June 2014
Intermediate to advanced
233 pages
5h 42m
English
Content preview from Applied Calculus of Variations for Engineers, 2nd Edition
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140 Applied calculus of variations for engineers
The control points to provide a smooth approximation of the given geometric
surface are selected from the variational problem of
I(
s)
(f(x, y) − s(x, y))
2
dxdy = extremum.
Substituting the surface spline definition and sampling of the given surface
results in another, albeit more difficult, system of linear equations from which
the control point locations may be resolved in a similar fashion as in the case
of spline curves before.
Finally, it is also possible to describe some geometrical volumes with the
B-spline technology. Consider the form
s(u, v, t)=
n
i=0
m
j=0
p
l=0
B
i,k
(u)B
j,k
(v)B
l,k
(t)Q
ijl
,
where now
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