equation for conic curve
equation for conic curve
(OP)
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?
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?





RE: equation for conic curve
(x/a)^2+(y/b)^2 = 1
RE: equation for conic curve
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?
RE: equation for conic curve
RE: equation for conic curve
RE: equation for conic curve