Changes between Version 1 and Version 2 of DevWikiAffineParameters

Timestamp:

Sep 13, 2011, 8:44:28 AM (13 years ago)

Author:

bnordgren

Comment:

—

DevWikiAffineParameters

@@ -5 +5 @@
 Geospatial rasters inherently have two coordinate systems associated with them: pixel indices and real world coordinates. 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 demonstrates how they may be combined to produce an affine transformation.
 
+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.
+
 == Individual operations == 
 
-This page discusses operations in two dimensions only. Each operation is presented as a 2x2 matrix, and each operation performs only one function.  These operations were taken from [http://en.wikipedia.org/wiki/Transformation_matrix#Examples_in_2D_graphics wikipedia]. While the matrices presented here contain the bulk of the functionality of a finished affine transform, they are not ''complete'' affine transforms themselves.
+This page discusses operations in two dimensions only. Each operation is presented as a 2x2 matrix, and each operation performs only one function.  These operations were taken from [http://en.wikipedia.org/wiki/Transformation_matrix#Examples_in_2D_graphics wikipedia]. While the matrices presented here contain the bulk of the functionality of a finished affine transform, they are not ''complete'' affine transforms themselves. Each transformation will be presented in matrix and equation form: they are equivilent representations.
 
+=== Rotation ===
+
+There are two directions one can rotate in two dimensions: clockwise and counter clockwise. The transformations are different. The counter-clockwise rotation is: 
+
+[[Image(CCW_rotation.png)]]
+
+ * x' = xcosθ − ysinθ
+ * y' = xsinθ + ycosθ