Best approximate circles on integer grids
ACM Transactions on Graphics (TOG)
Efficient algorithms for 3D scan-conversion of parametric curves, surfaces, and volumes
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Graphics gems
Digital circles with non-lattice point centers
The Visual Computer: International Journal of Computer Graphics
Fundamentals of surface voxelization
Graphical Models and Image Processing
3D scan-conversion algorithms for voxel-based graphics
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
A linear algorithm for incremental digital display of circular arcs
Communications of the ACM
Medical Imaging: Computer-Assisted Surgery
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Computer-Aided Simulation for Bone Surgery
IEEE Computer Graphics and Applications
Theoretical Computer Science
Graceful Planes and Thin Tunnel-Free Meshes
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Discrete linear objects in dimension n: the standard model
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
The supercover of an m-flat is a discrete analytical object
Theoretical Computer Science
Real Polygonal Covers of Digital Discs - Some Theories and Experiments
Fundamenta Informaticae
A low-complexity discrete radiosity method
Computers and Graphics
Digital Circularity and Its Applications
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Euclidean eccentricity transform by discrete arc paving
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Minimal offsets that guarantee maximal or minimal connectivity of digital curves in nD
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Matching 2D and 3D articulated shapes using the eccentricity transform
Computer Vision and Image Understanding
Introduction to digital level layers
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Analytical description of digital circles
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Optimal consensus set for annulus fitting
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Determining Digital Circularity Using Integer Intervals
Journal of Mathematical Imaging and Vision
Arithmetic discrete hyperspheres and separatingness
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Connectedness of offset digitizations in higher dimensions
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
Real Polygonal Covers of Digital Discs - Some Theories and Experiments
Fundamenta Informaticae
O(n 3logn) time complexity for the optimal consensus set computation for 4-Connected Digital Circles
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Efficient robust digital annulus fitting with bounded error
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Topological relations between separating circles
Discrete Applied Mathematics
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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.