Harmonic Warping

(Difference between revisions)
 Revision as of 10:52, 23 June 2009 (edit)← Previous diff Revision as of 13:20, 23 June 2009 (edit) (undo)Next diff → Line 21: Line 21: *mapping (x,y) from Euclidean plane unto (d(x),d(y)) in rectangle *mapping (x,y) from Euclidean plane unto (d(x),d(y)) in rectangle - ===Polar Harmonic Warping=== + ==Polar Harmonic Warping== Here Here - ===Infinite Poles=== + ==Infinite Poles== Here Here

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

Here

Here