The discrete analytical hyperspheres

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