POV-Ray : Newsgroups : povray.general : Offset surface : Re: Offset surface Server Time: 24 May 2019 01:26:06 GMT
 Re: Offset surface
 From: Mike Horvath Date: 20 Jul 2018 01:50:10
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