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Degree-driven Geometric Algorithm Design

This work explores an example problem in computational geometry: determining the closest site to each pixel on a grid containing `n` sites. Key questions include how much precision is necessary for accurate identification of these sites and the implications of precision on algorithm performance, referencing notable analytical methods. The research encompasses findings from Millman's thesis and various projects, including parallel geometric algorithms, Monte Carlo methods for neutron transport equations, and advanced volume calculations in solid geometry, emphasizing the importance of precision in geometric computations.

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Degree-driven Geometric Algorithm Design

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  1. Degree-driven Geometric Algorithm Design David L. Millman University Of North Carolina - Chapel Hill ITCS’12 9 January 2012

  2. An Example Problem Given n sites on a pixel grid, what is the closest site to each pixel? How much precision is needed to determine this?

  3. Why Precision [Y97]

  4. Analyzing Precision [LPT99] e.g. Precision of the Orientation test:

  5. Analyzing Precision [LPT99] e.g. Precision of the Orientation test:

  6. Analyzing Precision [LPT99] e.g. Precision of the Orientation test:

  7. Analyzing Precision [LPT99] e.g. Precision of the Orientation test:

  8. Analyzing Precision [LPT99] e.g. Precision of the Orientation test: Degree 2

  9. Some Results of My Thesis

  10. Other Projects Parallel computational geometry Vicente H.F. Batista, David L. Millman, Sylvain Pion, and Johannes Singler. Parallel geometric algorithms for multi-core computers. Computational Geometry, 43(8):663 – 677, 2010. Monte Carlo algos for the neutron transport equation David L. Millman, David P. Griesheimer, Brian Nease and Jack Snoeyink. Robust volume calculation for constructive solid geometry (CSG) components in Monte Carlo Transport Calculations. Under Review David P. Griesheimer, David L. Millman, and Clarence R. Willis. Analysis of distances between inclusions in finite binary stochastic materials. Journal of Quantitative Spectroscopy and Radiative Transfer in Journal of Quantitative Spectroscopy and Radiative Transfer, 112(4):577–598, March 2011.

  11. Contact Information David L. Millman dave@cs.unc.edu http://cs.unc.edu/~dave

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