Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Octrees for faster isosurface generation
ACM Transactions on Graphics (TOG)
Topological considerations in isosurface generation
ACM Transactions on Graphics (TOG)
On generating topologically consistent isosurfaces from uniform samples
The Visual Computer: International Journal of Computer Graphics
Polygonization of non-manifold implicit surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Octree-based decimation of marching cubes surfaces
Proceedings of the 7th conference on Visualization '96
The asymptotic decider: resolving the ambiguity in marching cubes
VIS '91 Proceedings of the 2nd conference on Visualization '91
Counting Cases in Marching Cubes: Toward a Generic Algorithm for Producing Substitopes
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In surface construction, existing marching cubes (MC) methods require sample values at cell vertices to be non-zero after thresholding, or modify them otherwise. The modification may introduce problems in the constructed surface, such as topological changes, representation errors, and preference for positive or negative values. This paper presents a generalized MC algorithm. It constructs surface patches by exploiting cycles in cells without changing the sample values at vertices, and thus allows cell vertices with zero sample values to lie on the constructed surface. The simulation results show that the proposed Zero-Crossing MC method preserves better topologies of implicit surfaces that pass through cell vertices, and represents the surfaces more accurately. Its efficiency is comparable to existing MC methods in constructing surfaces.