论文标题
基于串行封闭轮廓
Optimal lofted B-spline surface interpolation based on serial closed contours
论文作者
论文摘要
现代形状的设计和捕获技术通常会导致以数据点串行行的形式显示的几何数据。通常，数据点的数量因行而异。抬高或皮肤的B-Spline表面插值是一种生成B-Spline表面，可以精确地通过这些数据点。传统过程通常会导致所得的B频表面的控制点的数量大大增加。迄今为止，减轻这种增加的影响的大部分工作都限于开放式弯曲。在现有文献中尚未解决使用插值技术的顺序闭合轮廓的倾斜。在本文中，我们提出了与封闭的B-Spline曲线插值有关的两个新型猜想。我们为开放的B-Spline插值提供了良好成熟的Schoenberg-Whitney条件的等效闭合B-SPLINE插值条件，该条件应满足参数值和域结的满足，以确保系统矩阵总是可倒变的或全级别的。然后，我们将插值条件应用于较高的B-Spline表面插值问题，以串行封闭情况。这些猜想的正确性通过数值结果和几个实际实验验证。 github存储库https://github.com/shutaotang/lbsi-project
Modern shape design and capture techniques often lead to the geometric data presented in the form of serial rows of data points. In general, the number of data points varies from row to row. Lofted or skinned B-spline surface interpolation is a technique that generates a B-spline surface that passes through these data points precisely. The traditional process often causes a large increase in the number of control points of the resulting B-spline surface. Much of the work to date in mitigating the effects of this increase has been restricted to open section-curves. The lofting of sequential closed contours using the interpolation technique has not been addressed in the existing literature. In this paper, we present two novel conjectures relating to closed B-spline curve interpolation. We derive the equivalent closed B-spline interpolation condition of the well-established Schoenberg-Whitney condition for open B-spline interpolation, a condition that the parameter values and the domain knots should satisfy to guarantee the system matrix is always invertible or full-rank. We then apply the interpolation condition to the problem of lofted B-spline surface interpolation to serial closed contours. The correctness of these conjectures is validated via numerical results and several practical experiments. Github repository https://github.com/ShutaoTang/LBSI-Project
