POV-Ray : Newsgroups : povray.general : Offset surface : Re: Offset surface Server Time: 18 Jan 2019 01:50:07 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],
>    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
> 
> <math>\begin{align}
> x&=a\cos(\theta)\cos(\varphi),\\
> y&=b\cos(\theta)\sin(\varphi),\\
> z&=c\sin(\theta),\end{align}\,\!</math>
> 
> where
> <math>
> -\frac \pi 2 \le \theta\le \frac \pi 2,
> \qquad
> -\pi\le \varphi\le \pi.
> </math>
> 
> Not sure what the derivative of this is. (Calculus was years ago...)
> 
> 
> Mike


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