We elect to use dimension 3 (3 physical coordinates) and codimension 2 (2 parametric coordinates) parametric B-splines.
Surface fitting is problematic because a unique parametric coordinate should be assigned to each geometric data point, and the precision of the fit is quite sensitive to the distribution of these parametric coordinates.
where (u, v) denote the u and v parametric coordinates of the vertices of V(x, y, z).
Direct parametric surface fitting requires that we first assign a unique parametric coordinate to each of the N vertices of V(x,y,z).
[??] = ([N.sub.bx] + 2) x ([N.sub.by] + 2) such that the distance between the geometric data points and points on the surface with the same parametric coordinate is minimized.