Transcript CIS 6930 Final Project Marching Rhombic Dodecahedra by Yusuf Sahillioglu

CIS 6930 Final Project
Marching Rhombic Dodecahedra
by
Yusuf Sahillioglu
http://www.cise.ufl.edu/~ysahilli/vis/
5/27/2016
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Problem Definition
 Indirect volume rendering
 Isosurface Extraction from non-Cartesian sampling
Figure from A. Entezari et. al, A Granular Three Dimensional Multiresolution Transform, Eurographics’06
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Motivation
 Why non-Cartesian?
 Theoretically shown that volumetric data sampled on a nonCartesian lattice is (30%) more efficient than that of Cartesian
lattice
 T. Theussl, T. Moller, M. Groller, Optimal Regular Volume Sampling, IEEE Visualization’01
 Why Marching?
 Combines simplicity w/ high speed (look-up tables)
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Applications
 Visualize sophisticated mathematical functions (implicit)
 Visualize medical needs, e.g. CT images (thresholded)
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BCC Marching
 Voronoi cell of the BCC lattice: truncated octahedron
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BCC Marching
 First neighbors cell of the BCC lattice: rhombic dodecahedron
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non-Cartesian (BCC) Lattice
 Tile w/ rhombic dodecahedra
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Marching Rhombic Dodecahedra
 1 Rhombic dodecahedra  4 Hexahedra  6 Tetrahedra
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Tetrahedra Alignment
 Consistent Alignment within a rhombic dodecahedron
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Tetrahedra Alignment
 Consistent Alignment between rhombic dodecahedra
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Marcher
 March through either hexahedra or tetrahedra
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Results
 Marching Cubes (left) vs. Tetrahedra (right)
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Results
 Marching Cubes (left) vs. Tetrahedra (right)
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Results
 Marching Cubes
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Results
 Marching Tetra
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Results
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Results
 Marching Cubes
 (medium reso)
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Results
 Marching Tetra
 (medium reso)
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Results
 Marching Cubes
 (low reso)
 Marching Tetra
 (low reso)
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Results
 Marching Cubes
 (high reso)
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Results
 Marching Tetra
 (high reso)
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Appendix
 Isovalue function for implicit elephant & hand surfaces (my thesis)
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