### Technical Description

The installation consists of an overhead camera and projector aimed at the floor through an intermediate mirror. The camera and projector are connected to a PC computer, which performs tracking of the moving people on the floor below by processing the video image using custom software. The software then generates the Voronoi diagram, which is projected back onto the floor.

To produce its result, "Boundary Functions" uses an algorithmic chain of cause-and-effect. Above the floor, a camera is connected to a computer, which is in turn connected to a projector. First, the camera captures an image of the people standing on the platform. Next, a morphological algorithm is applied to the image to get rid of small variations, and fill the holes in the noisy image of the people below. After that, the instructions specify how to trace the contour of each continuous shape in the image, and then how to find each region’s center. This process reduces the hundreds of thousands of pixels in the image to a few points, each of which represents the location of one person below. The process is one of abstraction and meaning making. Although there is now a hundred thousand times less information than there was in the original image, this information can be used to construct greater meaning in the minds of the viewers.

These points on the simplified image then become the input to the next computational step – the creation of the Voronoi diagram (the created patterns are referred to as Voronoi diagrams, after the Ukranian mathematician who precisely defined their construction). A particular class of algorithm called "divide-and-conquer" produces this diagram by subdividing all the points until the computer code is only examining two points at a time (this is done by sorting the points in some order, e.g. by x-position). The algorithm then chooses adjacent pairs and computes the line that divides them. This line is perpendicular to the line drawn between the two points and intersects the half-way point along the line between the two points. The algorithm computes the line that separates the first two points, and then moves on to two other points. This happens for twos, then fours, eights, etc. When all the pairs have been divided by lines, the algorithm merges the lines

- the intersection between two side-by-side lines is computed and the lines are truncated to start forming the diagram.

The resulting Voronoi diagram is then drawn into a memory buffer, using a technique called rasterization that translate from the geometric description of the lines into the pixels within the computer's memory. Finally, the digital projector converts the memory pixels into light, and then projects the entire image back onto the floor below. (Scott Snibbe)

### Hardware / Software

Boundary Functions consists of two major components: a collection of equipment mounted approximately 5 meters overhead, and a 4 meter square constructed retro-reflective floor.