Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs
Proceedings of the seventh ACM symposium on Solid modeling and applications
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Harmonic skeleton for realistic character animation
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Shape analysis using the auto diffusion function
SGP '09 Proceedings of the Symposium on Geometry Processing
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Reverse engineering (RE) deal with an enormous number of irregular and scattered digitized points that require intensive processing in order to reconstruct the surfaces of an object. Surface reconstruction of freeform objects is based on geometrical and topological criteria. Current fitting methods reconstruct an object using a bottom-up approach, from points to a dense mesh and, finally, into smoothed connected freeform sub-surfaces. This type of reconstruction, however, can cause topological problems that lead to undesired surface fitting results. Such problems are particularly common with concave shapes.To avoid problems of this type, this paper proposes a new method that automatically detects the topological structure of an object as a base for surface fitting. The topological reconstruction method described in this paper is based on two stages: (1) creating 3D non-self-intersecting iso-curves from a 3D triangular mesh and (2) extracting a topological graph. The feasibility of the proposed topological reconstruction method is demonstrated on several examples using freeform objects with complex topologies.