Talk:Total circles area: Difference between revisions
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There are a few concerns about this algorithm: firstly, it's fast only if there are few circles. Its complexity is maybe O(N^3) with N = number of circles, while normal scanline method is probably O(N * n) or less, with n = number of scanlines. Secondly, step 4 needs to be accurate; a small precision error there may cause an arc to remain or be removed by mistake, with disastrous consequences. Also, it's difficult to estimate the error in the final result. The scanline or Monte Carlo methods have errors mostly due to statistics, while this method's error is due to floating point precision loss, which is a very different can of worms. --[[User:Ledrug|Ledrug]] 01:24, 15 October 2012 (UTC)
== Integral solution? ==
Does this solution with the Heaviside function (<math>H</math>) work?
:<math>\int_{(x,y)\in\mathbb{R}^2} (\prod_{i=1}^N H(r_i^2 - (x-c_x^{(i)})^2 - (y-c_y^{(i)})^2)) dx dy</math>
If it does maybe then we can write <math>H(x) = \lim_{k\to\infty}\frac{1}{1+e^{-2kx}}</math> and hope for things to simplify somehow?
--[[User:Grondilu|Grondilu]] ([[User talk:Grondilu|talk]]) 12:51, 3 October 2023 (UTC)
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