Computational geometry: an introduction
Computational geometry: an introduction
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Digital plane and grid point segments
Computer Vision, Graphics, and Image Processing
On the recognition of digital planes in three-dimensional space
Pattern Recognition Letters
A parametrization of digital planes by least-squares fits and generalizations
Graphical Models and Image Processing
Discrete analytical hyperplanes
Graphical Models and Image Processing
Combinatorics of patterns of a bidimensional Sturmian sequence.
Theoretical Computer Science
3D scan-conversion algorithms for voxel-based graphics
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Double sequences with complexity mn+11
Automatica (Journal of IFAC)
Thin discrete triangular meshes
Theoretical Computer Science
Palindromes and two-dimensional sturmian sequences
Journal of Automata, Languages and Combinatorics
Object discretizations in higher dimensions
Pattern Recognition Letters
Balance properties of multi-dimensional words
Theoretical Computer Science
Theoretical Computer Science
On Recursive, O(N) Partitioning of a Digitized Curve into Digital Straight Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Planarity of Rectangular Surface Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Double Description Method Revisited
Selected papers from the 8th Franco-Japanese and 4th Franco-Chinese Conference on Combinatorics and Computer Science
Supercover of Straight Lines, Planes and Triangles
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Recognizing arithmetic straight lines and planes
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
On a conjecture on bidimensional words
Theoretical Computer Science
Automatic Sequences: Theory, Applications, Generalizations
Automatic Sequences: Theory, Applications, Generalizations
Discrete linear objects in dimension n: the standard model
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Connectivity of discrete planes
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Periodicity and local complexity
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Plane digitization and related combinatorial problems
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
On digital plane preimage structure
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
An elementary digital plane recognition algorithm
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Three-Dimensional Digital Planes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discrete Representation of Straight Lines
IEEE Transactions on Pattern Analysis and Machine Intelligence
Curves, hypersurfaces, and good pairs of adjacency relations
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Functional stepped surfaces, flips, and generalized substitutions
Theoretical Computer Science
Formulas for the number of (n-2)-gaps of binary objects in arbitrary dimension
Discrete Applied Mathematics
A generalized preimage for the digital analytical hyperplane recognition
Discrete Applied Mathematics
Minimal arithmetic thickness connecting discrete planes
Discrete Applied Mathematics
Minimum decomposition of a digital surface into digital plane segments is NP-hard
Discrete Applied Mathematics
Gift-wrapping based preimage computation algorithm
Pattern Recognition
Some theoretical challenges in digital geometry: A perspective
Discrete Applied Mathematics
About the frequencies of some patterns in digital planes application to area estimators
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Gift-wrapping based preimage computation algorithm
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
An efficient and quasi linear worst-case time algorithm for digital plane recognition
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Digital segments and Hausdorff discretization
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Arithmetic discrete planes are quasicrystals
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Recognition of digital hyperplanes and level layers with forbidden points
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
About thin arithmetic discrete planes
Theoretical Computer Science
Determining Digital Circularity Using Integer Intervals
Journal of Mathematical Imaging and Vision
Combinatorial relations for digital pictures
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
A composite and quasi linear time method for digital plane recognition
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Fast Circular Arc Segmentation Based on Approximate Circularity and Cuboid Graph
Journal of Mathematical Imaging and Vision
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Digital planarity is defined by digitizing Euclidean planes in the three-dimensional digital space of voxels; voxels are given either in the grid-point or the grid-cube model. The paper summarizes results (also including most of the proofs) about different aspects of digital planarity, such as supporting or separating Euclidean planes, characterizations in arithmetic geometry, periodicity, connectivity, and algorithmic solutions. The paper provides a uniform presentation, which further extends and details a recent book chapter in [R. Klette, A. Rosenfeld, Digital Geometry-Geometric Methods for Digital Picture Analysis, Morgan Kaufmann, San Francisco, 2004].