"Curve discontinuity" node

[portnov]

Discontinuity of 1st curve is visible as a break (crisp) on the curve. Here we check only for "Geometric" continuity, which means that we only check directions of curve tangents, but do not check tangent lengths.

Here we check for "parametric" continuity instead of "geometric". Now we see two points of discontinuity. Point 1 is the same; at point 2, with curve's control polygon displayed we can see that control points are not symmetric around this point, in this case this means that curve tangent vector at the right of this point have much more length, than curve tangent to the left of this point.

Since this curve is composed of several Bezier segments, in all points where these segments are "glued" together there are points of discontinuity of 2nd order. If you look at curvature comb near these points, you can see that it can be discontinuous ("broken"). I.e., at these points curve's curvature may change suddenly.

This is a generic NURBS curve. It does not have discontinuity points of 1st or 2nd order. But it has discontinuity points of 3rd order; At these points the curve itself looks pretty smooth, but if you look closely at curvature comb you can see that, albeit continuous, curvature comb is not smooth at these points.

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• Code changes complete.
• Code documentation complete.
• Documentation for users complete (or not required, if user never sees these changes).
• Manual testing done.
• Unit-tests implemented.
• Ready for merge.