POV-Ray : Newsgroups : povray.general : isosurface functions : Re: isosurface functions Server Time
7 Dec 2022 08:01:42 EST (-0500)
  Re: isosurface functions  
From: Chris R
Date: 4 Mar 2022 10:20:00
Message: <web.62222dfd8c6c70add6fc33af5cc1b6e@news.povray.org>
Alain Martel <kua### [at] videotronca> wrote:

> > For some recent modeling work, I have had a need to create various objects based
> > on cylinder-based shapes, varying the radius of the cylinder based on the
> > y-axis.
> >
> > Examples:
> > sqrt(x*x+z*z) - Radius // cylinder
> > sqrt(x*x+z*z) - Radius*y/Height // inverted cone
> >
> > These seem to render as isosurfaces pretty consistently without high
> > max_gradients or the need for high accuracy.
> >
> > However:
> > sqrt(x*x+z*z) - Radius*(pow(y/Height,2)) // quadratic
> > or
> > sqrt(x*x+z*z) - Radius*sqrt(y/Height)
> >
> > is causing the object to look semi-transparent, allowing light to pass through
> > it in an almost even distribution.
> >
> > In a fit of frustration, after trying very high accuracy and max_gradient
> > values, I tried
> >
> > sqrt(x*x+z*z) - Radius*sin(0.5*pi*y/Height)
> >
> > and the object looks completely solid.
> >
> > So, I'm wondering what in the isosurface code could cause this difference?
> >
> > -- Chris R.
> >
> >
>
> What do you consider high and very high max_gradient ?
> Same for accuracy ?
>
> For sqrt(x*x+z*z) - Radius, the gradient should be barely above 1.
>
> For sqrt(x*x+z*z) - Radius*(pow(y/Height,2)), it tends to infinity
> around Height of zero. You are squaring a value that tent to infinity as
> it approach zero.
> Same for Radius*sqrt(y/Height), as y/Height tends toward infinity as
> height get near zero. Taking the square root delays it only slightly.
> Both will have at least some parts that go above max_gradient, even of
> you set it to 10000000 or more.
>
> One thing that you can do is to split the object. Pieces for the Height
> values larger than 0.01 and smaller than -0.01, and a slice for the
> -0.01..0.01 range. You may want to not use that slice at all.
>
> You may also hide the problem by using a container sized to not contain
> the problem area. contained_by{ sphere{0,5*Radius scale<1, 1000, 1>} }

Sorry, I should have been clearer in labeling the variables.  For any given
object, Radius and Height are fixed values, while x, y, and z vary over the
isosurface boundaries.  So, pow(y/Height,2) and sqrt(y/Height) both range
between 0 at y=0 and 1 at y=Height.


-- Chris R.


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