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Computers and Graphics
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Recent developments in analyzing molecular structures and representing solid models using simplicial complexes have further enhanced the need for computing structural information about simplicial complexes in R3. This paper develops basic techniques required to manipulate and analyze structures of complexes in R3.A new approach to analyze simplicial complexes in Euclidean 3-space R3 is described. First, methods from topology are used to analyze triangulated 3-manifolds in R3. Then, it is shown that these methods can, in fact, be applied to arbitrary simplicial complexes in R3 after (simulating) the process of thickening a complex to a 3-manifold homotopic to it. As a consequence considerable structural information about the complex can be determined and certain discrete problems solved as well. For example, it is shown how to determine homology groups, as well as concrete representations of their generators, for a given complex in R3