Thies Heidecke wrote:
> Hi,
> 
> I'm currently experimenting with Fourier-Series as isosurface-functions.
> For those who don't know what Fourier-Series are, short explanation:
> The theory behind Fourier-Series is that every (periodic) function can
> be represented through addition of sine/cosine-waves with variable
> amplitude and a frequency that is an integer multiple of a certain
> base frequency. The increasing multiples of the base frequencies are
> called the harmonics of the basic tone. The amplitudes of the harmonics
> are the Fourier-coefficients. Now, one can approximate a function by
> adding just the first few (of usually infinite) harmonics. The more
> harmonics one adds the better the approximation is.
> This concept is very much used in audio-applications (e.g. mp3, EQs).
> My thought was, that it should now be possible to represent every
> possible 3D-shape through a set of 3 Fourier-series (one for each axis).
> That's the big target :)
> One could do cool filtering of 3D-Shapes and morphing from every possible
> 3d-shape to every other just by interpolating its Fourier-coefficients.
> How cool would that be? =)
> For now i've started to test a bit around with 'classic' Fourier-series
> for functions like pulse,sawtooth,triangle,etc...
> and for each axis the same function which makes it a symmetric shape like
> a cube.
> I've appended 2 pics which show what i have achieved so far.
> The first shows 7 distinct Fourier-series (from left to right):
> 1.Square(symmetry like cosine)
> 2.Square(symmetry like sine)
> 3.Triangle
> 4.Parabol
> 5.Sphere
> 6.Superellipsoid-like shape (no true SE)
> 7.an unnamed interesting series i found
> From the bottom to the top row the maximum harmonics taken into account
> increase. The bottom row is just the basic tone. The top row consists of
> the basic tone and 9 harmonics. The only exception is the first square
> function. Due to some technical issues it gets 2 harmonics per row, so
> the first has two and the last 20.
> I'd like to hear what you think about the idea and if someone had the same
> idea or perhaps even tried something like this before.
> 
> Greetings
>     Thies Heidecke
> 
> 
> 
> 

Great Idea!
Could you make an animation?

Sebastian H.

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