Computational geometry: an introduction
Computational geometry: an introduction
Hierarchical spatial data structures
SSD '90 Proceedings of the first symposium on Design and implementation of large spatial databases
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Fundamentals of surface voxelization
Graphical Models and Image Processing
A linear algorithm for incremental digital display of circular arcs
Communications of the ACM
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Robust Adaptive Approximation of Implicit Curves
SIBGRAPI '01 Proceedings of the 14th Brazilian Symposium on Computer Graphics and Image Processing
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Isotopic meshing of implicit surfaces
The Visual Computer: International Journal of Computer Graphics
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Visualisation of Implicit Algebraic Curves
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Algorithm for computer control of a digital plotter
IBM Systems Journal
Dynamic reconstruction of complex planar objects on irregular isothetic grids
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Topological and geometrical reconstruction of complex objects on irregular isothetic grids
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Supercover model and digital straight line recognition on irregular isothetic grids
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Fast distance transformation on irregular two-dimensional grids
Pattern Recognition
Unsupervised polygonal reconstruction of noisy contours by a discrete irregular approach
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
A combined multi-scale/irregular algorithm for the vectorization of noisy digital contours
Computer Vision and Image Understanding
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The approximation of implicit planar curves by line segments is a very classical problem. Many algorithms use interval analysis to approximate this curve, and to handle the topology of the final reconstruction. In this article, we use discrete geometry tools to build an original geometrical and topological representation of the implicit curve. The polygonal approximation contains few segments, and the Reeb graph permits to sum up efficiently the shape and the topology of the curve. Furthermore, we propose two algorithms to process local cells refinement and local cells grouping schemes. We illustrate these schemes with a global system that efficiently handles manual or automatic fast updates on the global reconstruction, by considering topological or geometrical constraints. We also compare the speed and the quality of our approach with two classical methods.