: In order to synthesize distortionless texture on surfaces, we develop a direct and accurate approach for local resampling in vector fields, and then use the approach to synthesize textures on 2-D manifold surfaces directly from a texture exemplar. Regular-grid patches produced by the local resampling are used as building blocks for texture synthesis. Then texture optimization and patch-based sampling are generalized to synthesize texture directly in vector fields. The first scheme can create texture of higher quality; however the second scheme is faster and simpler and works well for a wide range of textures. Users can control the vector field on the mesh to generate textures with local variations including the orientation and scale. Many experimental results are presented to demonstrate the ease of use and reliable results provided by our system.