[PD] [PD-announce] one over zed (a conformal function on the complex plane)

Mathieu Bouchard matju at artengine.ca
Mon May 10 19:14:53 CEST 2010


On Mon, 10 May 2010, Martin Peach wrote:

> It's easier to see what's going on using the colourbar from hello-world.pd.

But hello-world.pd is unrelated to moving pixels around like 
[#remap_image] does. [#remap_image] is like a giant [tabread] from outer 
space whereas hello-world.pd (or [#hello]) is not.

> The [# + (120 160)] doesn't seem to have any effect, while the [# - (120 
> 160)] changes the position of the image.

the [# +] (that goes into [#remap_image]) changes the position in the 
source image, which leads to a more interesting transformation, in which 
the borders of the tiles (which are circles) change radius.

the [# -] (that [#remap_image] goes into) only changes the position of the 
image.

basically, it's the same operation, but depending on whether you apply it 
before or after the inversion, it has a different effect on it. It's like 
when you plot (1/z)+c versus 1/(z+c).

In this case (using [# put (30000 0)]), it's (1/(z-c))+c, which is sort of 
a special case because 1/z is sandwiched between a -c step and a +c step, 
which are exact opposites of each other, and thus you can see it as the 
1/z is happening relative to a point other than (0 0). It's just that you 
choose the position of your simple pôle.

It's like when you do a [# -] [#rotate] [# +] sequence, you are rotating 
the coordinates around a different point than (0 0).

This concept of applying A then B then "undoing" the A, is very useful and 
I often put things between [# *] [# /] pairs, [# <<] [# >>] pairs, [# c2p] 
[# p2c] pairs, with same arguments.

  _ _ __ ___ _____ ________ _____________ _____________________ ...
| Mathieu Bouchard, Montréal, Québec. téléphone: +1.514.383.3801


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