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beziers and lathe (by John Griessen)
I'm using the bezier curve creator function and see that a curve can contain 11 points and no more. If I want a smooth shape, (2nd derivative smooth), do I place curve endpoints together, then arrange the two control points near them and those coincident points to all be on a line?
Thu Apr 9 2015, 23:07:02
(no subject) (by Paul)
The point next to the endpoint of a spline sets the slope at the end. So using the same endpoint for two splines and making sure the first control point of each one is in line with those endpoints will get you a C1 smooth curve. I'm not sure what additional constrain may be required for C2, but it may be that those control points are equidistant from the common end point. Either way, this is different than having an actual bezier with more control points, but it may be useful to you anyway.
Sun Apr 12 2015, 19:24:14
(no subject) (by Paul)
Wow, I read that back and it's hard to follow! To get smooth curves, just make sure the beziers share a common end point. Then select both curves and click the parallel constraint button.

Visually you'll see that the 2 control points nearest to where the splines connect always stay collinear. I'm not sure if this is C1 or C2 continuity - I suspect C1.
Mon Apr 13 2015, 17:27:28
(no subject) (by Jonathan Westhues)
G1, really; parametric continuity isn't meaningful here.

The constraints for G2 would be rather complex. If you just want a nice-looking curve, then it's probably better just to constrain it G1 and drag the points to taste.
Mon Apr 13 2015, 22:05:27
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