基于序列闭合轮廓的最优放样B样条曲面插值
Optimal lofted B-spline surface interpolation based on serial closed contours
摘要：
现代形状设计和捕获技术通常导致几何数据以数据点的串行行的形式呈现。一般来说，数据点的数量因行而异。放样或蒙皮B样条曲面插值是一种生成精确通过这些数据点的B样条曲面的技术。传统的B样条曲面生成方法往往会导致曲面控制点数量的大量增加。到目前为止，在减轻这种增加的影响方面所做的许多工作仅限于开放截面曲线。在现有的文献中还没有提到使用插值技术的连续闭合轮廓的放样。本文提出了两种与闭B样条曲线插值有关的新算法。我们推导出了与开B样条插值的Schoenberg-Whitney条件等价的闭B样条插值条件，该条件是参数值和域节点必须满足的条件，以保证系统矩阵总是可逆或满秩的。然后，我们应用插值条件的放样B样条曲面插值问题的连续封闭的轮廓。数值结果和实际实验验证了这些理论的正确性。Github仓库https://github.com/ShutaoTang/LBSI-Project
英文摘要：
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
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