POV-Ray : Newsgroups : povray.binaries.images : Thightening an iso? : Re: Thightening an iso? Server Time
14 Aug 2024 03:23:46 EDT (-0400)
  Re: Thightening an iso?  
From: Mark Weyer
Date: 17 Dec 2002 04:51:22
Message: <3DFEF608.2F5B61A6@frege.mathematik.uni-freiburg.de>
> Is it possible to have my isosurface make a "round" shape on the z axis
> between (-x), (x), (-y) and (y), given a sinusoidal function that I
> would define myself like this:
> #macro myFunc(xy, z)
>   #if(xy == 0)
>     d*cos(z)
>   #else
>     d*sin(z)
>   #end
> #end

I still do not quite understand, what you want.
I assume at least that it could be described by
some 2-dimensional shape that is rotated around
the z-axis as it moves along the same. In that
case you need to describe the 2D shape by some
2D isosurface (isoperimeter, that is). Lets say
that is described by f(x,y)=c. Then the 3D-shape
is described by
  f(x*cos(w*z)+y*sin(w*z),y*cos(w*z)-x*sin(w*z))=c
which gives an isosurface all right. Now what I
need to know is: What is your 2D-shape? In your
scene it is defined by
  a*(x^2+y^2)+b*x=c
or, equivalently,
  (x+b/2a)^2+y^2=c/a+(b/2a)^2
Now this is a circle with center (-b/2a,0) and
radius sqrt(c/a+(b/2a)^2). Maybe you would be
more happy with an ellipse? To define one with
radii rx in x-direction, ry in y-direction and
center (cx,cy) take
  f(x,y)=((x-cx)/rx)^2+((y-cy)/ry)^2
and threshold 1. I do not know the scale in your
scene, but maybe you would like to try
  w=1/3, cx=2, cy=0, rx=3, ry=1

Regards,
  Mark


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