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How do I create a paraboloid where a slice through the object produces a
circle of a fixed and known size? Thanks!
Mike
--
http://isometricland.com
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Le 24/06/2011 04:03, SharkD a écrit :
> How do I create a paraboloid where a slice through the object produces a
> circle of a fixed and known size? Thanks!
Slice of paraboloid are circle only when the slice is perpendicular to
the axis of the paraboloid.
Ergo, if the slice is parallel to the z plane, the circle will be
a.(x²+y²) - b = 0
a.(x²+y²) is the square of the radius (r² := b).
If the equation of your paraboloid is (classical) z=k.(x²+y²), it seems
obvious that the slice must have a z so that k.(x²+y²) is the square of
the desired radius.
(i.e. #local z_position = sqrt( pow(r,2)/k ); )
--
Software is like dirt - it costs time and money to change it and move it
around.
Just because you can't see it, it doesn't weigh anything,
and you can't drill a hole in it and stick a rivet into it doesn't mean
it's free.
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Le 24/06/2011 09:05, Le_Forgeron a écrit :
> Le 24/06/2011 04:03, SharkD a écrit :
>> How do I create a paraboloid where a slice through the object produces a
>> circle of a fixed and known size? Thanks!
>
> Slice of paraboloid are circle only when the slice is perpendicular to
> the axis of the paraboloid.
>
> Ergo, if the slice is parallel to the z plane, the circle will be
> a.(x²+y²) - b = 0
>
> a.(x²+y²) is the square of the radius (r² := b).
>
> If the equation of your paraboloid is (classical) z=k.(x²+y²), it seems
> obvious that the slice must have a z so that k.(x²+y²) is the square of
> the desired radius.
>
> (i.e. #local z_position = sqrt( pow(r,2)/k ); )
Oups,
it's z_position = pow(r,2)/k;
Simpler that way.
--
Real software engineers work from 9 to 5, because that is<br/>
the way the job is described in the formal spec. Working<br/>
late would feel like using an undocumented external procedure.
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On 6/24/2011 9:51 AM, Le_Forgeron wrote:
> z_position = pow(r,2)/k;
But, what is k?
--
http://isometricland.com
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On 6/24/2011 3:07 PM, posfan12 wrote:
> On 6/24/2011 9:51 AM, Le_Forgeron wrote:
>> z_position = pow(r,2)/k;
>
> But, what is k?
>
Nevermind, got it to work. Thanks!!
--
http://isometricland.com
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On 6/24/2011 3:07 PM, posfan12 wrote:
> On 6/24/2011 9:51 AM, Le_Forgeron wrote:
>> z_position = pow(r,2)/k;
>
> But, what is k?
>
Here's my POV code:
#include "shapes.inc"
#local p_radius = 2;
#local p_scale = 2;
#local z_position = pow(p_radius,2)/p_scale;
intersection
{
object
{
Paraboloid_Z
scale p_scale
}
plane {+z,z_position}
pigment {color rgb 1}
}
cylinder
{
0, z*1, p_radius
translate z*z_position
}
--
http://isometricland.com
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On 6/23/2011 10:03 PM, SharkD wrote:
> How do I create a paraboloid where a slice through the object produces a
> circle of a fixed and known size? Thanks!
>
>
> Mike
>
>
OK, next challenge: the focus of the parabola must be located at the
center of the circle! I want to create a solar collector and need to
know the precise dimensions beforehand.
--
http://isometricland.com
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Le 26/06/2011 17:34, posfan12 nous fit lire :
> On 6/23/2011 10:03 PM, SharkD wrote:
>> How do I create a paraboloid where a slice through the object produces a
>> circle of a fixed and known size? Thanks!
>>
>>
>> Mike
>>
>>
>
> OK, next challenge: the focus of the parabola must be located at the
> center of the circle! I want to create a solar collector and need to
> know the precise dimensions beforehand.
>
>
http://en.wikipedia.org/wiki/Parabola
focus at <0,0,1/(4*k)>
for equation of paraboloid z= k(x²+y²)
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On 6/26/2011 11:47 AM, Le_Forgeron wrote:
> http://en.wikipedia.org/wiki/Parabola
>
> focus at<0,0,1/(4*k)>
>
> for equation of paraboloid z= k(x²+y²)
>
>
If you could use/modify the POV code in my previous post I would greatly
appreciate it, thank you.
Mike
--
http://isometricland.com
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