Smooth surface & plane = multiknot curve - why?

This example contains a smooth, single span, degree 3 surface and a plane. The theoretical intersection of such a surface and plane is a smooth curve, though probably not exactly a NURBS curve. The result of intersecting the surface and the plane in Rhino is a curve with a multi-knot curvature discontinuity. Sectioning the surface results in a similar but not quite identical curve with a multi-knot curvature discontinuity. I have previously had similar discontinuities in intersection curves which should be smooth, sometimes with more pronounced discontinuites. Results are the same in V6 and WIP V7.

Why is there a multi-knot curvature discontiuity in the intersection curve? I understand that the curve cannot be represented exctly as a NURBS curve but I expect the result to be a smooth NURBS curve.

A customer has been evaluating fairness of surfaces by looking at the curvature combs of contour curves (results of using Contour command), and concluding that the discontinuities in the contour curves means the surface is not smooth.

Discontinuous01.3dm (58.4 KB)

Yeah…intersections are fitted curves and should only be relied upon in the most general way for assessing surface curvature, is my understanding. Out of curiosity, I used the test command, in V7, testFitSplitSurface, with MeetCurve=On. This generates two untrimmed surfaces, the edge curves of which match the input surface structure. I used your orange ‘Section’ curve as the input (I needed to ExtendSrf the surface so the curve did not end on the exact corner as well - test command…) The resulting edge curve is within .03 of the input (file tolerance .01) and has a rather nicer graph…

-Pascal