ST_Affine
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## Name

ST_Affine — Apply a 3D affine transformation to a geometry.

## Synopsis

`geometry ST_Affine(`geometry geomA, float a, float b, float c, float d, float e, float f, float g, float h, float i, float xoff, float yoff, float zoff`)`;

`geometry ST_Affine(`geometry geomA, float a, float b, float d, float e, float xoff, float yoff`)`;

## Description

Applies a 3D affine transformation to the geometry to do things like translate, rotate, scale in one step.

Version 1: The call

    ST_Affine(geom, a, b, c, d, e, f, g, h, i, xoff, yoff, zoff)

represents the transformation matrix

    / a  b  c  xoff \
    | d  e  f  yoff |
    | g  h  i  zoff |
    \ 0  0  0     1 /

and the vertices are transformed as follows:

    x' = a*x + b*y + c*z + xoff
    y' = d*x + e*y + f*z + yoff
    z' = g*x + h*y + i*z + zoff

All of the translate / scale functions below are expressed via such an affine transformation.

Version 2: Applies a 2d affine transformation to the geometry. The call

    ST_Affine(geom, a, b, d, e, xoff, yoff)

represents the transformation matrix

    /  a  b  0  xoff  \       /  a  b  xoff  \
    |  d  e  0  yoff  | rsp.  |  d  e  yoff  |
    |  0  0  1     0  |       \  0  0     1  /
    \  0  0  0     1  /

and the vertices are transformed as follows:

    x' = a*x + b*y + xoff
    y' = d*x + e*y + yoff
    z' = z

This method is a subcase of the 3D method above.

Enhanced: 2.0.0 support for Polyhedral surfaces, Triangles and TIN was introduced.

Availability: 1.1.2. Name changed from Affine to ST_Affine in 1.2.2

Prior to 1.3.4, this function crashes if used with geometries that contain CURVES. This is fixed in 1.3.4+

This function supports Polyhedral surfaces.

This function supports Triangles and Triangulated Irregular Network Surfaces (TIN).

This function supports 3d and will not drop the z-index.

This method supports Circular Strings and Curves

## Examples

    --Rotate a 3d line 180 degrees about the z axis.  Note this is long-hand for doing ST_Rotate();
     SELECT ST_AsEWKT(ST_Affine(geom,  cos(pi()), -sin(pi()), 0,  sin(pi()), cos(pi()), 0,  0, 0, 1,  0, 0, 0)) As using_affine,
    	 ST_AsEWKT(ST_Rotate(geom, pi())) As using_rotate
    	FROM (SELECT ST_GeomFromEWKT('LINESTRING(1 2 3, 1 4 3)') As geom) As foo;
            using_affine         |        using_rotate
    -----------------------------+-----------------------------
     LINESTRING(-1 -2 3,-1 -4 3) | LINESTRING(-1 -2 3,-1 -4 3)
    (1 row)

    --Rotate a 3d line 180 degrees in both the x and z axis
    SELECT ST_AsEWKT(ST_Affine(geom, cos(pi()), -sin(pi()), 0, sin(pi()), cos(pi()), -sin(pi()), 0, sin(pi()), cos(pi()), 0, 0, 0))
    	FROM (SELECT ST_GeomFromEWKT('LINESTRING(1 2 3, 1 4 3)') As geom) As foo;
               st_asewkt
    -------------------------------
     LINESTRING(-1 -2 -3,-1 -4 -3)
    (1 row)

## See Also

ST_Rotate, ST_Scale, ST_Translate, ST_TransScale

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