Engineering with Computers

, Volume 6, Issue 1, pp 17–29

Symbolic analysis of linear polyhedra

  • Carlo Cattani
  • Alberto Paoluzzi

DOI: 10.1007/BF01200201

Cite this article as:
Cattani, C. & Paoluzzi, A. Engineering with Computers (1990) 6: 17. doi:10.1007/BF01200201


This paper concerns several analytical problems related to linear polyhedra in euclidean three-dimensional-space. Symbolic formulas for line, surface, and volume integration are given, and it is shown that domain integrals are computable in polynomial time. In particular, it is shown that mass, first and second moments, and products of inertia are computable inO(E) time, whereE is the number of edges of the boundary. Simple symbolic expressions for the normal derivatives of domain integrals are also derived. In particular, it is shown that they are closely linked to the topology of the integration domain, as well as that they are expressible as combinations of domain integrals over lower-order domains (faces, edges, and vertices). The symbolic results presented in this paper may lead to an easy incorporation of integral constraints, for example, concerning mass and inertia, in the engineering designing process of solid objects.

Copyright information

© Springer-Verlag New York Inc 1990

Authors and Affiliations

  • Carlo Cattani
    • 1
  • Alberto Paoluzzi
    • 2
  1. 1.Dip. di MatematicaUniversità “La Sapienza”RomaItalia
  2. 2.Dip. di Informatica e SistemisticaUniversità “La Sapienza”RomaItalia