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首页> 外文期刊>The International Journal of Advanced Manufacturing Technology >A new approach for lofted B-spline surface interpolation to serial contours
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A new approach for lofted B-spline surface interpolation to serial contours

机译：放样B样条曲面插补到串行轮廓的新方法

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摘要

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional approach to the problem creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion and performs B-spline surface lofting to get a B-spline surface that interpolates them. The approach tends to result in an astonishing number of control points in the lofted B-spline surface. This situation arises mainly from the inevitable process of progressively merging different knot vectors to make the B-spline curves compatible. This paper presents a new approach for fixing this problem. The approach includes a novel process of obtaining a set of compatible B-spline curves from the given contours. The process is based on universal parameterisation [1, 2], allowing the knots to be selected freely but leading to a more stable linear system for B-spline curve interpolation. Since the number of control points in each compatible B-spline curve is equal to the highest number of contour points, the proposed approach can realise efficient data reduction and provide a compact representation of a lofted B-spline surface while keeping the desired surface shape. Some experimental results demonstrate its usefulness and quality.
机译：本文解决了B样条曲面插补到连续轮廓的问题，在该轮廓上点的数量随轮廓的变化而变化。解决该问题的传统方法是通过B样条曲线插值为每个轮廓创建一组B样条曲线，通过度高和结点插入使它们兼容，并执行B样条曲面放样以获得对其进行插值的B样条曲面。该方法往往会导致放样B样条曲面中的控制点数量惊人。这种情况主要是由于不可避免地逐渐合并不同的结向量以使B样条曲线兼容而引起的。本文提出了解决此问题的新方法。该方法包括一种从给定轮廓中获得一组兼容的B样条曲线的新颖过程。该过程基于通用参数设置[1、2]，可以自由选择结，但可以为B样条曲线插值带来更稳定的线性系统。由于每个兼容的B样条曲线中控制点的数量等于轮廓点的最大数量，因此，所提出的方法可以实现有效的数据缩减，并提供放样的B样条曲面的紧凑表示，同时保持所需的曲面形状。一些实验结果证明了其有用性和质量。

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