Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Geometry for n-dimensional graphics
Graphics gems IV
Multiresolution tetrahedral framework for visualizing regular volume data
VIS '97 Proceedings of the 8th conference on Visualization '97
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VIS '97 Proceedings of the 8th conference on Visualization '97
Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows
Journal of Computational Physics
Constructing material interfaces from data sets with volume-fraction information
Proceedings of the conference on Visualization '00
Tools for Triangulations and Tetrahedrizations
Scientific Visualization, Overviews, Methodologies, and Techniques
The asymptotic decider: resolving the ambiguity in marching cubes
VIS '91 Proceedings of the 2nd conference on Visualization '91
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Machine Graphics & Vision International Journal
Multi-material interface reconstruction on generalized polyhedral meshes
Journal of Computational Physics
IStar: A Raster Representation for Scalable Image and Volume Data
IEEE Transactions on Visualization and Computer Graphics
Extraction of isosurfaces from multi-material CT volumetric data of mechanical parts
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Journal of Computational Physics
Non-manifold mesh extraction from time-varying segmented volumes used for modeling a human heart
EUROVIS'05 Proceedings of the Seventh Joint Eurographics / IEEE VGTC conference on Visualization
Integrating mesh and meshfree methods for physics-based fracture and debris cloud simulation
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
Discrete multi-material interface reconstruction for volume fraction data
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
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This paper presents an algorithm for material interface reconstruction for data sets where fractional material information is given as a percentage for each element of the underlying grid. The reconstruction problem is transformed to a problem that analyzes a dual grid, where each vertex in the dual grid has an associated barycentric coordinate tuple that represents the fraction of each material present. Material boundaries are constructed by analyzing the barycentric coordinate tuples of a tetrahedron in material space and calculating intersections with Voronoi cells that represent the regions where one material dominates. These intersections are used to calculate intersections in the Euclidean coordinates of the tetrahedron. By triangulating these intersection points, one creates the material boundary. The algorithm can treat data sets containing any number of materials. The algorithm can also create nonmanifold boundary surfaces if necessary. By clipping the generated material boundaries against the original cells, one can examine the error in the algorithm. Error analysis shows that the algorithm preserves volume fractions within an error range of 0.5 percent per material.