The Linear Transformation Grapher

If you draw in the (x,y) window you will see the image (under a linear transformation) of your drawing in the (u,v) window. Drawing in the (u,v) window produces the preimage in the (x,y) window. You can draw either lines, points, or rectangles, and vary the transformation as well. Clicking on the Increase, Decrease, or Reverse buttons will modify the transformation.

The transformation has the form

where the matrix

is one of the following:

• Rotation through t degrees:

  

  (Buttons change t)

• Rescale of the x coordinate:

  

  (Buttons change c)

• Rescale of the y coordinate:

  

  (Buttons change c)

• Interchange of the x-axis and y-axis:

  

  (Buttons do nothing)

• Shear along the x axis:

  

  (Buttons change c)

• Shear along the y axis:

  

  (Buttons change c)

• Produces random values for the coefficients a, b, c, d. (In this case the buttons produce a new random matrix of coefficients.)

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