Efficient online visualization of 3D mesh and photo realistic texture is essential for a variety of applications, such as museum exhibits and medical images. In these applications synthetic texture and a predefined set of views is not an option. We propose using a mesh simplification algorithm based on scale-space analysis of the feature point distribution, combined with an associated analysis of the surface texture, to address the needs of adaptive online transmission of high quality 3D objects. The premise of the proposed textured mesh (TexMesh) simplification is the following: minor variations in texture can be ignored in relatively smooth regions of a 3D surface, without significantly affecting human perception. Statistics on 3D feature point distribution and their associated texture fragments are gathered during preprocessing. Online transmission is based on these statistics, which can be retrieved in constant time. Based on monitored bandwidth a scaled mesh is first transmitted. Starting from a default texture quality, we apply an efficient Harmonic Time Compensation Algorithm based on the current bandwidth and a time limit, to adaptively adjust the texture quality of the next fragment. Properties of the algorithm are proved. Experimental results show the usefulness of our approach.