Last update: July 29, 2004
References in Computational Geometry by
Universität Dortmund
Publications:
BibTeX references
Robert Mencl and Heinrich Müller
To appear in the year 2000 in Proceedings of Dagstuhl'97 Scientific Visualization, (Dagstuhl, Germany, June 1997) pp. 223-232 , IEEE Publishers
State of the Art Report (STAR) for Eurographics '98, pp. 51-67, Lisbon, Portugal, Aug.31 - Sept.4, 1998.
Research Report No. 662, Fachbereich Informatik, Lehrstuhl VII, University of Dortmund, Germany, December 1997.
There is a wide range of applications for which surface interpolation or approximation from scattered data points in space is important. Dependent on the field of application and the related properties of the data, many algorithms were developed in the past. This contribution gives a survey of existing algorithms, and identifies basic methods common to independently developed solutions. We distinguish surface construction based on spatial subdivision, distance functions, warping and incremental surface growing. The systematic analysis of existing approaches leads to several interesting open questions for further research.
Robert Mencl and Heinrich Müller
Proceedings of CGI '98 (Computer Graphics International), Hannover, Germany, June 22th-26th, 1998.
Research Report No. 661, Fachbereich Informatik, Lehrstuhl VII, University of Dortmund, Germany, November/December 1997.
We present an algorithm for the reconstruction of a surface from an unorganized set of points in space. The point data may be obtained from a laser range scanner or any other digitizing tool to describe the shape of the object(s). The basic idea of the algorithm is to construct some kind of wire frame for the surface, the so--called surface description graph. This is performed by applying several steps. In the final part of the algorithm this wire frame is then filled with triangles. Each step uses a rule system for the reconstruction which is based on human knowledge in geometric structures. This rule system is designed to allow the reconstruction of artificial objects as well as natural objects and is extendable in many aspects for ongoing research. As a result of this approach, our algorithm is able to reconstruct surfaces in data sites with changing point density as well as high curvature of the surface. In addition, it automatically recognizes the number of objects covered in the point set. Several examples are given to demonstrate its features.
Robert Mencl
Published in Computer Graphics Forum 14(3), pages 445-456, 1995.
Proceedings of EUROGRAPHICS 1995, Maastricht, The Netherlands.
Also available as Research Report No. 568, University of Dortmund, 1995.
A new approach to the reconstruction of a surface from an unorganized set of points in space is presented. The point set may for example be obtained with a laser scanner or a manual digitizing tool, and is the only source of information about the shape of the acquired object. The basic idea is to calculate the Euclidean minimum spanning tree (EMST) of the given points. The EMST is then augmented to the so-called surface description graph (SDG). Finally the wire frame defined by the SDG is filled with triangles. The advantage of our approach is that also highly non-convex and even disconnected surfaces are reconstructed quite reliably. This is demonstrated for a variety of data sets.
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