Imagenation

Imagenation is a Lite Applet that enables curriculum developers and students to transform images. It relies on two key ideas -- an original image and a transformed image. The image below is an original image. The coordinates of this original image are denoted by the variables x and y. In this example the range of the variable x is from -2 to 2 and the range of the variable y also runs from -2 to 2. We use the variables u and v to denote the coordinates of the transformed image. The values of these variables in this example also range from -2 to 2. The simplest use of Imagenation defines the transformed image by means of a transformation:

T:R2 --> R2

defined by a pair of functions u(x, y) and v(x, y). For example, the image below can be turned upside down by using the functions:

u(x, y) =   x
v(x, y) = -y

Using the form below you can experiment with transformations like this. Simply enter two expressions defining the functions u(x, y) and v(x, y) in the appropriate boxes and press the Try it!! button. If you click the Try it!! button without changing the default expressions the image will be turned upside down.

Parameter Name Explanation Enter Expression
u_fcn Enter the function u(x, y) that defines the variable u in the transformed image as a function of the variables x and y used for the original image.
v_fcn Enter the function v(x, y) that defines the variable v in the transformed image as a function of the variables x and y used for the original image.

After you have experimented a bit using the form above click here for an example of a student-ready module using Imagenation to study coordinate systems and transformations.

We have just begun to scratch the surface of the power of Imagenation. Click here to learn more about this Lite applet. For another example application of this applet look at A Virtual Window