MULTIVARIABLE CURVE INTERPOLATION
MULTIVARIABLE CURVE INTERPOLATION
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DOI：
10.1145/321217.321225
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发表时间：
1964-01-01
影响因子：
2.5
通讯作者：
FERGUSON, J
中科院分区：
文献类型：
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作者：
FERGUSON, J
通过空间中的点阵列来定义光滑表面的问题是众所周知的。提出了几种解决方法。一般来说，这些限制点的集合是在平面矩形网格（X， y平面）上一对一定义的。然后确定一组函数z =F(X，Y)，每个函数代表复合光滑曲面的一个面段。在本文中，这些思想被推广到包括更广泛的允许的点阵列分布：即(1)点的排列（排序）在拓扑上等价于平面矩形网格，(2)得到的解是参数曲面段的光滑复合，即每个曲面块由一个向量（点）值函数表示。这里提出的解决方案很容易适用于各种问题，例如封闭表面体的定义和压力包络面的定义。该技术已成功应用于这些领域和其他领域，如数控铣削、牛顿冲击和边界层。
The problem of defining a smooth surface through an array of points in space is well known. Several methods of solution have been proposed. Generally, these restrict the set of points to be one-to-one defined over a planar rectangular grid (X,Y-plane). Then a set of functionsZ=F(X,Y) is determined, each of which represents a surface segment of the composite smooth surface. In this paper, these ideas are generalized to include a much broader class of permissible point array distributions: namely (1) the point arrangement (ordering) is topologically equivalent to a planar rectangular grid, (2) the resulting solution is a smooth composite of parametric surface segments, i.e. each surface piece is represented by a vector (point)-valued function. The solution here presented is readily applicable to a variety of problems, such as closed surface body definitions and pressure envelope surface definitions. The technique has been used successfully in these areas and others, such as numerical control milling, Newtonian impact and boundary layer.