Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Visualization and modeling contours of trivariate functions
Visualization and modeling contours of trivariate functions
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
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
VIS '97 Proceedings of the 8th conference on Visualization '97
Visualization of scalar topology for structural enhancement
Proceedings of the conference on Visualization '98
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Topology preserving and controlled topology simplifying multiresolution isosurface extraction
Proceedings of the conference on Visualization '00
Semi-regular mesh extraction from volumes
Proceedings of the conference on Visualization '00
IEEE Transactions on Visualization and Computer Graphics
Volume Data Mining Using 3D Field Topology Analysis
IEEE Computer Graphics and Applications
Solid Fitting: Field Interval Analysis for Effective Volume Exploration
Dagstuhl '97, Scientific Visualization
Accurate display of tensor product isosurfaces
VIS '90 Proceedings of the 1st conference on Visualization '90
The asymptotic decider: resolving the ambiguity in marching cubes
VIS '91 Proceedings of the 2nd conference on Visualization '91
Feature preserved volume simplification
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Morphology-driven simplification and multiresolution modeling of terrains
GIS '03 Proceedings of the 11th ACM international symposium on Advances in geographic information systems
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities
IEEE Transactions on Visualization and Computer Graphics
Direct extraction of surface meshes from implicitly represented heterogeneous volumes
Computer-Aided Design
Topology-Controlled Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Topological Landscapes: A Terrain Metaphor for Scientific Data
IEEE Transactions on Visualization and Computer Graphics
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Topology- and error-driven extension of scalar functions from surfaces to volumes
ACM Transactions on Graphics (TOG)
Topological analysis and characterization of discrete scalar fields
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Tessellation of quadratic elements
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Efficient isosurface tracking using precomputed correspondence table
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Introducing topological attributes for objective-based visualization of simulated datasets
VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
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Isosurfaces are commonly used to visualize scalar fields. Critical isovalues indicate isosurface topology changes: the creation of new surface components, merging of surface components or the formation of holes in a surface component. Therefore, they highlight "interesting" isosurface behavior and are helpful in exploration of large trivariate data sets. We present a method that detects critical isovalues in a scalar field defined by piecewise trilinear interpolation over a rectilinear grid and describe how to use them when examining volume data. We further review varieties of the Marching Cubes (MC) algorithm, with the intention to preserve topology of the trilinear interpolant when extracting an isosurface. We combine and extend two approaches in such a way that it is possible to extract meaningful isosurfaces even when a critical value is chosen as isovalue.