Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Computing shortest cycles using universal covering space
The Visual Computer: International Journal of Computer Graphics
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
Technical Section: Point-based rendering of implicit surfaces in R4
Computers and Graphics
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Riemann surfaces naturally appear in the analysis of complex functions that are branched over the complex plane. However, they usually possess a complicated topology and are thus hard to understand. We present an algorithm for constructing Riemann surfaces as meshes in ${\mathbb R}^3$ from explicitly given branch points with corresponding branch indices. The constructed surfaces cover the complex plane by the canonical projection onto ${\mathbb R}^2$ and can therefore be considered as multivalued graphs over the plane – hence they provide a comprehensible visualization of the topological structure. Complex functions are elegantly visualized using domain coloring on a subset of ${\mathbb C}$. By applying domain coloring to the automatically constructed Riemann surface models, we generalize this approach to deal with functions which cannot be entirely visualized in the complex plane.