AST_QUADAPPROX

Obtain a quadratic approximation to a 2D Mapping

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 " 6Nout" , 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: