The invention provides texture mapping techniques that facilitate
interactive painting of a three-dimensional virtual surface by a user in
object space, without requiring global parameterization. The texture
mapping techniques feature rendering texture for a given virtual object
using a plurality of composite textures, each formed by blending
collapsible texture layers. Texture coordinates in texture space are
derived using information determined at the time of surface mesh
generation. The invention features dynamic texture allocation and
deallocation, allowing a user to interactively modify the shape of a
painted, three-dimensional model. Finally, the invention features an
architecture for combined graphical rendering and haptic rendering of a
virtual object, allowing a user to experience force feedback during the
painting of the object in object space.