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High-resolution texture maps are necessary for representing real-world objects accurately with 3D meshes. The large sizes of textures can bottleneck the real-time rendering of high-quality virtual 3D scenes on devices having low computational budgets and limited memory. Downsampling the texture maps directly addresses the issue, albeit at the cost of visual fidelity. Traditionally, downsampling of texture maps is performed using methods like bicubic interpolation and the Lanczos algorithm. These methods ignore the geometric layout of the mesh and its UV parametrization and also do not account for the rendering process used to obtain the final visualization that the users will experience. Towards filling these gaps, we introduce GeoScaler, which is a method of downsampling texture maps of 3D meshes while incorporating geometric cues, and by maximizing the visual fidelity of the rendered views of the textured meshes. We show that the textures generated by GeoScaler deliver significantly better quality rendered images compared to those generated by traditional downsampling methods