Changes between Version 8 and Version 9 of DevWikiAffineParameters

Timestamp:

Nov 27, 2011, 1:16:38 PM (12 years ago)

Author:

bnordgren

Comment:

—

DevWikiAffineParameters

@@ -7 +7 @@
 [[Image(construction-step5.png)]]
 
+In the above image, the x and y axes represent geocoordinates (e.g., easting and northing in a projected system or longitude and latitude in a geographic system.) The basis vectors '''i,,b,,''' and '''j,,b,,''' are the ''transformed'' unit vectors '''i''' and '''j''', respectively. The magnitude of the basis vectors represent the distance between grid cells in the units of the geocoordinate system. The angle between the x axis and basis vector '''i,,b,,''' is given by θ,,i,,. The angle between the two basis vectors is designated by θ,,ij,,. In a "normal" right handed coordinate system, θ,,ij,, is +90 degrees, but the value -90 degrees (indicating that the j axis needs to be flipped) is also very common. Any value other than plus or minus 90 degrees indicates that the linear transform includes shearing parallel to the i axis.
 
-Although some rasters have a very complex relationship between these two coordinate systems, many have a set of simple linear relationships between the two coordinate systems. These simple linear relationships are ''modular'' and may be combined in many ways. Regardless of the order in which they are combined, an affine transform results. The transform is then used to convert coordinates between the two coordinate systems of the raster. This page describes a set of ubiquitous individual transformations and combines them to produce a specific affine transformation which adheres to the .
+These simple linear relationships between pixel coordinates and geocoordinates are typically represented as ''modular'' combinations of individual transformations. Regardless of the order in which they are combined, a linear transform results. The transform is then used to convert coordinates between the two coordinate systems of the raster. This page describes a set of ubiquitous individual transformations and combines them to produce a specific transformation which respects the physically significant parameters which a typical user is likely to be interested in.
+
+The physically significant inputs which drive the model are: 
+
+ * The magnitude of the '''i,,b,,''' basis vector (distance between pixels along i axis)
+ * The magnitude of the '''j,,b,,''' basis vector (distance between pixels along j axis)
+ * The angle θ,,i,, (the angle by which the raster's grid needs to be rotated, positive clockwise -- for compatibility with "heading/bearing")
+ * The angle θ,,ij,, (the angle from the i basis vector to the j basis vector positive counterclockwise -- for consistency with right-handed coordinate system)
 
 The level of math required to follow along is advanced high school algebra or introductory college algebra. It should be accessible to anyone with a science, math, or engineering background. Lacking this, the nontechnical introduction to [http://en.wikipedia.org/wiki/Matrix_multiplication matrix multiplication] on wikipedia should provide sufficient background.