On Mon, 29 Jul 2002 20:19:53 -0500, Dawn McKnight wrote:

> Tony LaVigne wrote:
>> Is the general equation for this sphere 1= (  (x-Xo)/40  )^2 + (
>> (y-Yo)/54  )^2  +( (z-Zo)/9.2 )^2   where (Xo,Yo,Zo) is the center of
>> the sphere?
> 
> Uh... I'm not sure.  Is that right?  You're setting it equal to one? Why
> not zero?  I'm confused.
> 

What Tony has done is put your values into the general equation of an
ellipsoid: ( (x-x0)/a )^2 + ( (y-y0)/b )^2 + ( (z-z0)/c )^2 = 1.
The point x0,y0,z0 is the center and a, b, and c are the semiaxes (or
"radii") in the x, y, and z directions respectively.  (This equation
isn't actually *totally* general; it doesn't take into account the
possibility of rotations.)  The fact that it's equal to one arises from
geometric considerations.

> I looked at the equation for the superquadratic elipsoid, which is in
> the docs, but it doesn't look like yours, and I'm not math-knowledgeable
> enough to get from one form to the other.
> 

The superquadric ellipsoid is a different beast.  :)

>> If so, and if the center of the sphere is (0,0,0) and your XY plane is
>> at z=0, then the equation might boil down to
> 
> That's a reasonable aproximation, yes.
> 
>> y= f(x) = sqrt{ [1-(x/40)^2] / [54^2]  }
> 
> When I plot that on my graphing calculator, I get an elipsoid shape that
> has the right x intercepts... but the y intercept is off by a factor of
> a thousand.
> 
> I'm not clever enough to figure out how to correct it....
 
This was probably a typo... I think it should be

y = f(x) = 54 * sqrt( 1 - (x^2)/(40^2) )


Good luck!

	-Ed

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