Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Level set diagrams of polyhedral objects
Proceedings of the fifth ACM symposium on Solid modeling and applications
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
SMA '97 Proceedings of the 1997 International Conference on Shape Modeling and Applications (SMA '97)
Topology Recognition of 3D Closed Freeform Objects Based on Topological Graphs
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Graph based topological analysis of tessellated surfaces
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Planar parameterization for closed 2-manifold genus-1 meshes
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Families of cut-graphs for bordered meshes with arbitrary genus
Graphical Models
Surface Capture for Performance-Based Animation
IEEE Computer Graphics and Applications
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
Computers and Graphics
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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.