Copyright © Philip M. Parker, INSEAD. Terms of Use.

QUADTREE COMPLEXITY THEOREM

Specialty Definition: QUADTREE COMPLEXITY THEOREM

DomainDefinition

Math

The number of nodes in a quadtree region representation for a simple polygon (i.e. with nonintersecting edges and without holes) is O(p+q) for a 2q × 2q 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. (references)

Source: compiled by the editor from various references; see credits.

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Alternative Orthography: QUADTREE COMPLEXITY THEOREM


Hexadecimal (or equivalents, 770AD-1900s) (references)

51 55 41 44 54 52 45 45      43 4F 4D 50 4C 45 58 49 54 59      54 48 45 4F 52 45 4D

Leonardo da Vinci (1452-1519; backwards) (references)

        

Binary Code (1918-1938, probably earlier) (references)

01010001 01010101 01000001 01000100 01010100 01010010 01000101 01000101 00100000 01000011 01001111 01001101 01010000 01001100 01000101 01011000 01001001 01010100 01011001 00100000 01010100 01001000 01000101 01001111 01010010 01000101 01001101

HTML Code (1990) (references)

&#81 &#85 &#65 &#68 &#84 &#82 &#69 &#69 &#32 &#67 &#79 &#77 &#80 &#76 &#69 &#88 &#73 &#84 &#89 &#32 &#84 &#72 &#69 &#79 &#82 &#69 &#77

ISO 10646 (1991-1993) (references)

0051 0055 0041 0044 0054 0052 0045 0045      0043 004F 004D 0050 004C 0045 0058 0049 0054 0059      0054 0048 0045 004F 0052 0045 004D

Encryption (beginner's substitution cypher): (references)

5155353854523939237494750463958435459254423949523947

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INDEX

1. Orthography
2. Bibliography


  

Copyright © Philip M. Parker, INSEAD. Terms of Use.