由点和曲线拟合B样条曲面研究

项目名称： 由点和曲线拟合B样条曲面研究

项目编号： No.61202335

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 计算机科学学科

项目作者： 王文珂

作者单位： 中国人民解放军国防科学技术大学

项目金额： 25万元

中文摘要： B样条曲面是CAD系统中曲面表示的基本形式之一。由点和曲线拟合B样条曲面是B样条曲面的重要生成方式，在计算机辅助设计和曲面造型等领域有着广泛的应用。本课题面向CAD系统曲面造型的应用需求，研究由点和曲线拟合B样条曲面的若干关键算法，提出误差可控的B样条曲面蒙皮方法，曲线所在平面不平行时的光滑曲面拟合算法，开闭截面线混合且存在分支情况下的B样条曲面拟合方法，误差可控且数值稳定的由无序B样条曲线拟合曲面的方法，由平面点云拟合多条B样条曲线的高效算法，以及利用切片技术由点云拟合B样条曲面的方法，并将提出算法实现到由点和曲线拟合B样条曲面软件原型系统中，验证所提出方法的有效性和实用性。本课题研究成果可用于提高CAD系统的曲面造型能力，有着重要的理论意义和实际应用价值。

中文关键词： 曲面拟合；曲面蒙皮；B样条曲线；曲线拟合；分支

英文摘要： B-spline surfaces are the base expressions of surfaces in CAD systems. Fitting a B-spline surface from points or curves is one of the most important way for B-spline surface construction, which is widely used in CAGD and surface modeling. This project faces the application requirement, and studies several key algorithms of B-spline surface construction by fitting points and curves. In the project, we try to propose the error bounded algorithm for approximate B-spline surface skinning, smooth surface fitting to unparallel B-spline sectional curves, the branching B-spline surface fitting algorithm for bosh open and close sectional curves whose number for each section may be different, error bounded and numerical stable B-spline surface fitting algorithm to unorganized curves, efficient multiple B-spline curves fitting to planar point cloud. In addition, we will combine the branching B-spline surface fitting algorithm with the B-spline curves fitting algorithm to construct B-spline surfaces from point cloud by slicing. To validate the effectiveness and practicability of our algorithms, we will develop a software system for B-spline surface fitting from points and curves, in which the proposed algorithms will be implemented. The research results will improve the surface modeling ability of the CAD system. Therefore,

英文关键词： Surface fitting；Surface skinning；B-spline curve；Curve fitting；Branching