Binary Subdivision Schemes for Functions over Irregular Knot Sequences
Binary Subdivision Schemes for Functions over Irregular Knot Sequences
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不规则结序列函数的二元细分方案
DOI：
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发表时间：
1995
期刊：
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通讯作者：
J. Warren
中科院分区：
文献类型：
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作者：
J. Warren
对于一类广泛的平稳细分方法，我们导出了这些方法产生ck连续极限曲线的充要条件。这些平稳方案包括由不规则间隔结序列的中点细分引起的平稳方案。我们还描述了一种矩阵方法，用于计算与此类平稳方案相关的各种导数方案。x1。细分是创建和表示复杂曲线形状的强大工具。考虑图1中描述的由Chaikin 2引起的过程。一个多边形被转换成一个具有两倍线段的新多边形。对于这个特殊的变换，新多边形的顶点位于旧顶点之间的14和34的距离。重复应用这个过程可以得到一个多边形，它有大量的片段，非常接近光滑的曲线。这条平滑曲线是什么？Riesenfeld[9]表明该曲线为均匀二次b样条，其控制点为原多边形。图1所示。一种细分方法。
For a wide class of stationary subdivision methods, we derive necessary and suucient conditions for these schemes to produce C k continuous limit curves. These stationary schemes include those arising from midpoint subdivision of irregularly-spaced knot sequences. We also describe a matrix method for computing various derivative schemes associated with such stationary schemes. x1. Introduction Subdivision is a powerful tool for creating and representing complex curved shapes. Consider the process due to Chaikin 2] depicted in gure 1. A polygon is transformed into a new polygon with twice as many segments. For this particular transformation, the vertices of the new polygon are placed 1 4 and 3 4 of the way between the old vertices. Applying this process repeatedly yields a polygon with a great number of segments that closely approximate a smooth curve. What is this smooth curve? Riesenfeld 9] shows that the curve is a uniform quadratic B-spline whose control points are the original polygon. Fig. 1. A subdivision method.