equation for conic curve

[boffin5]

Any cad system appropriate for aerospace has a conic curve function, where you can create a conic curve and change its shape with a rho parameter. Rho = .5 gives a parabola, and greater or lesser gives hyperbolas and ellipses, respectively.
What I am looking for is a cartesian equation incorporating the rho value that will give me point coordinates.
This will help me to create a spreadsheet to determine the volume of a propellant tank with conic section domes.
Any leads on such an equation?

 

[rb1957]

do you mean like the equation of an ellipse ...
(x/a)^2+(y/b)^2 = 1

 

[prost]

not knowing how 'rho' is used, one could only guess. By looking this up on the Internet, I found the general form for a conic:
Ax*x + Bxy + Cy*y + Dx + Ey + F = 0

Which type of curve you get depends on the value of the
discriminant D, in which D is D==B*B-4*A*C

If D=0 then curve is parabola, 2 parallel lines, 1 line or no curve.
If D<0 then curve is ellipse, circle, point or no curve.
If D>0 then curve is hyperbola or 2 intersecting lines.

You could artificially define another, auxiliary
constant called G, for instance, in which G==D+0.5.
In that way, when G=0.5, D=0, means you get parabola, 2
parallel lines, 1 line, or no curve.

In any case, you can see by doing this that you really do not necessarily get 1 of 3 curve types, parabola, ellipse, or hyperbola just by varying G or D--you could get one of the other object types: 2 parallel lines, 1 line, no curve, point, or 2 intersecting lines. There is quite a bit of ambiguity (and flexibility) built into the General Conic Equation above. Perhaps the CAD system you are using defines its own conic equation--shouldn't the Help manuals have this information?

 

[Compositepro]

According to the MMachinery's Handbook volume of an ellipsoid is (4/3)Pi(a)(b)(c), where a,b,and c are the radii of the three axes of revolution.

 

[boffin5]

Thanks for the help. I have gone through approaches similar to your suggestions, but the problem is holding tangencies at the ends of the curve. I think the answer is to define a pseudo conic curve with a Bezier curve, if I ever learn how to do it.

 

[Compositepro]

That was one of the points of the ellipsoid equation. If you cut the ellipsoid in half the tangents of the surface will blend into a cylinder with no discontinuity of slope. Using it in any other way would make for some more difficult math. But that is exactly what you want. I belive for your pupose b=c.