APPROXIMATING SMOOTH THICKNESS
APPROXIMATING SMOOTH THICKNESS
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近似平滑厚度
DOI：
10.1142/s0218216500000062
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发表时间：
2000
影响因子：
0.5
通讯作者：
E. Rawdon
中科院分区：
文献类型：
--
作者：
E. Rawdon
结的粗细是可以用来打结的最粗绳子的半径。确定了厚度的基本性质。然而，除了少数结节构象外，很难计算所有构象的厚度。因此，需要一个连续的多边形厚度函数来逼近它的光滑模拟。最自然的定义在平面圆上会产生不正确的估计。文中定义了一个多边形厚度函数，并用初等内切算法证明了该函数是连续的，并且正确地逼近了光滑厚度。文中还给出了厚度估算实例。
The thickness of a knot is the radius of the thickest rope with which the knot could be tied. Basic properties of thickness have been established. However, thickness is difficult to compute for all but a few knot conformations. Thus, a continuous polygonal thickness function is needed to approximate its smooth analogue. The most natural definition yields incorrect estimates on a planar circle. Here, a polygonal thickness function is defined and shown to be continuous and to correctly approximate smooth thickness with an elementary inscribing algorithm. Examples of thickness estimations are also given.