I know that's a convoluted title, but let me explain further with some pictures.
What I have is this nice series of paths that have been blended so that they are all perfectly separated by even amounts of degrees. Cool!
Now, what I want to do here is to connect each of these segments like so: (I'm trying to make a fork...)
But here is my problem, and I have always wondered about this.
As soon as I click on the point to create my new rounded segment, my beautifully precise handle placement that is controlling the preceding curve is thrown out of whack by the tiny little tangent handle that I just dragged out.
Is there any way to preserve the placement of the preceding handle, and only allow the new handle to be dragged out in such a way that it is tangent to the preceding line? I hope you didn't have to read those sentences too many times to absorb their meaning.
The only workaround I have found is this: Direct select my existing point before I drag the new handle out. Then place two intersecting guides at it's current location. Then drag out the new handle and get it close to where I want it to be. Then go back to my previous handle and align it to the point where the guides intersect. This is hardly a perfect or quick solution though. It seems to me that there should be built in functionality for this type of thing. After all, the pen tool is pretty much at the heart of Illustrator's functionality.
Any suggestions would be very welcome.
It doesn't have anything to do with "defeating the underlying math of Bezier curves." It's just Illustrator's poor interface design for handling Bezier curves. Illustator's interface simply does not provide for extraction of retracted handles one at a time. Users of FreeHand (which does provide that) have been complaining about this since the 80s.