Modern mesh generation pipelines whether learning-based or classical often produce outputs requiring post-processing to achieve production-quality geometry. This work introduces MeshCone, a convex optimization framework for guided mesh refinement that leverages reference geometry to correct deformed or degraded meshes. We formulate the problem as a second-order cone program where vertex positions are optimized to align with target geometry while enforcing smoothness through convex edge-length regularization. MeshCone performs geometry-aware optimization that preserves fine details while correcting structural defects. We demonstrate robust performance across 56 diverse object categories from ShapeNet and ThreeDScans, achieving superior refinement quality compared to Laplacian smoothing and unoptimized baselines while maintaining sub-second inference times. MeshCone is particularly suited for applications where reference geometry is available, such as mesh-from-template workflows, scan-to-CAD alignment, and quality assurance in asset production pipelines.

翻译：无论是基于学习的还是传统的现代网格生成流程，其输出通常需要后处理才能达到生产级几何质量。本文提出MeshCone，一种基于凸优化的引导式网格细化框架，通过参考几何来校正变形或退化的网格。我们将该问题建模为二阶锥规划，在通过凸边长度正则化强制平滑性的同时，优化顶点位置以对齐目标几何。MeshCone执行几何感知优化，在修正结构缺陷的同时保留精细细节。我们在ShapeNet和ThreeDScans的56个不同物体类别上验证了其鲁棒性能，相较于拉普拉斯平滑和未优化基线，实现了更优的细化质量，同时保持亚秒级推理时间。MeshCone特别适用于存在参考几何的应用场景，例如基于模板的网格生成流程、扫描到CAD的对齐以及资产生产流程中的质量保证。