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what is the purpose of this one ?
The tangent of the spline end is = the vector between last spline pole and the next to last spline pole.
If the distance between these two is zero, the tangent is undefined and obviously the curvature goes ...
Hi @1u7obd Thanks for your reply!
I try to develop an alternative to Combined Projection. The basic approach is to first create two splines in perpendicular sketches, e.g. two 6-pole splines, then use the two planar sets of poles (6×2) to produce a non-planar set of 6 poles, and finally create a 3D spline with the new set of 6 poles. Then it's possible for me to control the 3D spline with 2 sketches.
I'm not sure whether the attempt is reasonable not. I do want to control 3D splines as easily as control 2D splines in sketcher. Your comments would be appreciated. Thanks!
Maybe what you are looking for exists,
under the combine curve projection, toggle the advanced curve fit, then set the method to keep parameterization,
the resulting curve should have the same parameterization as your input curves.
In this case , single segment , degree 5.
Generally, if you make the first two (or the last two) poles of a spline coincident, you can expect some trouble. As another post mentioned, this will mean that the first derivative vector has zero length at the end-point, and there are quite a few cases where the obvious algorithm won't be able to deal with this situation. For example, the simple formulae for getting unit tangents and curvature both have the length of the derivative vector in the denominator of a fraction, so there's going to be trouble. It's not that the unit tangent or the curvature is undefined, it's just that the typical formulae for calculating them don't work, so the code has to do something rather more complicated. From your picture, it looks like the NX code for computing curvature combs isn't working properly, and that's not too surprising. I expect it could be fixed, but this is a pretty rare corner case, and there might be some performance implications, so developer effort is probably better spent elsewhere.
So, while there's nothing wrong with having coincident end poles in principle, they are likely to cause trouble, in practice, and you should probably avoid this.
Coincident poles in the middle of a curve will usually work OK.
There are some restrictions regarding construction of surfaces from splines that have coincident poles.
@FBergeron. You might be right. If the first three poles are collinear and distinct, then certainly the end curvature is zero (i.e. radius of curvature is infinite). But if the first two poles are coincident, I'm not yet convinced that the end curvature is zero. I'd have to do some math to make sure.
But, anyway, even if curvature analysis is working correctly, I'm sure there are other functions that will have trouble, so I still think that it's risky to have coincident poles at the end of a spline.
I did a little math, and it turns out that having end poles coincident does not necessarily cause the curvature to be zero at the end-point.
For example, take the single segment degree 4 curve with poles (0,0), (0,0), (1/6,0), (1/2,0), (1,1).
If you figure out the curve equation, it turns out to be just x(t) = t2, y(t) = t4. So, the curve is just y = x2, which is a parabola, of course. Its curvature at (0,0) is 2, radius of curvature is 0.5.
The curvature combs come out correct on this curve, so it looks like the curvature analysis function can deal with zero-length derivatives. But, I expect other things will go wrong.
Incidentally, I found it quite difficult to create this curve. NX tries to stop you making the first two poles coincident, and you have to do some work to defeat its efforts. I suppose these kinds of curves are not handled properly everywhere, so NX tries to discourage you from creating them.