Changes between Version 2 and Version 3 of DevWikiRealParameters

Timestamp:

Nov 29, 2011, 8:50:32 AM (12 years ago)

Author:

bnordgren

Comment:

—

DevWikiRealParameters

@@ -3 +3 @@
 == Introduction == 
 
-This page discusses how to compute conceptually meaningful parameters (i.e., rotation, scale in the x and y direction) when all you have is an affine transformation. The reverse process, calculating the affine parameters from the conceptually meaningful data, is articulated on [wiki:DevWikiAffineParameters another wiki page]. 
+This page discusses how to compute physically significant parameters from an arbitrary linear transformation. The reverse process, calculating the affine parameters from the physically significant parameters, is articulated on [wiki:DevWikiAffineParameters another wiki page]. The model used to describe how the raster maps onto real world coordinates is illustrated in the following figure:
 
-As described on the page which discusses calculation of affine transform parameters, the value of each affine coefficient is affected by which operations the transformation performs, as well as the order in which the transform performs the operations. In essense, this means that we have to make an assumption about which operations are performed by the transform and hope that we made the right guess.
+[[Image(model.png)]]
+
+This model contains all of the parameters except for translation. Translation may be added in after the coordinates have been scaled, rotated and sheared. The above illustration contains the physically significant parameters which will be calculated by this method. These are: θ,,i,,, θ,,ij,,, and the pixel size along the '''i,,b,,''' and '''j,,b,,''' basis vectors. 
+
+The inputs to this method are the four non-translation (non-offset) parameters of a linear transform.  These are shown below: 
+
+[[Image(geotransform.png)]]
+
+Although these parameters have "common names" within the GIS community, the names are both lengthy and misleading. Within the context of this page, the coefficients o,,11,,, o,,12,,, o,,21,,, and o,,22,, will be used.
 
 == The forward calculation ==