Simplifying Flexible Isosurfaces Using Local Geometric Measures
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Simple and optimal output-sensitive construction of contour trees using monotone paths
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Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree
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Simple and optimal output-sensitive construction of contour trees using monotone paths
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
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Morse theory and the Reeb graph give topological summaries of the behaviour of continuous scalar functions. The contour tree augments the Reeb graph for the isosurfaces in a volume to store seed sets, which are starting points for extracting isosurfaces by the continuation method. We replace the minimal seed sets of van Kreveld et al. with path seeds, which generate paths that correspond directly to the individual components of an isosurface. From a path we get exactly one seed per component, which reduces storage and simplifies isosurface extraction. Moreover, the correspondence allows us to extend the contour spectrum of Bajaj et al. to an interface that we call flexible isosurfaces, in which individual contours with different isovalues can be displayed, manipulated and annotated. The largest contour segmentation, in which separate surfaces are generated for each local maximum of the field, is a special case of the flexible isosurface.