{"abstract":[{"text":"We combine topological and geometric methods to construct a multi-resolution data structure for functions over two-dimensional domains. Starting with the Morse-Smale complex, we construct a topological hierarchy by progressively canceling critical points in pairs. Concurrently, we create a geometric hierarchy by adapting the geometry to the changes in topology. The data structure supports mesh traversal operations similarly to traditional multi-resolution representations.","lang":"eng"}],"author":[{"first_name":"Peer","full_name":"Bremer, Peer","last_name":"Bremer"},{"first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Hamann","full_name":"Hamann, Bernd","first_name":"Bernd"},{"last_name":"Pascucci","full_name":"Pascucci, Valerio","first_name":"Valerio"}],"citation":{"ista":"Bremer P, Edelsbrunner H, Hamann B, Pascucci V. 2003. A multi-resolution data structure for two-dimensional Morse-Smale functions. Proceedings of the 14th IEEE Conference on Visualization . VIS: IEEE Visualization, 139–146.","ieee":"P. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci, “A multi-resolution data structure for two-dimensional Morse-Smale functions,” in <i>Proceedings of the 14th IEEE Conference on Visualization </i>, Seattle, WA, USA , 2003, pp. 139–146.","ama":"Bremer P, Edelsbrunner H, Hamann B, Pascucci V. A multi-resolution data structure for two-dimensional Morse-Smale functions. In: <i>Proceedings of the 14th IEEE Conference on Visualization </i>. IEEE; 2003:139-146. doi:<a href=\"https://doi.org/10.1109/VISUAL.2003.1250365\">10.1109/VISUAL.2003.1250365</a>","mla":"Bremer, Peer, et al. “A Multi-Resolution Data Structure for Two-Dimensional Morse-Smale Functions.” <i>Proceedings of the 14th IEEE Conference on Visualization </i>, IEEE, 2003, pp. 139–46, doi:<a href=\"https://doi.org/10.1109/VISUAL.2003.1250365\">10.1109/VISUAL.2003.1250365</a>.","short":"P. Bremer, H. Edelsbrunner, B. Hamann, V. Pascucci, in:, Proceedings of the 14th IEEE Conference on Visualization , IEEE, 2003, pp. 139–146.","apa":"Bremer, P., Edelsbrunner, H., Hamann, B., &#38; Pascucci, V. (2003). A multi-resolution data structure for two-dimensional Morse-Smale functions. In <i>Proceedings of the 14th IEEE Conference on Visualization </i> (pp. 139–146). Seattle, WA, USA : IEEE. <a href=\"https://doi.org/10.1109/VISUAL.2003.1250365\">https://doi.org/10.1109/VISUAL.2003.1250365</a>","chicago":"Bremer, Peer, Herbert Edelsbrunner, Bernd Hamann, and Valerio Pascucci. “A Multi-Resolution Data Structure for Two-Dimensional Morse-Smale Functions.” In <i>Proceedings of the 14th IEEE Conference on Visualization </i>, 139–46. IEEE, 2003. <a href=\"https://doi.org/10.1109/VISUAL.2003.1250365\">https://doi.org/10.1109/VISUAL.2003.1250365</a>."},"publist_id":"2131","_id":"3997","publication_identifier":{"isbn":["0780381203"]},"type":"conference","language":[{"iso":"eng"}],"quality_controlled":"1","year":"2003","oa_version":"None","acknowledgement":"This work was performed under the auspices of the U. S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. H. Edelsbrunner is partially supported by the National Science Foundation (NFS) under grants EIA-99-72879 and CCR-00-86013. B. Hamann is supported by the NSF under contract ACI 9624034, through the LSSDSV program under contract ACI 9982251, and through the NPACI; the National Institute of Mental Health and the NSF under contract NIMH 2 P20 MH60975-06A2; the Lawrence Livermore National Laboratory under ASCI ASAP Level-2 Memorandum Agreement B347878 and under Memorandum Agreement B503159.","extern":"1","date_published":"2003-08-01T00:00:00Z","title":"A multi-resolution data structure for two-dimensional Morse-Smale functions","publisher":"IEEE","publication":"Proceedings of the 14th IEEE Conference on Visualization ","date_updated":"2024-02-27T11:12:50Z","month":"08","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","day":"01","page":"139 - 146","article_processing_charge":"No","doi":"10.1109/VISUAL.2003.1250365","status":"public","conference":{"location":"Seattle, WA, USA ","start_date":"2003-10-19","end_date":"2003-10-24","name":"VIS: IEEE Visualization"},"scopus_import":"1","date_created":"2018-12-11T12:06:21Z"}