Differential equations: a dynamical systems approach. Part I: ordinary differential equations
Differential equations: a dynamical systems approach. Part I: ordinary differential equations
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Topographic distance and watershed lines
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Visualizing Vector Field Topology in Fluid Flows
IEEE Computer Graphics and Applications
Molecular shape analysis based upon the morse-smale complex and the connolly function
Proceedings of the nineteenth annual symposium on Computational geometry
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
Isotopic meshing of implicit surfaces
The Visual Computer: International Journal of Computer Graphics
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality
IEEE Transactions on Visualization and Computer Graphics
Proceedings of the twenty-fifth annual symposium on Computational geometry
In Praise of Numerical Computation
Efficient Algorithms
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The Morse-Smale complex is an important tool for global topological analysis in various problems of computational geometry and topology. Algorithms for Morse-Smale complexes have been presented in case of piecewise linear manifolds. However, previous research in this field does not provide certified methods in the case of smooth functions. In the current paper we use interval arithmetic to compute a topologically correct approximation of Morse-Smale complex of smooth functions of two variables. The algorithm can also compute geometrically close Morse-Smale complex.