{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T22:00:22Z","timestamp":1790892022933,"version":"4.1.0"},"reference-count":29,"publisher":"SPIE-Intl Soc Optical Eng","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Electron. Imag."],"published-print":{"date-parts":[[2000,10,1]]},"abstract":"<jats:p>The visualization of vector fields has attracted much attention over the last decade due to the vast variety of applications in science and engineering. Topological methods have been used intensively for global structure extraction and analysis. Recently, there has been a growing interest in local structure analysis due to its connection to automatic feature extraction and speed. We present an algorithm that extracts local topological structure of arbitrary regions in a two-dimensional vector field. It is based on a mathematical analysis of the topological vector field structure in these regions. The algorithm deals with piecewise linear vector fields and arbitrary polygonal regions. We have tested the algorithm for well known analytic vector fields and data sets resulting from computational fluid dynamics.<\/jats:p>","DOI":"10.1117\/1.1289350","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T09:59:57Z","timestamp":1027677597000},"page":"356-367","source":"Crossref","is-referenced-by-count":28,"title":["Visualizing local vector field topology"],"prefix":"10.1117","volume":"9","author":[{"given":"Gerik","family":"Scheuermann","sequence":"first","affiliation":[{"name":"Univ. of California at Davis"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernd","family":"Hamann","sequence":"additional","affiliation":[{"name":"Univ. of California\/Davis"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kenneth I.","family":"Joy","sequence":"additional","affiliation":[{"name":"Univ. of California\/Davis"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wolfgang","family":"Kollmann","sequence":"additional","affiliation":[{"name":"Univ. of California\/Davis"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"189","reference":[{"key":"10.1117\/1.1289350_r1","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1063\/1.857730","volume":"2","author":"Chong","year":"1990","journal-title":"Phys. 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Shriver, Eds., pp. 6\u201313, Los Alamitos, California (1990).","DOI":"10.1109\/VISUAL.1990.146359"},{"key":"10.1117\/1.1289350_r5","doi-asserted-by":"crossref","unstructured":"A. Globus, C. Levit, and T. Lasinski, \u201cA tool for visualizing the topology of three-dimensional vector fields,\u201d in\n                      Proc. IEEE Visualization Conf.\n                      , pp. 33\u201340, San Diego, California (1991).","DOI":"10.1109\/VISUAL.1991.175773"},{"key":"10.1117\/1.1289350_r6","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/2945.694953","volume":"4","author":"Scheuermann","year":"1998","journal-title":"IEEE Trans. Visualization Computer Graphics"},{"key":"10.1117\/1.1289350_r7","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1109\/2945.773805","volume":"5","author":"Kenwright","year":"1999","journal-title":"IEEE Trans. Visualization Computer Graphics"},{"key":"10.1117\/1.1289350_r8","doi-asserted-by":"crossref","unstructured":"M. Roth and R. Peikert, \u201cA higher-order method for finding vortex core lines,\u201d in\n                      Proc. IEEE Visualization Conf.\n                      , pp. 143\u2013150, Los Alamitos, California (1998).","DOI":"10.1109\/VISUAL.1998.745296"},{"key":"10.1117\/1.1289350_r9","doi-asserted-by":"crossref","unstructured":"D. N. Kenwright, \u201cAutomatic detection of open and closed separation and attachment lines,\u201d in\n                      Proc. IEEE Visualization Conf.\n                      , pp. 151\u2013158, Los Alamitos, California (1998).","DOI":"10.1109\/VISUAL.1998.745297"},{"key":"10.1117\/1.1289350_r10","unstructured":"V. I. Arnold,\n                      Ordinary Differential Equations\n                      , Springer, Berlin (1992)."},{"key":"10.1117\/1.1289350_r11","doi-asserted-by":"crossref","unstructured":"J. Guckenheimer and P. Holmes,\n                      Dynamical Systems and Bifurcation of Vector Fields\n                      , Springer, New York (1983).","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"10.1117\/1.1289350_r12","unstructured":"M. W. Hirsch and S. Smale,\n                      Differential Equations, Dynamical Systems and Linear Algebra\n                      , Academic, New York (1974)."},{"key":"10.1117\/1.1289350_r13","doi-asserted-by":"crossref","unstructured":"S. Lang,\n                      Differential and Riemannian Manifolds\n                      , 3rd ed. Springer, New York (1995).","DOI":"10.1007\/978-1-4612-4182-9"},{"key":"10.1117\/1.1289350_r14","unstructured":"J. W. Milnor,\n                      Topology from the Differential Viewpoint\n                      , The University Press of Virginia, Charlottesville (1965)."},{"key":"10.1117\/1.1289350_r15","unstructured":"H. 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