院分区：
文献类型：
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作者：
G. G. Castro;H. Ugail
在整个这项工作中，使用偏微分方程的表面生成方法的形状变形的另一种技术。边界值的性质，这是固有的表面生成技术连同其数学性质，在此利用创建初始形状和最终形状之间的中间形状。本文提出了四种变形技术。第一个是基于使用与初始和最终表面相关联的边界条件的线性组合，第二个包括改变傅立叶模式，其中PDE被解决，而第三个结果从前两个的组合。第四种方法是基于对曲面的脊的操作，它是作为解的副产品计算的。给出了两个拓扑不等价曲面之间的变形序列的结果。因此，它表明，基于偏微分方程的变形方法是能够获得光滑的中间表面自动在大多数的方法在这项工作中，脊柱已被揭示为一个强大的工具，变形表面所产生的方法在这里提出。
An alternative technique for shape morphing using a surface generating method using partial differential equations is outlined throughout this work. The boundaryvalue nature that is inherent to this surface generation technique together with its mathematical properties are hereby exploited for creating intermediate shapes between an initial shape and a final one. Four alternative shape morphing techniques are proposed here. The first one is based on the use of a linear combination of the boundary conditions associated with the initial and final surfaces, the second one consists of varying the Fourier mode for which the PDE is solved whilst the third results from a combination of the first two. The fourth of these alternatives is based on the manipulation of the spine of the surfaces, which is computed as a by-product of the solution. Results of morphing sequences between two topologically nonequivalent surfaces are presented. Thus, it is shown that the PDE based approach for morphing is capable of obtaining smooth intermediate surfaces automatically in most of the methodologies presented in this work and the spine has been revealed as a powerful tool for morphing surfaces arising from the method proposed here.