POV-Ray : Newsgroups : povray.general : Offset surface : Re: Offset surface Server Time: 19 Jan 2019 03:49:56 GMT
  Re: Offset surface  
From: Mike Horvath
Date: 20 Jul 2018 01:34:43
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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