Re: [Geotools-gt2-users] affine transformation

[Jody G. <jod...@gm...>]

You may wish to add some of that to the wiki page :-)

I will note if you don't like math, you can just use the methods of
the AffineTransform object.

Jody


On Thu, Aug 19, 2010 at 1:01 PM,  <chr...@nv...> wrote:
>
> Some mathematical basics here.
> An affine transform is a powerful mechanism to transform coordinates.
> To get the new coordinates x' and y', the following calculation is done.
>
> [ x']   [  m00  m01  m02  ] [ x ]   [ m00x + m01y + m02 ]
> [ y'] = [  m10  m11  m12  ] [ y ] = [ m10x + m11y + m12 ]
> [ 1 ]   [   0    0    1   ] [ 1 ]   [         1         ]
>
> A simple example:
> if you want to shift a point 5 units on the x axis and -7 units at the
> y axis, the following matrix is needed
>
> [  1    0  5  ]
> [  0    1  -7  ]
> [  0    0  1   ]
>
> Of course, you can say this is easy, x'=x+5 and y'=y-7 would do the same.
>
> Another one, lets do some scaling, say factor 3
>
> [  3    0  0 ]
> [  0    3  0  ]
> [  0    0  1  ]
>
> This is easy too, x'=x*3 and y'=y*3 would the job.
>
> The power of affine transforms is that you can combine multiple
> matrices into a single one, doing a set of individual transformations
> within one step. There is a java method "concatenate(AffineTransform)"
> for the AffineTransform class. But be careful, given 3 transformatons
> A,B,C and you want to combine them in this order, you have to go from
> right to left.
> C concatenate B concatenate A will give you the expected result.
>
> A mapping from world coordinates to pixel coordinates needs some
> operations but can be done within one affine transformation.
>
> The second powerful feature is that you can create an inverse
> transform (Method createInverse), which will do the mapping in the
> other direction out of the box.
>
> Believe me, if you are used to use AffineTransform objects, you will
> use them forever.
>
> Hope this helps
> Cheers
> Christian
>
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> Quoting andrea antonello <and...@gm...>:
>
>> Hi Tommaso,
>> the easiest way to do a rotation for example is:
>>
>> Coordinate ancorPoint = ...;
>> AffineTransform affineTransform =
>> AffineTransform.getRotateInstance(angleRad, ancorPoint.x,
>> ancorPoint.y);
>> MathTransform mathTransform = new AffineTransform2D(affineTransform);
>>
>> Point point = ...point to rotate;
>> Geometry rotatedPoint = JTS.transform(point, mathTransform);
>>
>> Where point can be any geometry.
>>
>> Does that help?
>>
>> Ciao
>> Andrea
>>
>>
>> On Wed, Aug 18, 2010 at 11:26 PM, tommaso <tom...@go...> wrote:
>>> Hallo List,
>>>
>>> I would like to perform some geometry transformations on polygons, i.e
>>> rotate about a point, scale and translate.
>>>
>>> So I create the polygon:
>>>
>>> import com.vividsolutions.jts.geom.Coordinate
>>> import org.geotools.geometry.jts.JTSFactoryFinder
>>> import com.vividsolutions.jts.geom.GeometryFactory
>>> import com.vividsolutions.jts.geom.LinearRing
>>> import com.vividsolutions.jts.geom.Polygon
>>>
>>>         GeometryFactory geometryFactory =
>>> JTSFactoryFinder.getGeometryFactory( null );
>>>
>>>         Coordinate[] coords  = [new Coordinate(0, 0), new Coordinate(2, 0),
>>> new Coordinate(2, 2), new Coordinate(0, 2), new Coordinate(0, 0)]
>>>         LinearRing ring = new LinearRing(coords, geometryFactory)
>>>         Polygon polygon = geometryFactory.createPolygon(ring)
>>>
>>> I guess I have to use AffineTransform
>>> (com.vividsolutions.jts.geom.util.AffineTransformation ?) but I don't know
>>> exactly how.
>>> A code example or a link to a tutorial were very appreciated.
>>>
>>> Cheers,
>>> Tom
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