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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e-mail: qian@iit.edu
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September 2011
Research Papers
Topologically Enhanced Slicing of MLS Surfaces
Pinghai Yang,
Pinghai Yang
Department of Mechanical, Materials and Aerospace Engineering,
Illinois Institute of Technology
, Chicago, Illinois 60616
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Kang Li,
Kang Li
Department of Mechanical, Materials and Aerospace Engineering,
Illinois Institute of Technology
, Chicago, Illinois 60616
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Xiaoping Qian
Xiaoping Qian
Department of Mechanical, Materials and Aerospace Engineering,
e-mail: qian@iit.edu
Illinois Institute of Technology
, Chicago, Illinois 60616
Search for other works by this author on:
Pinghai Yang
Department of Mechanical, Materials and Aerospace Engineering,
Illinois Institute of Technology
, Chicago, Illinois 60616
Kang Li
Department of Mechanical, Materials and Aerospace Engineering,
Illinois Institute of Technology
, Chicago, Illinois 60616
Xiaoping Qian
Department of Mechanical, Materials and Aerospace Engineering,
Illinois Institute of Technology
, Chicago, Illinois 60616e-mail: qian@iit.edu
J. Comput. Inf. Sci. Eng. Sep 2011, 11(3): 031003 (9 pages)
Published Online: August 10, 2011
Article history
Received:
April 28, 2009
Revised:
March 30, 2011
Online:
August 10, 2011
Published:
August 10, 2011
Citation
Yang, P., Li, K., and Qian, X. (August 10, 2011). "Topologically Enhanced Slicing of MLS Surfaces." ASME. J. Comput. Inf. Sci. Eng. September 2011; 11(3): 031003. https://doi.org/10.1115/1.3615683
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