Biconic surfaces

erich_grossman

I need to create a "biconic" surface, i.e. an ellipse in each principal plane, but different ellipses for x and y. I think it's a bad idea (futile?) to try to do it with ellipses and lofts or rotations. Need to just make a featurescript that defines z(x,y) algebraically, and smoothly interpolates through a (user-specified) number of samples points in x,y.
Does any one have such a FS?

MBartlett21

@konstantin_shiriazdanov
Do you have one?

EDIT: @mahir has one:
https://cad.onshape.com/documents/57a62df8e4b03de4c9fcf154

MBartlett21

@konstantin_shiriazdanov
Do you have one?

EDIT: @mahir has one:
https://cad.onshape.com/documents/57a62df8e4b03de4c9fcf154

konstantin_shiriazdanov

I have Variable section sweep FS see the description in this thread

lana

@erich_grossman
In this case you can use revolve followed by non-uniform scale 

erich_grossman

This creates uniform ellipsoids (same profile in the x-z and y-z planes). Sorry I wasn't clear enough with my question.
Erich 

lana

This creates uniform ellipsoids (same profile in the x-z and y-z planes). 

Not as far as I can tell.




Notice Transform 1 feature doing non-uniform scaling.

I added xRadius, yRadius, zRadius variables to explicitly control the ellipses.
If this is still not what you wanted, please sketch the profiles you want to fit and share the document here.

erich_grossman

Lana, This is a somewhat complicated bit of solid geometry, and I'm honestly not sure whether a triaxial ellipsoid (semidiameters a,b,c in the x,y,z direction), which is what nonuniformly scaling a sphere would give, is or is not equivalent to what I want. I'm coming from an optics context, where ellipses are characterized by R (vertex curvature) and delta (conic constant). The surface I want is a prolate ellipsoid (-1<delta<0) in the x-z plane and an oblate ellipsoid (delta>1) in the y-z plane. I have to get this *algebraically exactly* right since this an optical mirror, not just "looks right". I know that there is more than one way to interpolate between the two profiles, and I know the algebraic formula for the one I want, while I don't know exactly (algebraically) how OnShape would do it. For now, I will use Mahir's FS to do the algebraically correct thing. I would like to work out algebraically if the non-uniform scaling approach would work, but am not sure I'll have time.

ilya_baran

Scaling a sphere, like Lana (who is one of our top geometry experts, btw) suggests should yield an ellipsoid to machine precision (an ellipsoid *is* an affinely transfomed sphere -- you can specify it in multiple ways, but there is always an affine transform of a unit sphere that will get you any desired ellipsoid).  Mahir's FS will give a worse approximation to an ellipsoid if you pass in the ellipsoid equations, because it works by sampling and interpolating.

If however, what you want is not actually an ellipsoid, but rather some other oblong shape, non-uniform scaling won't give you the right result, and the custom feature will be the best you can do.  If you post your equation, chances are we'll be able to tell pretty quickly if it yields an actual ellipsoid or not.

lana

@erich_grossman
I see, indeed what you want is not an ellipsoid. Something like this? https://cad.onshape.com/documents/775a3c0cbfaedb3ab26e085f/w/99fccecaa8c76bcce71c66c8/e/6ce437f5c1472d745da0ec16