CurvRender: Curvature-aware 3D mesh refinement from 3D Gaussian Splatting via differentiable rendering

Explicit triangle meshes remain indispensable for geometry processing and surface analysis, whereas Gaussian Splatting (GS) predominantly targets high-quality novel-view synthesis. We present CurvRender, a conservative two-stage post-processing pipeline for GS-derived explicit meshes. Stage 1 reconstructs a conventional mesh from a pre-trained GS point cloud; Stage 2 preserves face connectivity and optimizes vertex offsets through differentiable rasterization with photometric and geometric regularization. Across Lego and all nine Mip-NeRF 360 scenes, the mean minimum triangle angle increases in all ten scenes (mean ), with stronger relative effects toward the lower-quality tail: improvements reach at P5, at P1, and for the worst-1% mean. The fraction below and two focused cotangent-weight diagnostics improve in every scene. Connectivity is preserved exactly, mean vertex displacement is only of the Stage 1 bounding-box diagonal, and photometric metrics remain essentially unchanged. Open3D self-intersection pair and involved-face counts never increase, but reductions are not statistically significant and the involved-face area ratio does not decrease consistently; Stage 2 is therefore not a topology-repair method. On the official 15-scan DTU protocol, Stage 1 obtains 1.339 mm Overall Chamfer distance, comparable to SuGaR but behind 2DGS and GOF. Ablation shows that the no-curvature variant yields a larger mean minimum-angle gain than exponential curvature weighting, so the curvature term is interpreted as a curvature-dependent modulation mechanism rather than the principal source of improvement. Overall, CurvRender is a bounded mesh-quality refinement module rather than a replacement for dedicated surface reconstruction or mesh repair.