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Mathematics in Computer Animation

What kinds of mathematics go into making a computer animated film? We start by describing some simple object, say a square, and we then proceed to display it on a two-dimensional screen. This requires determining the size of the square, and the relationship of its sides to the horizontal and vertical axes, and the position of its center. We can then give instructions to have the square move through a sequence of positions just by telling where the center should move.


  You will need to enable Java in order to use this demonstration.  

Please be patient while the applet is loaded...

Interaction Controls

Click on the "DEMO" button at the left to start the demonstation. It may take a few moments to open the windows needed for this applet. You should eventually get two new windows: the "Controls" window and the "2D Graph" window.

The center of the square has coordinates c and d that appear in the "Controls" window. Selecting the right arrow next to c will make that coordinate change until it reached its top value, and selecting the left arrow will move it back to its lowest value. Clicking on a double arrow will animate the movement either to the right or to the left.

Controlling d in the same way will move the square up and down on the screen.

When you are done with the demonstration, choose the "Exit Demo" menu item from the "Windows" menu of the "Controls" window. The applet will not exit until you do so.

Just imagine how many thousands of small triangles are required to make the realistic picture of Geri, and how complicated it must be to make all of his different parts work together to simulate the movement of a human being.

Mathematics Awareness Month is sponsored each year by the Joint Policy Board for Mathematics to recognize the importance of mathematics through written materials and an accompanying poster that highlight mathematical developments and applications in a particular area.