Traditional bilateral filters, effective in 2D image processing, often fail to account for the 3D structure of meshes, leading to artifacts in texture filtering. This thesis introduces On-Mesh Bilateral Filtering, a novel method that adapts the bilateral filter to work with non-contiguous texture mappings by incorporating 3D spatial distances and face adjacency information into the filtering process. The On-Mesh Bilateral Filter combines mesh surface sampling techniques with heat geodesic distance calculations to create a geometry-aware kernel that achieves more accurate and context-sensitive smoothing operations, respecting both the mesh topology and texture space properties. This paper hopes to encourage further research in the area of geometry-aware texture filters.