# Harmonic Warping

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 Revision as of 13:55, 22 June 2009 (edit)← Previous diff Revision as of 13:56, 22 June 2009 (edit) (undo)Next diff → Line 4: Line 4: |ImageIntro=D |ImageIntro=D - |ImageDescElem=basic here + |ImageDescElem= Look at [[Blue Wash]] for more information to learn how the image that is tiled was created. Look at [[Blue Wash]] for more information to learn how the image that is tiled was created. |ImageDesc= |ImageDesc= - [[Image:HarmonicWarp.png|thumb|]] + [[Image:HarmonicWarp.png|thumb|300px]] Essentially, an equation was used to map the points of Essentially, an equation was used to map the points of

Harmonic Warping
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# Basic Description

Look at Blue Wash for more information to learn how the image that is tiled was created.

# A More Mathematical Explanation

Note: understanding of this explanation requires: *Single Variable Calculus

Essentially, an equation was used to map the points of

• eq [...]

Essentially, an equation was used to map the points of

• equation $d(x) = 1 - \frac{1}{1+x}$, limit is 1

$d(y) = 1 - \frac{1}{1+y}$, limit is 1

• distance compressing warp
• infinite tiling of Euclidean plane mapped onto a rectangle (or ellipse)
• mapping (x,y) from Euclidean plane unto (d(x),d(y)) in rectangle

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