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.