The CAVE’s immersive virtual environment enables participants to walk around mathematical shapes, step through complex surfaces, or move a surface through itself. Virtual reality encourages users to see shapes from a new perspective - from the inside, looking out - and to explore and manipulate complex surfaces in order to better understand them.

Topology is the study of the characteristics of mathematical surfaces, such as their number of sides, edges, or holes. This program uses free-form deformations to study the topology of mathematical surfaces. Deforming a surface changes its shape, but not its characteristics; an edge remains an edge, and a hole remains a hole, no matter how distorted the edge or hole appears. The claim of topologists that a donut (torus) and a coffee cup are topologically equivalent is one of the deformations demonstrated in this program.

This application was a part of Experiential Science in The Virtual Reality Theater venue at Supercomputing ’93, and VROOM - the Virtual Reality Room event showcased at SIGGRAPH 94.