VARKON Version 1.15 1997-10-16

### The bicubic parametric surface

A CUB_SUR is either defined by interpolation or by approximation. Lets begin with a look at interpolation...
sur_splarr(id,method,nu,nv,p,tu,tv,twist);
Suppose we have a nu=10 by nv=20 rectangular grid of positions. In that case p is a two-dimensional array of positions declared as follows...
VECTOR p(10,20);
Optional arrays declared the same way with tangents in the U-direction (tu) and V-direction (tv) can be supplied as well as twist vectors (tw). Any tangents not supplied will be splined using the Variable Stiffness Spline algorithm and twist vectors will be calculated using the named method.
sur_splarr can also be used to interpolate data created in other systems. Using MBS it is easy to open a file and copy data to internal variables before calling sur_splarr.
Approximation is done using....
sur_approx(id,other_surface,"CUB_SUR",method,tol_1,tol_2);
The quality of the approximation is controlled by method and 2 optional tolerance values. One method is to use a fix number of evenly distributed patches. Another method is to let the system adjust the number of patches so that a maximum value of positional error or error in normal direction is not exceeded.
MBS can also be used to export a CUB_SUR. Patch coefficients are available through a get routine and any geometric data is easy to retrieve using on, norm or eval.

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