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<H1>quadtree complexity theorem</H1>
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(definition)
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<strong>Definition:</strong>
The number of nodes in a <a href="quadtree.html" tppabs="http://hissa.nist.gov/dads/HTML/quadtree.html"><em>quadtree</em></a> region representation for a simple polygon (i.e. with nonintersecting edges and without holes) is O(p+q) for a 2<sup>q</sup> × 2<sup>q</sup> image with perimeter p measured in pixel widths. In most cases, q is negligible, and thus, the number of nodes is proportional to the perimeter. It also holds for three-dimensional data where the perimeter is replaced by surface area, and in general for d-dimensions where instead of perimeter we have the size of the (d-1)-dimensional interfaces between the d-dimensional objects.
<P><em>Note:
From Algorithms and Theory of Computation Handbook, page 18-24, Copyright © 1999 by CRC Press LLC.</em>
<P>Author: <a href="terms.html#authorCRC-A" tppabs="http://hissa.nist.gov/dads/terms.html#authorCRC-A">CRC-A</a>
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Entry modified Thu Jun 17 09:56:40 1999.<BR>
HTML page formatted Mon Jan 10 09:20:56 2000.
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