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Development of Delaunay Triangulation Algorithm Using Oct-subdivision in Three Dimensions  

Park S.H. (건국대학교 대학원 기계설계학과)
Lee S.S. (건국대학교 기계설계학과)
Publication Information
Korean Journal of Computational Design and Engineering / v.10, no.3, 2005 , pp. 168-178 More about this Journal
Abstract
The Delaunay triangular net is primarily characterized by a balance of the whole by improving divided triangular patches into a regular triangle, which closely resembles an equiangular triangle. A triangular net occurring in certain, point-clustered, data is unique and can always create the same triangular net. Due to such unique characteristics, Delaunay triangulation is used in various fields., such as shape reconstruction, solid modeling and volume rendering. There are many algorithms available for Delaunay triangulation but, efficient sequential algorithms are rare. When these grids involve a set of points whose distribution are not well proportioned, the execution speed becomes slower than in a well-proportioned grid. In order to make up for this weakness, the ids are divided into sub-grids when the sets are integrated inside the grid. A method for finding a mate in an incremental construction algorithm is to first search the area with a higher possibility of forming a regular triangular net, while the existing method is to find a set of points inside the grid that includes the circumscribed sphere, increasing the radius of the circumscribed sphere to a certain extent. Therefore, due to its more efficient searching performance, it takes a shorer time to form a triangular net than general incremental algorithms.
Keywords
Delaunay triangulation; Incremental construction algorithm; Triangle patch; Uniform grid; Subdivision algorithm;
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Times Cited By KSCI : 1  (Citation Analysis)
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