Obtain a quadratic approximation to a 2D Mapping
"
lbnd"
and "
ubnd"
. The Mapping must have 2 inputs, but
may have any number of outputs. The i’
th Mapping output is modelled as a quadratic
function of the 2 inputs (x,y):
output_i = a_i_0 $+$ a_i_1$\ast $x $+$ a_i_2$\ast $y $+$ a_i_3$\ast $x$\ast $y $+$ a_i_4$\ast $x$\ast $x $+$ a_i_5$\ast $y$\ast $y
The "
fit"
array is returned holding the values of the co-efficients
a_0_0, a_0_1, etc.
’
s Nin attribute. This box should specify the region over which the fit is to
be performed. "
lbnd[0]"
and
the last is at "
ubnd[0]"
. If a value less than three is supplied a value of three
will be used. "
lbnd[1]"
and the last is at "
ubnd[1]"
. If a value
less than three is supplied a value of three will be used. "
6$\ast $Nout"
, elements. The first 6 elements hold the fit to the first Mapping output. The next 6
elements hold the fit to the second Mapping output, etc. So if the Mapping has 2
inputs and 2 outputs the quadratic approximation to the forward transformation
is:
X_out = fit[0] $+$ fit[1]$\ast $X_in $+$ fit[2]$\ast $Y_in $+$ fit[3]$\ast $X_in$\ast $Y_in $+$ fit[4]$\ast $X_in$\ast $X_in $+$ fit[5]$\ast $Y_in$\ast $Y_in Y_out = fit[6] $+$ fit[7]$\ast $X_in $+$ fit[8]$\ast $Y_in $+$ fit[9]$\ast $X_in$\ast $Y_in $+$ fit[10]$\ast $X_in$\ast $X_in $+$ fit[11]$\ast $Y_in$\ast $Y_in
This function fits the Mapping’
s forward transformation. To fit the inverse
transformation, the Mapping should be inverted using astInvert before invoking this
function.
A value of zero will be returned if this function is invoked with the global error status set, or if it should fail for any reason.