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Graphics Theory Educational Applets
As part of my PhD comprehensive exams, I created two applets designed to help teach basic graphics theory to an undergraduate audience.
2D Transformations
The first applet teaches the connection between transformation matrices and the effects they have on a particular object. The user can adjust translation, rotation, and scaling parameters, and rearrange the corresponding matrices so the transformations are applied in a different order. An animation demonstrates the transformations in action, which are applied from right to left since points in an object would be multiplied by the matrices in that order.
One of the main objectives of this applet was to get students to see how differently an object would be transformed if they were to rotate it without first translating it to the origin. Not doing so when a rotation about an object's center is desired is a common mistake for beginners.
Surface Shading
In this applet, the user can adjust RGB parameters for ambient lighting, direct light, and surface reflectance. They can also drag the direct light source and the viewer's eye, as well as tilt the surface we are lighting, to change the angles involved in the final calculations. Phong shading can be turned on and off.
The idea here is to allow students to see specifically how each portion of a simple shading equation actually affects the final visual result. It can be very difficult to imagine from the math alone.