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Hi,
I was reading the manual about planes, and I saw that povray uses the
equitation: A*x + B*y + C*z = D*sqrt(sqr(A) + sqr(B) + sqr(C))
Now I was wondering, why that sqrt(sqr(A) + sqr(B) + sqr(C))? Isn't it
enough to have A*x + B*y + C*z = D?
Remco Poelstra
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hello,
they both describe plane but the one used in pov-ray allows to describe the
*real* distance from the origin to the plane with the 'D' value, while in
the other it describes the distance from origin to where the plane cut axis
Baillp
ps : you should say "equation" not "equitation" ;)
3A2### [at] home nl...
> Hi,
>
> I was reading the manual about planes, and I saw that povray uses the
> equitation: A*x + B*y + C*z = D*sqrt(sqr(A) + sqr(B) + sqr(C))
> Now I was wondering, why that sqrt(sqr(A) + sqr(B) + sqr(C))? Isn't it
> enough to have A*x + B*y + C*z = D?
>
> Remco Poelstra
>
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Normally you wouldn't need it, but POV-Ray describes a plane a bit
differently and normal geometry would. In POV-Ray, D is the minimum
distance from the origin to the plane. It is envsioned by going D units
along the normal vector of the plane <A,B,C> and putting the plane there
In normal mathematical circumstance, D is not the mininum distance from
the origin to the plane, it has a different meaning.
For instance, mathematically, if you have a plane with normal vector
<1,1,2> and it goes through point <2,1,3>, it satisfies the equation 1*2 +
1*1 + 2*3 = D, so D= 9.
In POV-Ray, the same plane would have the same normal vector, but the
disatance from the plane is less than 9.
Josh
Remco Poelstra wrote:
> Hi,
>
> I was reading the manual about planes, and I saw that povray uses the
> equitation: A*x + B*y + C*z = D*sqrt(sqr(A) + sqr(B) + sqr(C))
> Now I was wondering, why that sqrt(sqr(A) + sqr(B) + sqr(C))? Isn't it
> enough to have A*x + B*y + C*z = D?
>
> Remco Poelstra
--
Josh English -- Lexiphanic Lethomaniac
eng### [at] spiritonecom
The POV-Ray Cyclopedia http://www.spiritone.com/~english/cyclopedia/
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Pascal Baillehache wrote:
>
> ps : you should say "equation" not "equitation" ;)
>
...and I already have thought, it has something to do with horses (from
equus (lat.) = horse).
;-))
ReVerSi
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Josh English wrote:
> Normally you wouldn't need it, but POV-Ray describes a plane a bit
> differently and normal geometry would. In POV-Ray, D is the minimum
> distance from the origin to the plane. It is envsioned by going D units
> along the normal vector of the plane <A,B,C> and putting the plane there
>
> In normal mathematical circumstance, D is not the mininum distance from
> the origin to the plane, it has a different meaning.
> For instance, mathematically, if you have a plane with normal vector
> <1,1,2> and it goes through point <2,1,3>, it satisfies the equation 1*2 +
> 1*1 + 2*3 = D, so D= 9.
> In POV-Ray, the same plane would have the same normal vector, but the
> disatance from the plane is less than 9.
Thanks both!
Where I need this information for, is a little program I'm writing,
which does some calculations at points/planes. I want to calculate the
distance of a point to a plain, with :
abs(A*x+B*y+C*z-D)/sqrt(sqr(A)+sqr(B)+sqr(C)). I use that distance for
some things and want the result being displayed by povray, but when
povray uses another equation, the graphic would be false. How do I have
to calculate the distance in my program, so that my calculations are
correct with what povray displays?
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abs((A*x+B*y+C*z)/sqrt(sqr(A)+sqr(B)+sqr(C))-D)
will do the job
Baillp
3A2### [at] homenl...
> Thanks both!
> Where I need this information for, is a little program I'm writing,
> which does some calculations at points/planes. I want to calculate the
> distance of a point to a plain, with :
> abs(A*x+B*y+C*z-D)/sqrt(sqr(A)+sqr(B)+sqr(C)). I use that distance for
> some things and want the result being displayed by povray, but when
> povray uses another equation, the graphic would be false. How do I have
> to calculate the distance in my program, so that my calculations are
> correct with what povray displays?
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Pascal Baillehache wrote:
> abs((A*x+B*y+C*z)/sqrt(sqr(A)+sqr(B)+sqr(C))-D)
> will do the job
Ok, thanks!
Remco
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Thank you, I was thinking this, but I didn't have a chance to answer last
night.
Josh
Pascal Baillehache wrote:
> abs((A*x+B*y+C*z)/sqrt(sqr(A)+sqr(B)+sqr(C))-D)
> will do the job
>
> Baillp
>
> 3A2### [at] homenl...
> > Thanks both!
> > Where I need this information for, is a little program I'm writing,
> > which does some calculations at points/planes. I want to calculate the
> > distance of a point to a plain, with :
> > abs(A*x+B*y+C*z-D)/sqrt(sqr(A)+sqr(B)+sqr(C)). I use that distance for
> > some things and want the result being displayed by povray, but when
> > povray uses another equation, the graphic would be false. How do I have
> > to calculate the distance in my program, so that my calculations are
> > correct with what povray displays?
--
Josh English -- Lexiphanic Lethomaniac
eng### [at] spiritonecom
The POV-Ray Cyclopedia http://www.spiritone.com/~english/cyclopedia/
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