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.