CIS 6930 Final Project

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CIS 6930 Final Project
Marching Rhombic Dodecahedra by Yusuf
Sahillioglu http//www.cise.ufl.edu/ysahilli/vis/

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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, Eurographics06

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Motivation

• Why non-Cartesian?
• Theoretically shown that volumetric data sampled
  on a non-Cartesian lattice is (30) more
  efficient than that of Cartesian lattice
• T. Theussl, T. Moller, M. Groller, Optimal
  Regular Volume Sampling, IEEE Visualization01
• 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)