#787 – Transforming a Point Using Matrix Multiplication

In WPF, all 2D transformations (e.g. scale, rotate, translate) are done internally using matrix multiplication.

Every point that you want to transform is represented as a 2 x 1 matrix (two rows and one column).  For example:

787-001

 

Assume that you want to transform this point, represented by x and y, into a new point.  We do this by multiplying a 2 x 2 transformation matrix by our original 2 x 1 matrix.  The result is another 2 x 1 matrix, containing our new (transformed) point.

The operation is written as follows, assuming that a, b, c and represent the four values in our 2 x 2 matrix.  We multiply the 2 x 2 transformation matrix by the original 2 x 1 matrix to get a new 2 x 1 matrix.

787-002

 

(Don’t worry about the values of a, b, c and d for now–we’ll fill them in later).  The actual multiplication is done as follows:

787-003

Advertisements

About Sean
Software developer in the Twin Cities area, passionate about software development and sailing.

3 Responses to #787 – Transforming a Point Using Matrix Multiplication

  1. Pingback: Dew Drop – March 29, 2013 (#1,517) | Alvin Ashcraft's Morning Dew

  2. Kiming Alfred Kintuh says:

    Iam an undergraduate physics student who appreciates every thing that has to do with scientific related software.
    i want to simulate all 3D 2D and all related scientific stuff

  3. Pingback: #791 – Matrix Multiplication, Part I – Rows and Columns | 2,000 Things You Should Know About WPF

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: