点集曲面的偏差控制及尖锐特征构造

Point set surfaces (PSSs) have attracted more and more attentions in areas such as computer graphics, CAD/CAM, and so on because their data structures are simple, they are easy to be obtained, be plotted, and represent objects with complex topologies. But current PSSs can not effectively reduce influences of noises in input points, while keep the accuracy of the surface construction and be adaptive for small or sharp features at the same time. This research intends to define PSSs based on energy fields, search for inherent relationships between deviations of PSSs and energy functions or weighting functions, develop algorithms of PSS projection and deviation control, obtain curvature formulas of PSSs, and construct PSSs with sharp features. The project will improve the accuracy of the surface construction, the robust to noises, and the ability to represent sharp features of PSSs, and provide theory bases and technology supports for better application of PSSs in digital manufacturing.

点集曲面具有数据结构简单、易于获取、便于绘制、易表示复杂拓扑物体等优点，因而在计算机图形学、CAD、CAM等领域受到越来越多的关注。但现有的点集曲面无法在有效减弱输入点中噪声影响的同时，保证曲面的构造精度和对细小、尖锐等特征的较好适应性。本研究旨在建立基于能量场的点集曲面表示形式，探索能量函数或权值函数与点集曲面偏差的内在联系，开发点集曲面投影算法和偏差控制算法，获取基于点集曲面的曲率计算公式，构造带尖锐特征的点集曲面。本项目将提高点集曲面的构造精度、对噪声的鲁棒性及对尖锐特征的表示能力，为点集曲面更好地应用到数字制造中提供理论基础和技术支撑。

点集曲面具有数据结构简单、易于获取、便于绘制、易表示复杂拓扑物体等优点，因而在计算机图形学、CAD、CAM等领域受到越来越多的关注。但现有的点集曲面无法在有效减弱输入点中噪声影响的同时，保证曲面的构造精度和对细小、尖锐等特征的较好适应性。本项目定义基于能量函数和向量场的点集曲面表示形式，提出基于稳健估计和曲面定向的散乱点分割方法，构造了集成数据分割的点集曲面，提高了点集曲面的构造精度、对噪声的鲁棒性及对细小特征的表示能力，为点集曲面在数字制造中的应用提供了理论基础和技术支持。