[postgis-users] use of the affine() function

[Dylan Beaudette]

On Monday 28 May 2007 13:51, Martin Davis wrote:
> In order to turn a set of [src, dest] coordinate pairs into an affine
> transformation, you have to solve a system of linear equations.  The
> solution is the entries in the require affine transformation matrix.  In
> order to fully determine an affine transformation you need 3 control
> points and their images under the transformation.
>
> I don't know if PostGIS has this functionality available, but if you can
> hack Java (so to speak) JTS provides a class called
> AffineTransformationBuilder which can do this.
>

Martin,

Thanks for pointing this out. I was suspecting that solving the affine matrix 
equation was the only way to do this. It turns out that there is a simple 
way[1] to do this in R, as suggested by Prof Brian Ripley on the R-help 
mailing list. I am not completely sure if the resulting matrix is formatted 
in the way that the PostGIS affine() function is expecting it.

attached is a sample figure of 'good' (red) and 'bad' (black) control points, 
with the affine transformation.

Here is the solution to the affine equation:
                    nx          ny
(Intercept) 4.67820316 5.073777014
x           0.99583870 0.002349727
y           0.01727790 1.002291282

.. i will do some checking and post a complete example once I verify that this 
is doing what I think it is doing.


1. the approach involves a multivariate regression:
lm(cbind(nx,ny) ~ x + y, data=g)

where (nx,ny) are the 'good' data, and (x,y) are the 'bad' data.

cheers,

dylan


> Dylan Beaudette wrote:
> > I have a problematic TIGER  module - i.e. a single county in Ca is really
> > messed up. I thought that a simple translate() would do the job, but it
> > looks like there is both a translation and rotation involved. I do not
> > really understand the postgis manual entry for the affine function.
> >
> > How would one go about converting a series of coordinate pairs ([good],
> > [bad]) into the terms of the affine transform matrix?
> >
> > thanks,

-- 
Dylan Beaudette
Soils and Biogeochemistry Graduate Group
University of California at Davis
530.754.7341
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