Question about interpCrv(interpolation curve) degree in relation to polynomial interpolation


(Andrew Jinho AHN) #1

rhino uses polynomial interpolation for its InterpCrv.
(http://docs.mcneel.com/rhino/5/help/en-us/commands/changedegree.htm#Degree)

Since polynomial interpolation method makes N-1 degree polynomial function(ex. to interpolate 5 points, highest polynomial degree is 4), where degree cannot be an option to change,

how does interpcrv function has a ‘degree’ input with it?

if I am interpolating N points into a curve, isn’t degree become automatically N-1?

Does ‘degree’ input in interpcrv has different meaning than ‘degree’ as used in polynimial function?


(Chuck Welsh) #3

Hi Andrew. NURBS curves are piece-wise polynomial. Each span is a (probably different) polynomial function of the given degree. If you call InterpCrv, degree=3, and choose 7 points, you get a degree 3 NURBS with 9 control points, so it has 6 spans. Each span is its own polynomial function of degree 3.


(Andrew Jinho AHN) #4

Thank you @chuck. I think I am finally getting a grasp on this matter but not quite there yet.

If span curves are mutually discrete N degree polynominals, since overall interpolated curve should be differentialble at any point withn the domain of curve, each span curve consisting interpolated curve are affected by ajacent span curve(s) to cope with G continuity which I think is going to be a progressive process(since none of the span curve can be definite to start with.) in algorithm wise. Is this right?


(Chuck Welsh) #5

Yes, that’s correct. The knot multiplicity determines the guaranteed degree of continuity at the breaks between adjacent polynomials separated by that knot.