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- W1970244902 abstract "We formulate and give partial answers to several combinatorial problems on four-tuples of n points in three-space. (i) The number of minimum (nonzero) volume tetrahedra spanned by n points in R3 is Θ(n3). (ii) The number of unit-volume tetrahedra determined by n points in R3 is O(n7/2), and there are point sets for which this number is ω(n3 log log n). (iii) The tetrahedra determined by n points in R3, not all on a plane, have at least ω(n) distinct volumes, and there are point sets for which this number is O(n); this gives a first partial answer for the three-dimensional case to an old question of Erdos, Purdy, and Straus. We also give an O(n3) time algorithm for reporting all tetrahedra of minimum nonzero volume, and thereby extend an early algorithm of Edelsbrunner, O'Rourke, and Seidel." @default.
- W1970244902 created "2016-06-24" @default.
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- W1970244902 date "2007-01-07" @default.
- W1970244902 modified "2023-09-23" @default.
- W1970244902 title "On the number of tetrahedra with minimum, unit, and distinct volumes in three-space" @default.
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- W1970244902 doi "https://doi.org/10.5555/1283383.1283503" @default.
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