Thanks for the examples!
Some time ago I theorized the possibility to implement in Csound an
oscillator in which a variable bi-dimensional phase (i.e.an orbit) gives
the x-y coordinates of a
tri-dimensional continuos surface generating the amplitude values of the
output. Actually, in the case of very complex surfaces the lookup table
method can
save processing time during Csound performance.
The shape of the orbit (for example circular, elliptical,
cycloid or any other shape) as well as its translation in the x-y plane
could be modified during the performance of a note, giving a dynamic
timbre. One of the problems is to define bi-dimensional tables (in which
the 3-D surface will be stored)  in Csound.
Another problem is interpolation (to increase sound quality and reduce
table length): how can I interpolate the points falling into the area
bounded by the triangles of the 3-d surface table?
I believe that it is possible to extend this concept beyond the 3rd
dimension, creating 3d orbits pointing to a four-dimensional surface
(but at present time I have not the mathematical background to formulate
this process).

Any idea?

--
Gabriel Maldonado

mailto:g.maldonado@agora.stm.it
http://www.agora.stm.it/G.Maldonado/home2.htm
http://www.geocities.com/SiliconValley/Way/7041/home2.htm



Hans Mikelson wrote:

> Hello,
>
> I was in the book store tonight paging through Curtis Rhoades' (sp?)
> book
> on Computer Music and noticed a page with a picture of a surface being
>
> traced by an orbit.  I've had a small collection of complex 3D
> surfaces of
> the form Z(x,y) which I wasn't sure how best to use to generate
> sounds.  In
> the past I had just rastored through them snaking back and forth.
> Using
> orbit opens up a large number of possibilities.  For example a
> circular
> orbit could trace along the surface and the Z(x(t), y(t)) is taken as
> the
> amplitude.  Modulations could be applied to the circle center point,
> circle->ellipse.  Instead of circular orbits chaotic oscillators could
>
> define the X, Y coordinates although these would not be tuned.
>
> I think something like the following will work:
>
> y=sin(t)
> x=cos(t)
>
> Z(x, y)=sin^2*(sqrt(x^2+y^2))
> Z(x, y)=ln(x^2+y^2)
> Z(x, y)=x-1/12*x^3-1/4*y^2+1/2
> Z(x, y)=-5*x/(x^2+y^2+1)
> Z(x, y)=1/3*x^3-x*y^2
> etc...
>
> These equations are from Clifford Pickover's "Computers and the
> Imagination"
> Start oscil can be used to generate sine and cosine.  Then modulate by
>
> varying radius, center etc.  This opens up a large class of
> synthesis...
>
> Bye,
> Hans Mikelson