Shape modeling using homotopy

Abstract

Introduces a new method of shape modeling using homotopy and object-oriented modeling. Homotopy is a kind of topology that gives more general ideas of presenting invariant properties of geometrical objects and is further expanded to conceptual objects. The conventional shape modeling method, using polygonalization, has serious difficulties in preserving invariant properties, leading to the necessity of a massive amount of data. On the other hand, the combination of homotopy and object-oriented modeling, which uses class hierarchy, helps to preserve invariant properties at all abstraction levels. We explain how our new method helps us to preserve invariant properties, which keeps the amount of data to the minimum possible level, using an example of a tennis ball rolling on a slope.