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Description:
This
function returns the co-efficients of a quadratic fit to the supplied
Mapping over the input area
specified by 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_1x
a_i_2y
a_i_3xy
a_i_4xx
a_i_5yy
The FIT array is returned holding the values of the co-efficients a_0_0, a_0_1, etc.
Invocation
RESULT = AST_QUADAPPROX( THIS, LBND, UBND, NX, NY, FIT, RMS,
STATUS )
Arguments
THIS = INTEGER (Given)
Pointer to the Mapping.
LBND(
) =
DOUBLE PRECISION (Given)
An array containing the lower bounds of a box defined within the input
coordinate system of the Mapping. The number of elements in this array should equal the value of the
Mapping
’
s
Nin attribute. This box should specify the region over which the fit is to be performed.
UBND(
) = DOUBLE PRECISION (Given)
An array containing the upper bounds of the box specifying the
region over which the fit is to be performed.
NX = INTEGER (Given)
The number of points to place
along the first Mapping input. The first point is at LBND( 1 ) and the last is at UBND( 1 ). If a value
less than three is supplied a value of three will be used.
NY = INTEGER (Given)
The number of
points to place along the second Mapping input. The first point is at LBND( 2 ) and the last is
at UBND( 2 ). If a value less than three is supplied a value of three will be used.
FIT(
) =
DOUBLE PRECISION (Returned)
An array in which to return the co-efficients of the
quadratic approximation to the specified transformation. This array should have at least
"
6
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(1)
fit(2)X_in
fit(3)Y_in
fit(4)X_inY_in
fit(5)X_inX_in
fit(6)Y_inY_in
Y_out = fit(7)
fit(8)X_in
fit(9)Y_in
fit(10)X_inY_in
fit(11)X_inX_in
fit(12)Y_inY_in
RMS = DOUBLE PRECISION (Returned)
The RMS residual between the fit and the Mapping,
summed over all Mapping outputs.
STATUS = INTEGER (Given and Returned)
The global status.
Returned Value
AST_QUADAPPROX = LOGICAL
If a quadratic approximation was created,
.TRUE is returned. Otherwise .FALSE. is returned and the fit co-efficients are set to AST__BAD.
Notes:
-
This function fits the Mapping’
s forward transformation. To fit the inverse transformation, the
Mapping should be inverted using AST_INVERT before invoking this function.
-
A value of .FALSE. will be returned if this function is invoked with the global error status set, or if it
should fail for any reason.
Copyright (C) 2014 Science & Technology Facilities Council
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A Library for Handling
World
Coordinate Systems
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