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?



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Feeler

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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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Le_Forgeron <lef### [at] freefr> wrote:
> 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)


Thanks a lot. Its very helpfull to me. But these quadric equations formed
infinite hyperboliod and peraboloid. Is there a way to limit these to.
I have a starting point and a height point i.e. I have to make it between these
two point, is it possible?

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Le 05/08/2015 05:18, Feeler a écrit :
>
> Thanks a lot. Its very helpfull to me. But these quadric equations formed
> infinite hyperboliod and peraboloid. Is there a way to limit these to.
> I have a starting point and a height point i.e. I have to make it between these
> two point, is it possible?
>

you can add the object modifier "clipped_by { ... }" to limit the region 
of space in which an object such as a quadric is to be present.

for the paraboloid, the easiest value for ... is a plane (remember that 
povray's plane are not just an infinite surface, it's also an infinite 
volume splitting the universe in two).

You "just" have to position the plane at the "height point", with the 
normal away from the starting point.

For the hyperboloid, a box is probably what you are expecting. The 
delicate part is to compute the two corners from your two points. 
(that's easy is the hyperboloid is along the axis, it becomes less easy 
if it is rotated in the formula itself)

quadric { < 1, 0, 1> ,< 0, 0, 0>,< 0, -1, 0>, 0
    clipped_by { y, 4 }
         }

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Le 05/08/2015 07:28, Le_Forgeron a écrit :
>
> quadric { < 1, 0, 1> ,< 0, 0, 0>,< 0, -1, 0>, 0
>     clipped_by { plane { y, 4 } }
>          }

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