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Integral ear elimination and virtual point-based updating algorithms for constrained Delaunay TIN

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Abstract

Constrained Delaunay Triangular Irregular Networks (CD-TIN), a kind of special data structure, have many practical applications in Geoinformatics, especially in the representation of linear constrained triangulation for DTM and DSM, such as in digital city and digital mine. Past researches on D-TIN mainly focused on point insertion and deletion without consideration of constraint, and that on CD-TIN usually paid more attention to the insertion algorithms for points and edges, but little to the deletion algorithms. The presented algorithms are far insufficient for the dynamic updating of CD-TIN. In this paper, the constraint edge in CD-TIN is considered to be any set of broken lines, i.e., polygon edges, broken lines and simple segments. The constraint edge may be composed of one or more constraint segments, and it is allowed to be in any form: Open or close, intersection or self-intersection. By improving to present insertion and deletion algorithms for D-TIN, two new algorithms for CD-TIN updating are presented. According to the polymorphism of the constraints in CD-TIN, virtual point is adopted to represent the crossing node between constraint edges when a constraint edge is inserted in CD-TIN. Two new algorithms named as Integral Ear Elimination (IEE) and Influence Domain Retriangulation for Virtual Point (IDRVP) are presented, the former is for constraint point deletion, while the later is for the insertion and deletion of constraint edge. The principle of IDRVP is that to divide the influence domain of a virtual point into some parts by the constraint-keeping edges, and to retriangulate each part of the influence domain individually referring to the constraint visible property and constraint empty circle (CEC) criterion. Finally, a prototype system is developed with VC++, one case on the integration of 3D terrain and buildings is demonstrated to test the correctness of new algorithms. It shows that the new algorithms are effective for the updating of CD-TIN.

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Authors and Affiliations

  1. Institute for Geo-informatics & Digital Mine Research, Northeastern University, Shenyang, 110004, China

    LiXin Wu

  2. Institute for GIS/RS/GPS & Subsidence Engineering Research, China University of Mining & Technology, Beijing, 100085, China

    LiXin Wu, YanBing Wang & WenZhong Shi

  3. Laboratory of 3D Information Acquisition & Application, Capital Normal University, Beijing, 100037, China

    YanBing Wang

  4. Center for Advanced GIS Research, LSGI, Polytechnic University Hong Kong, Hong Kong, China

    WenZhong Shi

Authors
  1. LiXin Wu
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  2. YanBing Wang
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  3. WenZhong Shi
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Correspondence to LiXin Wu.

Additional information

Supported by the National Natural Science Funds of China for Outstanding Youth (Grant No. 50525414), the National Natural Science Foundation of China (Grant Nos. 10172090, 40771171), the National Hi-Tech Research and Development Program of China (Grant No. 2006AA12Z216) and Science Development Plan Awarded by Beijing Municipal Commission of Education Science (Grant No. KM200710028014)

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Wu, L., Wang, Y. & Shi, W. Integral ear elimination and virtual point-based updating algorithms for constrained Delaunay TIN. Sci. China Ser. E-Technol. Sci. 51 (Suppl 1), 135–144 (2008). https://doi.org/10.1007/s11431-008-5018-1

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  • DOI: https://doi.org/10.1007/s11431-008-5018-1

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