Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-dimensional alpha shapes   Frequently, data in scientific computing is in its abstract form a finite
point set in space, and it is sometimes useful or required to compute what one
might call the ``shape'' of the set. For that purpose, this paper introduces
the formal notion of the family of $\alpha$-shapes of a finite point set in
$\Real^3$. Each shape is a well-defined polytope, derived from the Delaunay
triangulation of the point set, with a parameter $\alpha \in \Real$ controlling
the desired level of detail. An algorithm is presented that constructs the
entire family of shapes for a given set of size $n$ in time $O(n^2)$, worst
case. A robust implementation of the algorithm is discussed and several
applications in the area of scientific computing are mentioned.

28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn