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Vector field editing and periodic orbit extraction using Morse decomposition

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dc.creator Oregon State University. School of Electrical Engineering and Computer Science
dc.creator Chen, Guoning
dc.creator Mischaikow, Konstantin Michael
dc.creator Laramee, Robert S.
dc.creator Pilarczyk, Pawel
dc.creator Zhang, Eugene
dc.date.accessioned 2012-08-08T15:41:20Z
dc.date.available 2012-08-08T15:41:20Z
dc.date.issued 2006
dc.identifier.uri http://hdl.handle.net/1957/31985
dc.description.abstract Design and control of vector fields is critical for many visualization and graphics tasks such as vector field visualization, fluid simulation, and texture synthesis. The fundamental qualitative structures associated with vector fields are fixed points, periodic orbits, and separatrices. In this paper we provide a new technique that allows for the systematic creation and cancellation of fixed points and periodic orbits. This technique enables vector field design and editing on the plane and surfaces with desired qualitative properties. The technique is based on Conley theory which provides a unified framework that supports the cancellation of fixed points and periodic orbits. We also introduce a novel periodic orbit extraction and visualization algorithm that detects, for the first time, periodic orbits on surfaces. Furthermore, we describe the application of our periodic orbit detection and vector field simplification algorithm to engine simulation data demonstrating the utility of the approach. We apply our design system to vector field visualization by creating datasets containing periodic orbits. This helps us understand the effectiveness of existing visualization techniques. Finally, we propose a new streamline-based technique that allows vector field topology to be easily identified. en_US
dc.language.iso en_US en_US
dc.publisher Corvallis, OR : Oregon State University, Dept. of Computer Science en_US
dc.relation.ispartofseries Technical report (Oregon State University. School of Electrical Engineering and Computer Science) en_US
dc.relation.ispartofseries 2006-27 en_US
dc.subject Vector field design en_US
dc.subject Vector field visualization en_US
dc.subject Vector field topology en_US
dc.subject vector field simplification en_US
dc.subject Morse decomposition en_US
dc.subject Conley index en_US
dc.subject periodic orbit detection en_US
dc.subject connection graphs en_US
dc.subject.lcsh Vector fields -- Design en_US
dc.subject.lcsh Information visualization en_US
dc.subject.lcsh Computer graphics en_US
dc.title Vector field editing and periodic orbit extraction using Morse decomposition en_US
dc.type Technical Report en_US
dc.description.peerreview no


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