Improving the Shape of Surfaces by Perturbation

几何建模在制造业或工业中的许多应用 可视化需要切平面连续表面， 内插数据。 虽然存在许多算法， 局部的解析光滑度，生成的曲面通常具有 与（非光滑）相比， 分段线性曲面 这些特征是拐点， 曲率的变化、数据点之间的凸起等。 这些“形状缺陷”对人体的功能和美学影响 建模对象可能很严重。 该项目将查明来源， 特殊表面结构和设计特征的性质 用于系统地修改数据和/或底层表面的算法 为了减少或去除特征，可以使用表示法。 在 特别是，研究将建立在一些经验的基础上， 算法，并将调查和量化的影响： 1.在面片边界上连续性约束的更改， 特别是，重新参数化的选择; 2）扰动的 数据点和法线的位置; 3）表示的变化 的补丁;特别是，从一个多项式到一个 有理表示; 4）邻域的扰动 数据之间的关系，例如通过删除或插入重新划分网格 边界

Many applications of geometric modeling in manufacturing or for visualization require tangent plane continuous surfaces to interpolate data. While a number of algorithms exist that guarantee local, analytic smoothness, the resulting surfaces often have undesirable extraneous features when compared to a (nonsmooth) piecewise linear surface. Such features are inflection, sharp changes of curvature, bulging between the data sites, etc. The functional and aesthetic implications of these 'shape defects' on the modeled object can be severe. This project will pinpoint sources and nature of the features for specific surface constructions and devise algorithms to systematically modify data and/or the underlying surface representation in order to reduce or remove the features. In particular, the research will build on the experience with a number of algorithms and will investigate and quantify the effects of: 1. a change of continuity constraints across patch boundaries, in particular, the choice of reparametrization; 2) a perturbation of the location of data sites and normals; 3) a change of the representation of the patches; in particular, changing from a polynomial to a rational representation; 4) a perturbation of the neighborhood relations between the data, such as remeshing by removing or inserting boundaries.