# Harmonic Warping

(Difference between revisions)
 Revision as of 12:58, 22 June 2009 (edit) (New page: {{Image Description |ImageName=Harmonic Warping |Image=Harmonic warp.jpg |ImageIntro=D |ImageDescElem=basic here |ImageDesc=detailed here |other=Single Variable Calculus |AuthorName=Paul C...)← Previous diff Revision as of 13:55, 22 June 2009 (edit) (undo)Next diff → Line 3: Line 3: |Image=Harmonic warp.jpg |Image=Harmonic warp.jpg |ImageIntro=D |ImageIntro=D + |ImageDescElem=basic here |ImageDescElem=basic here - |ImageDesc=detailed here + Look at [[Blue Warp]] for more information to learn how the image that is tiled was created. + + + |ImageDesc= + [[Image:HarmonicWarp.png|thumb|]] + 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 + + + + |other=Single Variable Calculus |other=Single Variable Calculus |AuthorName=Paul Cockshott |AuthorName=Paul Cockshott

Harmonic Warping
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# Basic Description

basic here

Look at Blue Warp 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

• equatio [...]

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