Class lsst::meas::astrom::SipForwardTransform

class SipForwardTransform : public lsst::meas::astrom::SipTransformBase

A transform that maps pixel coordinates to intermediate world coordinates according to the SIP convention.

The SIP forward transform is defined as

\[\begin{split} \left[\begin{array}{ c } x \\ y \end{array}\right] = \mathbf{Z} \left[\begin{array}{ c } (u - u_0) + {\displaystyle\sum_{p,q}^{2 \le p + q \le N}} \mathrm{A}_{p,q} (u-u_0)^p (v-v_0)^q \\ (v - v_0) + {\displaystyle\sum_{p,q}^{2 \le p + q \le N}} \mathrm{B}_{p,q} (u-u_0)^p (v-v_0)^q \end{array}\right] \end{split}\]
where

  • \((u,v)\) are pixel coordinates (zero-indexed).

  • \((x,y)\) are “intermediate world coordinates” the result of applying the gnomonic (TAN) projection at sky origin CRVAL to sky coordinates).

  • \(\mathbf{Z}\) is the \(2 \times 2\) linear transform ( \(\mathrm{CD}\)) matrix.

  • \((u_0,v_0)\) is the pixel origin \(\mathrm{CRPIX}\) (but zero-indexed; the FITS standard is 1-indexed).

  • \(\mathrm{A}\), \(\mathrm{B}\) are the polynomial coefficients of the forward transform.

The SIP convention encourages (but does not require) nulling the zeroth- and first-order elements of \(\mathrm{A}\) and \(\mathrm{B}\), which ensures the representation of a given transform is unique. This also makes fitting a SIP transform to data a nonlinear operation, as well as making the conversion from standard polynomial transforms to SIP form impossible in general. Accordingly, this class does not attempt to null low-order polynomial terms at all when converting from other transforms.

SipForwardTransform instances should be confined to a single thread.