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Solid Works Curve Fit Limitations (Splines are it?)

Solid Works Curve Fit Limitations (Splines are it?)

Solid Works Curve Fit Limitations (Splines are it?)

(OP)
As a new SW user, I am a little suprised at what seems to be a serious limitation in its paramtric curve/surface modeling.  Or perhaps I am still a bonehead novice, and haven't figured out how to use equations!

Often times you may have a complex surface upon which you know specific points.  A spline is sometimes a good choice to model this.  Other times, though, an algabraic representation is MUCH better.

For instance, it is pretty easy to get polynomial curve fits to the 10th plus order that can represent very complex surfaces.  In my case I am modeling hydraulics for centrifugal pumps.  

Is there a way to do the following that I am missing/have not yet figured out:?

1.  Create a parametric curve (to be used as a profile for a surface of rotation) where y=f(x) = high order polynomial across some defined x bound (say 1.3 to 10 for instance)

2.  Once this curve is used to create a surface of revolution, I need another parametric curve to represent a 3D curve 100% coincident on the revolved surface.  In This case it is easiest to use cylindrical coordinates, R, Theta and Z (where R=SQRT(x2+y2) from above).  (BTW, what was my x axis above in #1, is now my Z axis)

This second curve is sort of like a helix, and it sits 100% conincident on the surface.  R changes with Z (but not with Theta because of course every section through the SURFACE normal to z is a circle.  So this new curve, in the cylindrical coordinates will be defined by the following:

R=f(z)  This polynomial is of the same exact form as in #1.  This in effect insures my curve is 100% conincident with the surface.
 
AND

Theta = f(z)  This can be any function.  A simple helix type curve would be F(z) = constant*z.

I can not find a way to do this ELEGANTLY.  It seems so simple using an algbraic approach.  But in SW I have to do all the above work, but then plot the profile curve as a series of points that make up a spline. (A design table would help here, but it is still extra work)  I then have a surface made by a revolved spline.  I then do the same for the 3D spline, evalutation both my polynomials to get a series of x,y,z points.  I then use these to define a 3D spline.  The weird thing is that the spline surface and 3D curve, shuould be 100% coincident, but the fits don't work that well, and when I use the curve to create a vane, I have to extend the surfaces back/normal to my surface to cove some gaps.

It all seems like a LOT of work for a surface and curve on a surface which could be represented by TWO SIMPLE polynomials.  Any suggestions??

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