Berkeley CSUA MOTD:Entry 39243
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2025/04/03 [General] UID:1000 Activity:popular
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2005/8/24-25 [Computer/Theory] UID:39243 Activity:high
8/24    Computational Geometry question: I have a bunch of points which I
        use to generate a tiling of unit sqaure by Delaunay triangulation.
        Given an arbitrary point in the unit square, I want to determine which
        triangle the point is in. Does this problem have a name? I'm trying
        to find see what algorithms are out there for doing this, but my
        Google fu is weak. I'd appreciate any tips/links.
        By the way, go Republicans! We kick ass!                -jblack
       \_ Yes, the problem is called 'point location.'  You can adopt
          binary search for this problem without much difficulty.  You can
          also use fast randomized algorithms for this problem, see:
          http://citeseer.ist.psu.edu/cke96fast.html -- ilyas
          \_ Yeah, binary search was my intuition, I just wanted to confirm
             that. Thanks for the info / link. - op
        \_ Without actually computing the triangulation?
        \_ jblack, you're still on probation. I'm letting you post this
           time, since you signed your name.
        \_ Let me get this straight. First you harrass us by constantly
           posting freeper crap, hiding URL by using IPs, mass posting,
           insulting and provoking liberals, hiding your identity, so on and
           so forth even though we asked you to stop, and then you have the
           nerve to come back to us and ask for help? HELLO??? Either you're
           an autistic socially inept retard, or you simply need help.
           SERIOUS help, from a good psychiatric institution.
           \_ While I can certainly appreciate your zeal, I'd rather not be
              included in your inclusive 'we' and 'us'.  While I don't
              agree with jblack's politics, he has a right to speak his
              agree with danh's politics, he has a right to speak his
              peace.  On the other hand, I'm absolutely not going to back
              up anyone that espouses a philosophy of censorship, and would
              rather not be implicitly or explicitly represented by anyone
              that does.                                            -mice
           \_ I find it amusing that you're not signing your name. -emarkp
           \_ also, you've been trolled.
           \_ Dude, you're a damn retard. Do you seriously not see the
              irony here? You're the one looking unstable.
              \_ Pot. Kettle. Etc.
                 \_ Haha.  This response is truly stupid.
                    \_ This whole thread is stupid.
                       \_ This whole motd is stupid.
                          \_ Stupid is as stupid does.
2025/04/03 [General] UID:1000 Activity:popular
4/3     

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Cache (1116 bytes)
citeseer.ist.psu.edu/cke96fast.html
The proposed pro cedure finds the query point simply by "walking through" the triangulati on, after selecting a "good starting point" by random sampling. The anal ysis generalizes and extends a recent result for d = 2 dimensions by pro ving this procedure to take expected time close to O(n 1=(d+1) ) for poi nt location in Delaunay triangulations of n random points in d = 3.. All perform a walk in the triangulation to accelerate point location . The advantage of that category of incremental Delaunay... Based on this approach, there exists several incre mental algorithms. The complexity of the location step, which strongly depends on the location strategy will be evoked in the next section.... Fast randomized point locati on without preprocessing in two- and three-dimensional Delaunay triangul ations. cke and I Saias and B Zhu", title = "Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations", text = "Ernst P M#cke, Isaac Saias, and Binhai Zhu. Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations.