An analytical definition of a discrete hypersphere with arbitrary center, radius, and thickness in dimension n is introduced. The new discrete hypersphere is called a 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 (1992) classically defined circle. Efficient incremental circle and hypersphere generation algorithms are provided.
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