algorithm - How to effectively distribute points on plane -

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i have plane (screen) width , height (monitor resolution, not square). , i'd distribute points on plane (approximately) same distance each other.

for example:

  • 1 point in middle,
  • 2 points in middle of y axis, , x axis divided 3
  • 3 points may triangle, if sceen wide enough, thay can alighned in same y
  • 4 second part of above, or rectangle..
  • etc 8 points max

is there algorithm this?

thank time!

edit: same distance each other , plane border

edit2: compute centers of mass groups of objects on behavior simulate on plane.

depending on precision want:

  • you can stochasticaly correct answer poisson disk sampling. specifically, poisson disk sampling random sampling such no points closer specified radius. such thing can efficiently (linear time) implemented in high dimension - e.g. : c++ code robert bridson : http://www.cs.ubc.ca/~rbridson/download/curlnoise.tar.gz implementing paper http://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph07-poissondisk.pdf

  • you can optimize position of points. leads lloyd algorithms , similar optimization procedures : compute voronoi diagram of initial set of points, , move these points the centroid of voronoi cell. can done efficiently, , can sped using newton's method rather lloyd iteration. ultimately, if domain square, should obtain hexagonal grid (which minimizes function above).

if need approximate results, i'd suggest first approach should faster.


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