Hi Scott, the "real" control points for an exact circle actually look like what you see there on the top with the segmented pieces. As you see they're not very squishable because of those corner points between arc pieces.
When you turn on control points for a circle, MoI actually shows you control points of an automatically rebuilt version since it assumes that you want to squish around some of those points and that you want a squishy result.
That kind of alternate "squishy" points method will only happen if a whole curve is an exact circle, arc, or ellipse, not when only one segment of it is. That's why you get the different look after the join.
Probably the easiest way to get a squishy result without corner points is to use the Rebuild command on it, see here for some info:
http://moi3d.com/2.0/docs/moi_command_reference10.htm#rebuild
The Rebuild command will reconstruct a curve by sampling points along it and building a new curve going through those points. Part of what it does is if you have smoothly meeting segments (different segments will always meet at a type of point that will make a sharp corner if you disturb it, they're basically different curve pieces glued together at their endpoints only) it will take those segments and build just one single smooth segment out of them.
Since you want squishable pieces it also may not be bad to run Rebuild on your circle before you join it in, that will convert it from one of the "exact but segmented" circle type splines to a general spline that does not have any internal segmentation in it.
Let me know if any of this does not make sense. Basically often times for precise conic section curves (exact arcs, circles, ellipses, etc...) they are often made up of internal sub segments which then do not deform very well.
- Michael
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