“Hierarchical splatting: a progressive refinement algorithm for volume rendering” by Laur and Hanrahan

  • ©David Laur and Patrick (Pat) Hanrahan




    Hierarchical splatting: a progressive refinement algorithm for volume rendering



    This paper presents a progressive refinement algorithm for volume rendering which uses a pyramidal volume representation. Besides storing average values, the pyramid stores estimated error, so an octtree can be fit to the pyramid given a user-supplied precision. This octtree is then drawn using a set of splats, or footprints, each scaled to match the size of the projection of a cell. The splats themselves are approximated with RGBA Gouraud-shaded polygons, so that they can be drawn efficiently on modern graphics workstations. The result is a real-time rendering algorithm suitable for interactive applications.


    1. Larry Bergman, Henry Fuchs, Eric Grant, and Susan Sl~aC.b .|~nage rendering by adaptive refnement. Computer Graphics (SIGGRAPH ’86 Proceedings), 20(4):29-38, August 1986.
    2. Jules Bloomenthal. Polygonization of implicit surfaces. Computer Aided Geometric Design, 5(4):341-555, November 1988.
    3. Harvey E. Cline, William E. Lorensen, Sigwalt Ludke, Carl R. Crawford, and Bruce C. Teeter. Two algorithms for the reconstruction of surfaces from tomograms. Medical Physics, 15(3):320-327, June, 1988.
    4. Marc Levoy. Efficient ray tracing of volume data. A CM Transactions on Graphics, 9(3):245-261, July 1990.
    5. Marc Levoy and Ross Whitaker. Gaze-directed volume rendering. Computer Graphics (Symposium on Interactive 31) Graphics}, 24(2):217-223, March 1990.
    6. Nelson Max, Pat Hanrahan, and Roger Crawfis. Area and volume coherence for efficient visualization of 3d scalar functions. Computer Graphics (San Diego Workshop on Volume Visualizaton), 24(5):27-33, November 1990.
    7. Thomas Porter and Tom Duff. Compositing digital images. Computer Graphics (SIGGRAPH ’84 Proceedings), 18(3):253-260, July 1984.
    8. Peter Shirley and Allan Tuchman. A polygonal approximation to direct scalar volume rendering. Computer Graphics (San Diego Workshop on Volume Visualizaton), 24(5):63-70, November 1990.
    9. Craig Upson and Michael Keeler. V-buffer: Visible volume rendering. Computer Graphics (Proceedings of SIGGRAPH ’88), 22(4):59-64, August 1988.
    10. Lee Westover. Footprint evaluation for volume rendering. Computer Graphics, 24(4):367-376, August 1990.
    11. Jane Wilhelms. A coherent projection approach to direct volume rendering. Computer Graphics (SIG- GRAPH ‘9i Proceedings}, July 1991.
    12. Jane Wilhelms and Allan Van Gelder. Octrees for faster isosurface generation. Computer Graphics (San Diego Workshop on Volume Visualizaton), 24(5):57-62, November 1990.
    13. Lance Williams. Pyramidal parametrics. Computer Graphics (SIGGRAPH ’83 Proceedings), 17(3):1-1 1, July 1983.
    14. Brian Wyvill, Craig McPheeters, and Geoff WyviU. Data structure for soft objects. The Visual Computer, 2(4):227-234, 1986.

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