POV-Ray : Newsgroups : povray.advanced-users : How to make Elliptical Hyperboloid and paraboloid : Re: How to make Elliptical Hyperboloid and paraboloid Server Time
14 May 2024 11:13:30 EDT (-0400)
  Re: How to make Elliptical Hyperboloid and paraboloid  
From: Le Forgeron
Date: 4 Aug 2015 03:49:36
Message: <55c06e90$1@news.povray.org>
Le 04/08/2015 07:47, Feeler a écrit :
> I'm trying to make a elliptical hyperboloid like
>
> http://img.ctrlv.in/img/15/08/04/55c051410afa4.png
> and
> paraboloid like
>
> http://img.ctrlv.in/img/15/08/04/55c0511271b75.png
>
> As I was searching on POV-Ray I got
> http://www.povray.org/documentation/view/3.6.1/471/
>
> Is there a good way to draw these two? Is there any macro for these?
>

no real need of macro, your two objects are basic quadric.

If you get the equations for them, the transcription is easy

http://www.povray.org/documentation/3.7.0/r3_4.html#r3_4_5_3_6

For instance, a paraboloid on y axis, with circular base is

quadric { < 1, 0, 1> , <0, 0, 0>, < 0, -1 , 0>, 0 }

(To reverse it's direction, toggle the minus sign.
To translate it along the y axis, change the single 0 at the end.)

An hyperboloid can have 2 forms: one with a single surface (sheet), 
another with two sheets.

http://mathworld.wolfram.com/Hyperboloid.html

http://mathworld.wolfram.com/EllipticHyperboloid.html

quadric { < a2, b2, -c2> , <0,0,0>,<0,0,0>, -1 }

for an hyperboloid along z axis (a2, b2 and c2 being the squared 
coefficients of the reference ellipsoid)


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