NDLI: Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs

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Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs

Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs

Content Provider	ACM Digital Library
Author	Fischer, Anath Steiner, Dvir
Abstract	In reverse engineering, surface reconstruction methods for freeform objects are based mainly on geometrical criteria, while topological factors are neglected. Current methods use a bottom-up approach based on local parameterization to reconstruct the object from points to a dense mesh and finally to smooth connected patches. This type of reconstruction, however, can have topological problems that might lead to parameterization difficulties, noisy surface behavior and texture anomalies. Such problems are particularly common with concave objects and shapes with complex topology of genus-n. To avoid the above problems, a new global topological approach for cutting objects with genus-n was developed and implemented. The proposed process is based on two main stages: (1) computing iso-curves on the mesh and extracting the topological graph, and (2) cutting the mesh according to the curve cutting guidelines that are calculated from the topological graph. The resulting mesh is a single boundary mesh and therefore can be flattened onto a disk. The time complexity of the algorithm is O(n log(n)). To demonstrate the feasibility of the cutting process, the mesh was also flattened. The flattened mesh can then be used for global parameterization, surface fitting and texture mapping. The robustness of the cutting process is demonstrated on several examples using sculptured freeform objects with genus-n.
Starting Page	336
Ending Page	343
Page Count	8
File Format	PDF
ISBN	1581135068
DOI	10.1145/566282.566330
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2002-06-17
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Surface reconstruction Flattening Reverse engineering Topological graphs Genus-n Curve cutting guidelines
Content Type	Text
Resource Type	Article

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