Hi Burr,

> Do all conic curves have only those three points.

Well, all ones made with the conic tool do...

It's possible to have a curve that is a "conic section" that has more points in it though, for things like an ellipse or a circle. But those are actually the equivalent of several 3-point conic beziers that are glued together into a longer curve.

Also it is possible to have a conic sections that are defined by other ways than how the conic command happens to do it, so there is not necessarily an automatic Rho value to associate with every kind of possible conic curve, because the Rho only applies to the particular construction method of the "Conic" command. I don't think it is a thing that is universal that applies to every possible conic section if that is what you were thinking. There is something else called "eccentricity" that is like that - that is an inherent property of all conic sections. But that is different than the Rho value.

> I was more asking as a means to understand it's value and derivation.

I think it was historically used as a convenient way to describe a curve in compact form for use in airfoil tables or something like that.

If you want some more technical information, you could try The NURBS Book, 2nd edition, Les Piegl and Wayne Tiller, pg. 294, "Conics and Circles".

But basically it is just a way to control a shape by manipulating a parameter value.

If Rho < 0.5, the shape is an ellipse

If Rho = 0.5, the shape is a parabola

If Rho> 0.5 and < 1.0 the shape is a hyperbola

> and the value itself seems "relative" as a 0 to 1 ratio of "Whatever"?

If I remember right, it actually ends up as a percentage of the distance from the midpoint between the 2 endpoints being 0.0, and the point at the corner being 1.0. That's for a location of where the curve will pass through.

So for example say you've got these 3 shoulder points, where the distance from the corner to the line between the ends is 10 units like this:

If you make a conic there and type in 0.25 for the Rho value, that will place the high point of the curve at 25% of the distance, so in this case the high point of the curve will be at 2.5 units tall (25% of 10 units), like this:

Does that help?

Note that this also involves setting a special "weight" value on the control points of the curves to get the particular conic section shape.

Just because you see any curve that happens to be made up of 3 points does not necessarily mean it is a conic section curve.

- Michael