     POV-Ray : Newsgroups : povray.general : Offset surface : Re: Offset surface Server Time: 24 May 2019 01:18:07 GMT  Re: Offset surface    From: And Date: 20 Jul 2018 14:05:00    Mike Horvath <mik### [at] gmail com> wrote:
> See here:
>
>
https://math.stackexchange.com/questions/2857219/formula-for-the-offset-curve-of-an-ellipsoid
>
> Mike
>
>
>
> On 7/19/2018 9:36 PM, Mike Horvath wrote:
> > On 7/19/2018 8:25 PM, Bald Eagle wrote:
> >>
> >> Also of interest:
> >>
> >> http://xahlee.info/SpecialPlaneCurves_dir/Parallel_dir/parallel.html
> >>
> >
> > Xah Lee says the parametric formula for an offset curve is
> >
> > { xf[t] + d yf'[t]/Sqrt[xf'[t]^2 + yf'[t]^2],
> >  Â  yf[t] - d xf'[t]/Sqrt[xf'[t]^2 + yf'[t]^2] }
> >
> > Not sure how to extend that into three dimensions. (I might be able to
> > make an SOR using that formula, but I'd rather not.)
> >
> >
> > Wikipedia says the parametric formula for an ellipsoid is
> >
> > \begin{align} > > x&=a\cos(\theta)\cos(\varphi),\\ > > y&=b\cos(\theta)\sin(\varphi),\\ > > z&=c\sin(\theta),\end{align}\,\!
> >
> > where
> > $> > -\frac \pi 2 \le \theta\le \frac \pi 2, > > \qquad > > -\pi\le \varphi\le \pi. > >$
> >
> > Not sure what the derivative of this is. (Calculus was years ago...)
> >
> >
> > Mike

Many years ago I ever do something for the same goal.
http://news.povray.org/povray.binaries.images/thread/%3Cweb.5264d1b954cff585cc1fd1150%40news.povray.org%3E/?ttop=423056
&toff=750

But not the same, I used the math formula, not parametric formula. And just suit
for a small offset(a thin shell)
Because it is just an approximation.    