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The Discrete Analytical Hyperspheres
January-March 1997 (vol. 3 no. 1)
pp. 75-86
ASCII Text
x 
 
Eric Andres, Marie-Andrée Jacob, "The Discrete Analytical Hyperspheres," IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 1, pp. 75-86, January-March, 1997.
 
 
BibTex
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@article{ 10.1109/2945.582354,
author = {Eric Andres and Marie-Andrée Jacob},
title = {The Discrete Analytical Hyperspheres},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {3},
number = {1},
issn = {1077-2626},
year = {1997},
pages = {75-86},
doi = {http://doi.ieeecomputersociety.org/10.1109/2945.582354},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - The Discrete Analytical Hyperspheres
IS - 1
SN - 1077-2626
SP75
EP86
EPD - 75-86
A1 - Eric Andres,
A1 - Marie-Andrée Jacob,
PY - 1997
KW - Circle
KW - sphere
KW - hypersphere
KW - raster
KW - arbitrary dimension
KW - nonlattice center
KW - noninteger radius
KW - discrete analytical definition.
VL - 3
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 

Abstract—An analytical definition of a discrete hypersphere with arbitrary center, radius, and thickness in dimension n is introduced. The new discrete hypersphere is called discrete analytical hypersphere. The hypersphere has important original properties including exact point localization, space tiling, k-separation, etc. These properties are almost obvious with this new discrete analytical definition contrary to the classical approaches based on digitization schemes. The analytically defined circle is compared to Pham's classically defined circle. Efficient incremental circle and hypersphere generation algorithms are provided.

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Index Terms:
Circle, sphere, hypersphere, raster, arbitrary dimension, nonlattice center, noninteger radius, discrete analytical definition.
Citation:
Eric Andres, Marie-Andrée Jacob, "The Discrete Analytical Hyperspheres," IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 1, pp. 75-86, Jan.-March 1997, doi:10.1109/2945.582354
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