Akima. Algorithm 761. Scattered data surface fitting (TOMS1996)(T)(10s).djvu: eKnigu

Akima. Algorithm 761. Scattered data surface fitting (TOMS1996)(T)(10s).djvu

Size 0.1Mb
Date Dec 18, 2004

In the Fortran notation, these six functions are written as
F1(X, Y) = 0.75*EXP(-((9.0*X-2.0)**2+(9.0*Y-2.0)**2)/4.0)
1 +0.75*EXP(-((9.0*X+1.0)**2)/49.0-(9.0*Y+1.0)/10.0)
2 +0.50*EXP(-((9.0*X-7.0)**2+(9.0*Y-3.0)**2)/4.0)
3 -0.20*EXP(-(9.0*X-4.0)**2-(9.0*Y-7.0)**2)
F2(X, Y) = (TANH(9.0*Y-9.0*X)+1.0)/9.0
F3(X, Y) = A.25+COS*E.4*Y))/F.0*A.0+C.0*X-1.0)**2))
F4(X, Y) = EXP(-81.0*((X-0.5)**2+(Y-0.5)**2)/16.0)/3.0
F5(X, Y) = EXP(-81.0*((X-0.5)**2+(Y-0.5)**2)/4.0)/3.0
F6(X, Y) = SQRTF4.0-81.0*((X-0.5)**2+(Y-0.5)**2))/9.0-0.5
Franke tested the methods on the following data point sets:
A) a somewhat uniform 100-point set;
B) a sparse 33-point set; and
C) a 25-point set...
Since the patterns for rms errors are
somewhat similar to those of mean errors, Renka dropped the rms errors,
and we follow suit...