Reconstructing high-fidelity, animatable human avatars from monocular videos remains a critical challenge. Existing 3DGS-based human animation methods constrain Gaussian parameters but exclude scale, which we argue is crucial for adapting human poses to challenging out-of-distribution poses. To achieve robust animation under unseen poses, we propose Tavatar, which derives key parameters such as scale, rotation, and other geometric attributes directly from the local mesh geometry, instead of learning them through unconstrained optimization. This paradigm shift enforces topological consistency by design, as each Gaussian is analytically anchored to the local mesh geometry, inheriting its spatial structure and deformation behavior. Specifically, we bind Gaussians to mesh faces and vertices, deriving their scales and orientations from triangle properties and local edge lengths to ensure coherent surface coverage. To ensure the stability of this analytical mapping, we introduce a crucial equilateral regularization term that preserves mesh integrity. Extensive experiments demonstrate that Tavatar achieves superior animation robustness on challenging out-of-distribution poses, reducing normal error by 13.8% on X-Avatar and 17.9% on PeopleSnapshot against the best baseline, while maintaining competitive rendering quality.