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    <p>Here is a more compact version. It uses the same data structure as the original version. The functions <code>splitBox</code> and <code>insideBox</code> are essentially the same as well (just written in a slightly different way). </p> <p>Instead of adding points one-by-one, the initial box contains all the points at the beginning so there is no need for the <code>qtInsert</code> routines. In each recursion step, the boxes containing more than one point are split and the points are distributed over the sub-boxes. This means that all nodes with more than one point are leafs so there is no need to check for that either.</p> <pre><code>qtMakeNode[bb_, pts_] := {{}, {}, {}, {}, qtbb @@ bb, pts} splitBox[bx_] := splitBox[{min_, max_}] := {min + #, max + #}/2 &amp; /@ Tuples[Transpose[{min, max}]] insideBox[pt_, bb_] := bb[[1, 1]] &lt;= pt[[1]] &lt;= bb[[2, 1]] &amp;&amp; bb[[1, 2]] &lt;= pt[[2]] &lt;= bb[[2, 2]] distribute[qtree_] := Which[ Length[qtree[[6]]] == 1, (* no points in node -&gt; return node unchanged *) qtree, Length[qtree[[6]]] == 1, (* one point in node -&gt; replace head of point with qtpt and return node *) ReplacePart[qtree, 6 -&gt; qtpt @@ qtree[[6, 1]]], Length[qtree[[6]]] &gt; 1, (* multiple points in node -&gt; create sub-nodes and distribute points *) (* apply distribute to sub-nodes *) Module[{spl = splitBox[qtree[[5]]], div, newtreelist}, div = Cases[qtree[[6]], a_ /; insideBox[a, #], 1] &amp; /@ spl; ReplacePart[qtree, Join[Table[i -&gt; distribute[qtMakeNode[spl[[i]], div[[i]]]], {i, 4}], {6 -&gt; {}}]]]] </code></pre> <p>Example (using the original version of <code>qtDraw</code>):</p> <pre><code>len = 50; pts = RandomReal[{0, 2}, {len, 2}]; qt = makeTree[qtMakeNode[{{0.0, 0.0}, {2.0, 2.0}}, pts]]; qtDraw[qt] </code></pre> <p>Result:</p> <p><img src="https://i.stack.imgur.com/kNyrg.jpg" alt="Quadtree example"></p>
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    1. COThanks for the code - lots of interesting usage. But I do think that the ability to add points one by one is important. For instance, consider a 2D simulation in which particles are coming in one by one.
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    2. CO@Heike Either your image is blank or my machine has some difficulty with it.
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    3. CO@belisarius: strange, on my screen it is visible. Can you see it when you following this link? http://i.stack.imgur.com/kNyrg.jpg
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