NURBS
The NURBS (nonuniform rational B-spline) curve is defined by expandable arrays of knots, weights, and control points.
Data Format:
degree Degree of the basis function
params[] Array of knots
weights[] Array of weights for rational
NURBS, otherwise NULL.
c_pnts[][3] Array of control points
params[] Array of knots
weights[] Array of weights for rational
NURBS, otherwise NULL.
c_pnts[][3] Array of control points
Definition:
k = degree of basis function
N = (number of knots) - (degree) - 2
wi = weights
Ci = control points (x, y, z) * wi
Bi,k = basis functions
N = (number of knots) - (degree) - 2
wi = weights
Ci = control points (x, y, z) * wi
Bi,k = basis functions
By this equation, the number of control points equals N+1.
References:
Faux, I.D., M.J. Pratt. Computational Geometry for Design and Manufacture. Ellis Harwood Publishers, 1983.
Mortenson, M.E. Geometric Modeling. John Wiley & Sons, 1985.