Now I want to intersect each couple of curves with identical degrees (intersect the two with degree one; then intersect the two with degree two; then intersect the two with degree three and so on until intersect the two with degree eleven)

Generally when I create a copy of curve and move just one control point of the copied version, and then intersect the curve with itsâ€™ modified version, I supposed to see witch parts of the curve remains the same an witch parts change under the influence of that one control point: I supposed to see the range of influence of control points; ok?!

Intersect gives unpredictable results when used with curves or surfaces which partially coincide.

A simpler approach is to start with straight curves of differing degrees, and then move control points at a single location.

A key to understanding the range of influence of control points of NURBS curves and surfaces is the concept of â€śspansâ€ť. A curve of degree d with d+1 control points is a single span curve (sometimes called a Bezier curve) and each control point influences the entire curve (except for the points at the ends of the curve which are only influenced by the corresponding end control points.

A curve of degree d with n control points n > d+1 is a multi-span curve and will have n - d spans. A curve can be converted into a set of single span curves using the ConvertToBezier command.

Example with 11 control points and degree 1 though 6 curves: CPInfluenceDC.3dm (2.9 MB)

so we know unselected spans shows the range of influence of that control point

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Back to first post I did these steps for all the curves from degree 1 to 11 in that post and I marked the range of effect of control point with each degree with the number showing the degree

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After all I wanna to know about the logic behind ConvertToBezier command and span concept (I know some basics like how a Bezier curve of any degree is made); Please introduce some sources that describe these concepts (also) visually. (Something very deep of course, because I read many and couldnâ€™t fully understand things; most of them are really shallow)