Topological graphics

Topological graphics opens up completely new worlds in computer graphics applications. It is supported by advances in modern algebraic topology homotopy theory and cellular spatial structures in particular. Topological graphics lays out the framework to interactively construct cyberworlds emerging on the World Wide Web. It guides graphics software design to make it minimal and reusable. This progress report on our own frontier researches gives abundant examples as well as a brief summary of theoretical foundations.