ISSN:
1573-7683
Keywords:
support hyperplane data
;
data consistency criteria
;
computational geometry
;
set reconstruction
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Support functions and samples of convex bodies in R n are studied with regard to conditions for their validity or consistency. Necessary and sufficient conditions for a function to be a support function are reviewed in a general setting. An apparently little known classical such result for the planar case due to Rademacher and based on a determinantal inequality is presented and a generalization to arbitrary dimensions is developed. These conditions are global in the sense that they involve values of the support function at widely separated points. The corresponding discrete problem of determining the validity of a set of samples of a support function is treated. Conditions similar to the continuous inequality results are given for the consistency of a set of discrete support observations. These conditions are in terms of a series of local inequality tests involving only neighboring support samples. Our results serve to generalize existing planar conditions to arbitrary dimensions by providing a generalization of the notion of nearest neighbor for plane vectors which utilizes a simple positive cone condition on the respective support sample normals.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00119842
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