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

[Martin Peach]

Mathieu Bouchard wrote:
> 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.

Of course, I just meant that it's easier to see the transformation that 
[#remap_image] is applying with a simple fixed image.

> 
>> 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.
> 

So I probably need to use an source image that has texture in both 
dimensions, as with vertical bars it does nothing obvious.

> 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.

for anything non-commutative, where [a then b] is not the same as [b 
then a].

I attached my hacked-up version of your patches.

Martin

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