Treffer: The Fine Art of Teaching Functions

The correct use of visual perspective is one of the main reasons that virtual reality environments and realistic works of art look lifelike. Geometric construction techniques used by artists to achieve an accurate perspective effect were developed during the Renaissance. With the rise of computer graphics, translating the geometric ideas of 600 years ago into algebra-based algorithms became necessary. Today's algorithms can be understood via the function concept: Each point of a three-dimensional (3D) environment is mapped to a point on a two-dimensional (2D) screen. The purpose of the activity described in this article is to use the input/output definition of a function as a crucial step in developing the Perspective Projection Rule (PPR). This simple yet powerful rule turns out to be a function that governs the creation of a wide range of realistic images from virtual reality environments to three-dimensional illusion art. Students were intrigued by the real-world applications of this activity, such as computer graphics, and overwhelmingly reported the appeal of the artwork component.

ERIC