Growing use of massive scan data in various engineering applications has necessitated research on point-set surfaces. A point-set surface is a continuous surface defined directly with a set of discrete points. This paper presents a new approach that extends our earlier work on slicing point-set surfaces into planar contours for rapid prototyping usage. This extended approach can decompose a point-set surface into slices with guaranteed topology. Such topological guarantee stems from the use of Morse theory based topological analysis of the slicing operation. The Morse function for slicing is a height function restricted to the point-set surface, an implicitly defined moving least-squares (MLS) surface. We introduce a Lagrangian multiplier formulation for critical point identification from the restricted surface. Integral lines are constructed to form Morse-Smale complex and the enhanced Reeb graph. This graph is then used to provide seed points for forming slicing contours, with the guarantee that the sliced model has the same topology as the input point-set surface. The extension of this approach to degenerate functions on point-set surface is also discussed.
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ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 15–18, 2010
Montreal, Quebec, Canada
Conference Sponsors:
- Design Engineering Division and Computers in Engineering Division
ISBN:
978-0-7918-4411-3
PROCEEDINGS PAPER
Topologically Enhanced Slicing of MLS Surfaces
Pinghai Yang,
Pinghai Yang
Illinois Institute of Technology, Chicago, IL
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Kang Li,
Kang Li
Illinois Institute of Technology, Chicago, IL
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Xiaoping Qian
Xiaoping Qian
Illinois Institute of Technology, Chicago, IL
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Pinghai Yang
Illinois Institute of Technology, Chicago, IL
Kang Li
Illinois Institute of Technology, Chicago, IL
Xiaoping Qian
Illinois Institute of Technology, Chicago, IL
Paper No:
DETC2010-29125, pp. 1063-1074; 12 pages
Published Online:
March 8, 2011
Citation
Yang, P, Li, K, & Qian, X. "Topologically Enhanced Slicing of MLS Surfaces." Proceedings of the ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 3: 30th Computers and Information in Engineering Conference, Parts A and B. Montreal, Quebec, Canada. August 15–18, 2010. pp. 1063-1074. ASME. https://doi.org/10.1115/DETC2010-29125
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