Harmonic Warping
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- | |ImageDesc= | + | Look at [[Blue Warp]] for more information to learn how the image that is tiled was created. |
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+ | [[Image:HarmonicWarp.png|thumb|]] | ||
+ | Essentially, an equation was used to map the points of | ||
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+ | *equation <math>d(x) = 1 - \frac{1}{1+x}</math>, limit is 1 | ||
+ | <math>d(y) = 1 - \frac{1}{1+y}</math>, limit is 1 | ||
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+ | * 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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|other=Single Variable Calculus | |other=Single Variable Calculus | ||
|AuthorName=Paul Cockshott | |AuthorName=Paul Cockshott |
Revision as of 14:55, 22 June 2009
- D
Basic Description
basic hereLook 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
- equation , limit is 1
, 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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Harmonic Warping |
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