12.4.6 CT_MathTransformFactory` Class
Creates math transforms. CT_MathTransformFactory is a low level factory that is used to create CT_MathTransform
objects. Many high level GIS applications will never need to use a CT_MathTransformFactory directly; they can use a CT_CoordinateTransformationFactory instead. However, the
CT_MathTransformFactory interface is specified here, since it can be used directly by applications that wish to transform other types of coordinates e.g. color coordinates, or image
pixel coordinates.
The following comments assume that the same vendor implements the math transform factory interfaces and math transform interfaces.
A math transform is an object that actually does the work of applying formulae to coordinate values. The math transform does not know or care how the coordinates relate to positions in the
real world. This lack of semantics makes implementing CT_MathTransformFactory significantly easier than it would be otherwise.
For example CT_MathTransformFactory can create affine math transforms. The affine transform applies a matrix to the coordinates without knowing how what it is doing relates to the real world.
So if the matrix scales Z values by a factor of 1000, then it could be converting meters into millimeters, or it could be converting kilometers into meters.
Because math transforms have low semantic value but high mathematical value, programmers who do not have much knowledge of how GIS applications use coordinate systems, or how those
coordinate systems relate to the real world can implement CT_MathTransformFactory.
The low semantic content of math transforms also means that they will be useful in applications that have nothing to do with GIS coordinates. For example, a math transform could be used to
map color coordinates between different color spaces, such as converting red, green, blue colors into hue, light, saturation colors.
Since a math transform does not know what its source and target coordinate systems mean, it is not necessary or desirable for a math transform object to keep information on its source and
target coordinate systems.
12.4.6.1 createAffineTransform matrix:PT_Matrix : CT_MathTransform
Creates an affine transform from a matrix. If the transforms input dimension is M, and output dimension is N, then the matrix will have size [N+1][M+1]. The +1 in the matrix dimensions allows
the matrix to do a shift, as well as a rotation. The [M][j] element of the matrix will be the jth ordinate of the moved origin. The [i][N] element of the matrix will be 0 for i less than M, and 1 for i
equals M.
12.4.6.2 createConcatenatedTransform transform1:CT_MathTransform, transform2:CT_MathTransform : CT_MathTransform
Creates a transform by concatenating two existing transforms. A concatenated transform acts in the same way as applying two transforms, one after the other.
The dimension of the output space of the first transform must match the dimension of the input space in the second transform. If you wish to concatenate more than two transforms, then you
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can repeatedly use this method.
12.4.6.3 createFromWKT wellKnownText:CharacterString : CT_MathTransform
Creates a math transform from a Well-Known Text string.
12.4.6.4 createFromXML xml:CharacterString : CT_MathTransform
Creates a math transform from XML.
12.4.6.5 createParameterizedTransform classification:CharacterString, parameters:SequenceCT_Parameter : CT_MathTransform
Creates a transform from a classification name and parameters. The client must ensure that all the linear parameters are expressed in meters, and all the angular parameters are expressed in
degrees. Also, they must supply semi_major and semi_minor parameters for cartographic projection transforms.
12.4.6.6 createPassThroughTransform firstAffectedOrdinate:Integer,
subTransform:CT_MathTransform : CT_MathTransform
Creates a transform which passes through a subset of ordinates to another transform. This allows transforms to operate on a subset of ordinates. For example, if you have Lat,Lon,Height
coordinates, then you may wish to convert the height values from meters to feet without affecting the Lat,Lon values. If you wanted to affect the Lat,Lon values and leave the Height values
alone, then you would have to swap the ordinates around to Height,Lat,Lon. You can do this with an affine map.
12.4.6.7 isParameterAngular parameterName:CharacterString : Boolean
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