degree. Each curve is defined by four interpolating points, whose vertical position, the Z coordinate, is variable. Each variable point can move within the confines of a vertical line 20 meters long, they can move 10 meters above or 10 meters bellow the starting point Z = 0. By modifying the coordinate of the interpolating point, the section curves change and so does the surface. In such a way, a set of 12 real numbers is used to completely define the surface shape. The other NURBS parameters of the surface, as the degree of interpolating functions or the number and position of control points, are set constants in the problem. We have established that there are a total of 16 control point in the surface, but 4 of them are not variable. Also we established that only the Z coordinate of these points is variable, so we can say that the number of variables in this problems is equal to 12. This gives us a vector of variables X where: X = z1 , z2 , z3 , z4 , z5 , z6 , z7 , z8 , z9 , x10 , z11 , z12
(10.2)
We can also se this vector in a more general way: X = x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8 , x9 , x10 , x11 , x12
(10.3)
where in this case xith = zith .
(a)
(b)
(c)
(d)
(e)
(f )
Figure 10.4: Possible individuals with the parametric model developed for the roof Problem.
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