Abstract: This paper presents Texture Brush, an interactive interface for texturing 3D surfaces. We extend the conventional exponential map to a more general setting, in which the generator can be an arbitrary curve. Based on our extended exponential map, we develop a local parameterization method which naturally supports anisotropic texture mapping. With Texture Brush, the user can easily specify such local parameterization with a free-form stroke on the surface. We also propose a set of intuitive operations which are mainly based on 3D painting metaphor, including texture painting, texture cloning, texture animation design, and texture editing. Compared to the existing surface texturing techniques, our method enables a smoother and more natural work flow so that the user can focus on the design task itself without switching back and forth among different tools or stages. The encouraging experimental results and positive evaluation by artists demonstrate the efficacy of our Texture Brush for interactive texture mapping.