NDLI: Quaternion frame approach to streamline visualization

Content Provider	IEEE Xplore Digital Library
Author	Hanson, A.J. Hui Ma
Copyright Year	1995
Abstract	Curves in space are difficult to perceive and analyze, especially when they form dense sets as in typical 3D flow and volume deformation applications. We propose a technique that exposes essential properties of space curves by attaching an appropriate moving coordinate frame to each point, reexpressing that moving frame as a unit quaternion, and supporting interaction with the resulting quaternion field. The original curves in 3-space are associated with piecewise continuous 4-vector quaternion fields, which map into new curves lying in the unit 3-sphere in 4-space. Since 4-space clusters of curves with similar moving frames occur independently of the curves' original proximity in 3-space, a powerful analysis tool results. We treat two separate moving-frame formalisms, the Frenet frame and the parallel-transport frame, and compare their properties. We describe several flexible approaches for interacting with and exploiting the properties of the 4D quaternion fields.<>
Sponsorship	IEEE Computer Society Technical Committee on Computer Graphics IEEE Computer Society
Starting Page	164
Ending Page	174
Page Count	11
File Size	1932334
File Format	PDF
ISSN	10772626
Volume Number	1
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1995-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Quaternions Geometry Shape measurement Mesh generation Application software Joining processes Data visualization Tensile stress Differential equations Fluid flow measurement
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Signal Processing Computer Vision and Pattern Recognition Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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