Improving the Shape of Surfaces by Perturbation

通过扰动改善表面形状

• 批准号: 9211322
• 负责人: jorg peters
• 金额: $ 1.46万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-15 至 1992-08-17
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9211322&HistoricalAwards=false
• 关键词: Improving; Shape; Surfaces; Perturbation

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.

制造或可视化中几何建模的许多应用都需要切平面连续曲面来插值数据。 虽然存在许多保证局部解析平滑度的算法，但与（非平滑）分段线性表面相比，所得表面通常具有不需要的无关特征。 这些特征包括拐点、曲率的急剧变化、数据点之间的凸出等。这些“形状缺陷”对建模对象的功能和美学影响可能是严重的。 该项目将查明特定表面结构特征的来源和性质，并设计算法来系统地修改数据和/或底层表面表示，以减少或删除这些特征。 特别是，该研究将建立在许多算法的经验基础上，并将调查和量化以下效果： 1. 跨补丁边界的连续性约束的变化，特别是重新参数化的选择； 2) 数据站点位置和法线的扰动； 3）改变补丁的表示；特别是从多项式变为有理式表示； 4) 数据之间邻域关系的扰动，例如通过删除或插入边界来重新划分网格。