Downloaded from https://www.everyspec.com APPENDIX C MIL-STD-31000A Greville points are the 3D locations on NURBS geometry evaluated at knot average values. The average knot values, called Greville abscissae, are defined as follows: Given a non-decreasing unique knot vector values {U0, U1, U2,...,Un), the Greville abscissae are defined by Gi = 1/D*Sum(Uj) where D = Degree over the knot vector i=0 to Number of control points j=i to (i+D-1) Thus, for a NURBS curve, C(u), the Greville points are evaluated as Pi=C(Gi) Similarly for a NURBS surface, S(U,V), a grid of Greville points are generated given the two non- decreasing unique knot vectors {U0,U1,U2,...,Un} and {V0,V1,V2,...Vn}.
The Greville abscissae for U and V directions are defined by Gi = 1/Du*Sum(Uj) Gk= 1/Dv*Sum(Vm) Where Du = Degree in the U direction Dv = Degree in the V direction i=0 to Number of control points in the U direction k=0 to Number of control points in the V direction j=i to (i+Du-1) m=k to (k+Dv-1) Then, the Greville points are evaluated as Pi,k = S(Gi,Gk) 72