Changes between Version 3 and Version 4 of DevWikiAffineParameters

Timestamp:

Sep 13, 2011, 9:33:13 AM (13 years ago)

Author:

bnordgren

Comment:

—

DevWikiAffineParameters

@@ -57 +57 @@
 
 Whenever more than one of the above operations is required, they may be combined using [http://en.wikipedia.org/wiki/Matrix_multiplication matrix multiplication]. As an example, all of the above matrices will be combined into one. The result of such a combination is still not an affine transform, however. It is just a 2x2 matrix has all the individual functions aggregated into it.
+
+We will be calculating a new matrix, '''O''', which is the aggregate of the following individual operations:
+
+ 1. scaling
+ 1. clockwise rotation
+ 1. shearing parallel to the x axis
+ 1. shearing parallel to the y axis
+
+We do this by multiplying the 2x2 matrices of the individual operations together, as follows: 
+
+[[Image(aggregate_step1.png)]]
+
+The above matrix equation is shorthand for four equations: one equation each for o,,11,,, o,,12,,, o,,21,, and o,,22,,. We will perform the multiplications on the right hand side one at a time.