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LINE SEGMENTS IN THE ISOTROPIC PLANAR STIT TESSELLATION
Advances in Applied Probability
Vol. 45, No. 2 (JUNE 2013), pp. 295-311
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/43563302
Page Count: 17
You can always find the topics here!Topics: Vertices, Tessellations, Density distributions, Mathematical theorems, Line segments, Geometry, Daughter cells, Mathematics, Ergodic theory, Terminology
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This paper presents a powerful characterisation for the structure of internal vertices of the STIT's I-segments. The characterisation allows certain mathematical analyses to be performed easily. We demonstrate this by deriving new results for various topological properties of the tessellation: for example, the numbers of various types of edge and cell side within the typical I-segment. The characterisation also provides a tool for the calculations of metric properties of the tessellation; many new length distributions and frame-coverage results are given.
Advances in Applied Probability © 2013 Applied Probability Trust