Affine Transformer
Use the mouse to draw a figure (in black). The applet draws the image (in red) of the figure under the affine transformation f(P) = AP + B.

Time to get a Java-capable browser.

Familiar motions of the plane such as translations, reflections, and rotations are affine transformations. An affine transformation of the plane is a function from the plane to itself defined by f(P) = AP + B, where P is a point on the plane expressed as a 2x1 matrix, and A, B are 2x2, 2x1 matrices, respectively. The applet above starts with A[1,1] = -1, A[1, 2] = 0, A[2, 1] = 0, A[2, 2] = 1, and B the zero matrix. This affine transformation is reflection in the y-axis.

You can change the entries of A and B by entering the desired values in the textboxes, then clicking on the "Enter/Clear" button.

Suggestion: Try A[1,1] = 2, A[1, 2] = 0, A[2, 1] = .5, A[2, 2] = .5, and B the zero matrix, to set up a "caricature generator".

See the book Modern Geometry with Applications (Springer-Verlag) by G. Jennings for more information on representing rigid motions of the plane (e.g., translations, rotations, reflections) as affine transformations.