Obtain a linear approximation to a Mapping, if appropriate
’
s forward transformation within the specified
range of output coordinates. If the transformation is not sufficiently linear,
no coefficients are returned. ’
s Nin attribute. This box should specify the region over which linearity is
required. "
( Nin
$+$ 1 )
$\ast $ Nout"
, elements. The first Nout elements hold the constant offsets for the transformation
outputs. The remaining elements hold the gradients. So if the Mapping has 2
inputs and 3 outputs the linear approximation to the forward transformation
is:
X_out = fit[0] $+$ fit[3]$\ast $X_in $+$ fit[4]$\ast $Y_in
Y_out = fit[1] $+$ fit[5]$\ast $X_in $+$ fit[6]$\ast $Y_in
Z_out = fit[2] $+$ fit[7]$\ast $X_in $+$ fit[8]$\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.
If a Mapping output is found to have a bad value (AST__BAD) at one or more of the test points used in the linearity test, then all the values in the returned fit that correspond to that output are set to AST__BAD. However, this does not affect the linearity tests on the other Mapping outputs - if they are all found to be linear then usable coefficients will be returned for them in the fit, and the function will return a non-zero value. Consequently, it may be necessary to check that the values in the returned fit are not AST__BAD before using them. If all Mapping outputs generate bad values, then zero is returned as the function value.
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.
If all tested positions within the supplied box generate bad output positions, then the returned function value will be zero. However, the returned coefficients will represent a unit transformation, except that the constant term for each output will be set to AST__BAD.