Elsevier

Information Sciences

Volume 50, Issue 1, February 1990, Pages 73-91
Information Sciences

Hyperspheres in digital geometry

https://doi.org/10.1016/0020-0255(90)90005-UGet rights and content

Abstract

An analysis of volumes and surface areas of hyperspheres defined by m-neighbor distance is carried out for n-dimensional grid-point space. Closed-form expressions for volumes and surface areas are derived. Analogous to Euclidean geometry, these expressions are found to be polynomials of degree n and n−1 respectively. Like the underlying m-neighbor distance, these measures are also shown to be order-preserving. An efficient algorithm for obtaining the coefficients of volume and surface polynomials has been presented. The utility of these measures as indices of digital approximations of Euclidean space is discussed.

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