Open Access
2003-2004 Pseudo-characteristic functions for convex polyhedra.
W. A. Beyer, Stephen L. Judd, Johndale C. Solem
Author Affiliations +
Real Anal. Exchange 29(2): 821-835 (2003-2004).


An algorithm is given for constructing polynomials that determine approximately whether a point $p$ is inside or outside a given polyhedron $C_n$ in Euclidean $n$-dimensional space. The polynomials are of degree $2r$, where $r$ is a positive integer and the order of the approximation can be made arbitrarily small by taking $r$ sufficiently large. For $n=2$, the square, triangle, trapezoid, and pentagon are used as examples. For $n=3$ and $n=4$, the tetrahedron and equilateral simplex are used as examples. We conjecture that the center of mass of the region determined by the approximating polynomial is the same for all values of $r$, and hence coincides with the center of the polyhedra.


Download Citation

W. A. Beyer. Stephen L. Judd. Johndale C. Solem. "Pseudo-characteristic functions for convex polyhedra.." Real Anal. Exchange 29 (2) 821 - 835, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 7 June 2006

zbMATH: 1072.52002
MathSciNet: MR2083817

Primary: 51M15 , 52A20 , 52B11

Keywords: characteristic functions , Convex Polyhedra , Euclidean N-space , psuedo-characteristic functions , simplex

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 2 • 2003-2004
Back to Top