nurbs - Is it a reasonable to have the following in the BSpline? -

nurbs - Is it a reasonable to have the following in the BSpline? -

i have closed 3-order(degree 2) bspline has next parameters

9 command points 14 knot points

why relation 9 + 3 + 2 = 14?

the relationship between b-spline's order (n), number of command points (c) , number of knots (k) either

k = c + o - 2

or

k = c + o

the selection depends on convention used initial , final knots.

some libraries, opengl's old auxiliary library beingness of import example, store duplicate of initial , final knot value. these implementations have k = c + o. if examine algorithms used evaluating b-spilnes, duplicate initial , final knot values values not required. reason other libraries, opennurbs , rhino 3d's sdk beingness notable examples, have k = c + o -2.

more info available @ http://wiki.mcneel.com/developer/onsuperfluousknot

nurbs bspline opennurbs