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Defining discrete function on intervals from mean of continuous function

Posted 10 years ago
I'm learning with Mathematica and I need an advice. I'd like to 'pixelize' a function. What I mean is, that I have continuous complex function
and I'd like to create new one defined by means of f in discrete intervals, that means something like this:
g[w]=Integrate[f[##], {Re[##], i, i + 1}, {Im[##], j, j + 1}]
for x from (i,i+1>
for y from (j,j+1>
for i from 1,...,10
for j from -10,...,10
Is it possible to define such function for the whole domain or at least part of it, f.e.
Thanks for any help given. There can be some mistakes in code above, I'm not familiar with Mathematica syntax yet, so I wanted to at least describe my problem. I'm also sorry for my English, I hope it makes sense.
POSTED BY: Jakub Lelek
2 Replies
Hello Jakub,
Here is a suggestion
pointAverage[function_, i_, j_] :=Integrate[function[x, y], {x, i, i + 1}, {y, j, j + 1}]

which takes a function defined wth two arguments and a grid point i,j.  For example:
 cfunc[x_, y_] := x Sin[Pi x] + y Cos[Pi y] I
 pointAverage[cfunc, 1, 2]
 pixels = Table[pointAverage[cfunc, i, j], {i, 1, 10}, {j, -10, 10}];
 Image[Im[pixels], ImageSize -> 200] // Colorize
Image[Re[pixels], ImageSize -> 200] // Colorize
Image[Arg[pixels], ImageSize -> 200] // Colorize

(*or another example*)

cfuncOther[x_, y_] := Exp[x + I y] (x + I y)

pointAverage[cfuncOther, 2, 2]

pixels = Table[pointAverage[cfuncOther, i, j], {i, 1, 10}, {j, -10, 10}] (*may take a while*)

Image[Arg[pixels], ImageSize -> 200] // Colorize
Image[Im[pixels], ImageSize -> 200] // Colorize
POSTED BY: W. Craig Carter
Posted 10 years ago
Thanks a lot, that was what I needed
POSTED BY: Jakub Lelek
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