Sample Curriculum Materials, Part III

Moving Images Around

Open the OSSLET that we will use in this section. Click the Play button to see our next example. This example is different from most of the examples we've examined so far. In those examples the center point of the image (the point (0, 0)) stayed fixed at the center of the screen. Now this point (and the whole image) is jumping around. We accomplish this effect by using the vector \vec b in the transformation:

\vec y = A \vec x + \vec b \quad \quad {\rm or} \quad \quad \left[{\begin{array}{c}y_1 \\ y_2 \\ \end{array}}\right] = \left[{\begin{array}{cc}a_{11} & a_{12} \\ a_{21} & a_{22} \\ \end{array}}\right] \left[{\begin{array}{c} x_1 \\ x_2 \\ \end{array}}\right] + \left[{\begin{array}{c}b_1 \\ b_2 \\ \end{array}}\right] \quad \quad {\rm or} \quad \quad \begin{eqnarray} y_1 &=& a_{11} x_1 + a_{12} x_2 + b_1\\ y_2 &=& a_{21}x_1 + a_{22} x_2 + b_2\\ \end{eqnarray}.

Questions

For this set of questions use the same live window you used for the example above. Click each of the questions buttons -- Question 1 -- Question 6 -- in the upper right area of the window and reproduce the given animation by changing the elements of the matrix A. Note these entries are highlighted in pink. To see each question and check your work, click the Play button.

Be Creative and Challenge Your Classmates

Come up with an interesting animation and challenge your classmates to reproduce it.