An algebraic topological method for feature identification

We develop a mathematical framework for describing local features of a geometric object-such as the edges of a square or the apex of a cone in terms of algebraic topological invariants. The main tool is the construction of a "tangent complex" for an arbitrary geometrical object, generalising the usual tangent bundle of a manifold. This framework can be used to develop algorithms for automatic feature location. We give several examples of applying such algorithms to geometric objects represented by point-cloud data sets.