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Unstructured Volume Rendering

Explore advanced techniques in volume rendering using structured grids, unstructured grids, and ray-casting to achieve high-quality visualizations. Learn about Projected Tetrahedra for optimizing rendering efficiency.

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Unstructured Volume Rendering

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  1. Unstructured Volume Rendering

  2. Grid Types Structured Grids: uniform regular rectilinear curvilinear Unstructured Grids: regular irregular hybrid curved

  3. OR Ray-Casting • For each ray • find intersection with first cell • interpolate a color, opacity value • while not outside the volume • find exit point of ray in cell • interpolate a color, opacity value • integrate opacity/color along ray within cell

  4. Ray-Casting • Computationally more expensive • Point location is much more complicated (adjacency info is needed) • Degeneracy in intersection test (hit vertex, edge etc) • Interpolation could be more expensive (cell type dependent)

  5. Projected Tetrahedra (PT) • Shirley and Tuchman 1990 • object order (cell by cell) • Utilize graphics hardware (Gouraud shading) • makes sense if one cell projects to many pixels • based on tetrahedral decomposition

  6. PT – Basic Idea Final Image Back to Front Blending

  7. PT - basic algorithm • Decompose volume into tetrahedral cells • classify each tetrahedron according to its projected profile relative to a viewpoint • find the positions of the tetrahedra vertices after the perspective transformation • decompose projections of the tetrahedra into triangles • find color and opacity values for the triangle vertices using ray integration in the original world coordinates • scan convert the triangles on a graphics workstation

  8. PT – tetrahedra decomposition • Decompose volume into tetrahedral cells • 5 or 6 tetrahedra are possible • want least amount of computation • for 5 - need to make sure that there will be no “cracks”

  9. PT - tetrahedra • for 5 - need to make sure that there will be no “cracks” • I.e. edges need to line up properly

  10. PT – projection & classification • Classify each tetrahedron according to its projected profile relative to a viewpoint • Based on the normal directions • Point toward (+) • Point away from (-) • Perpendicular to the eye (0) • +++- • - - + • - + + • ++ - 0 • - + 0 • + - 00

  11. PT - Decompose • Decompose projections of the tetrahedra into triangles • Find the triangle vertex positions (tetrahedron vertex or edge intersection) after perspective projection

  12. PT – Rendering • Render the tetrahedra (decomposed triangles) back to front • Need to calculate the color and opacity at each triangle vertex – precomputed ray integration is needed • Graphics hardware for Gouraud shading

  13. PT – Vertex Color/Opacity • Zero opacity at “thin” vertices • Data color at “thin” vertices • Ray integration needed for “thick” vertices

  14. PT – Ray Integration • Let’s do it on the board …

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