MeshCone: Second-Order Cone Programming for Geometrically-Constrained Mesh Enhancement

We propose a remeshing-enhanced method for generatively deforming shapes with visual losses. It is intuitive that sufficiently drastic deformations of a mesh without changing its triangulation can easily compromise element quality, even if such large geometry changes may be semantically desired. Shape deformation methods could thus benefit from changing the triangulation; however, this is not done by most generative, text-based, visually-supervised mesh deformation methods. Remeshing is a discrete operation, proven to be especially challenging to couple with the notoriously noisy supervision signal provided by visual losses. We propose a vertex-based deformation optimization quantity capable of large deformations and robustness to such noise; we periodically remesh using an isotropic remesher that interpolates and carries forward the deformation optimization state. This enables continuous, geometry-informed progress in coarse-to-fine addition of resolution. The resulting shapes' triangulations fit their optimized geometry and have neat isotropic elements. Further, our method is localizable, able to grow new features on a base shape with expressive detail, leaving the rest unchanged. We showcase the effectiveness of our method on a variety of shapes and prompts, both local and global deformations, and demonstrate its superior visual quality and triangle efficiency. Our project page is at https://threedle.github.io/radmesh.

Meshes remain the most practical representation for geometry reasoning and integration into graphics pipelines, yet existing reconstruction methods struggle to produce high-quality meshes. Most state-of-the-art approaches initially learn an intermediate representation (NeRF/3DGS) and treat mesh extraction as a post-processing step, which often leads to oversmoothed surfaces or poor quality meshes with excessive triangle counts.Existing mesh-native optimization methods alleviate some of these issues but suffer from fixed-resolution discretizations and unstable optimization behavior. In this paper, we introduce an adaptive mesh-based optimization framework and a practical mesh rendering technique to address these challenges. Our representation combines an optimizable Delaunay-triangulated tetrahedral grid with a multi-resolution hash grid. The former is refined through point pruning and insertion, while the latter provides latent features for SDF/appearance value predictions. We use volumetric rendering to bootstrap a coarse geometry while leveraging mesh-based rendering for recovering fine-grained details. Additionally, we propose a differentiable, rasterization-based depth-offset rendering formulation, reducing geometric artifacts and improving reconstruction quality. Our method significantly outperforms existing mesh optimization approaches across a variety of object-centric benchmarks while being competitive with state-of-the-art NeRF/3DGS methods.

We propose MeshOn, a method that finds physically and semantically realistic compositions of two input meshes. Given an accessory, a base mesh with a user-defined target region, and optional text strings for both meshes, MeshOn uses a multi-step optimization framework to realistically fit the meshes onto each other while preventing intersections. We initialize the shapes' rigid configuration via a structured alignment scheme using Vision-to-Language Models, which we then optimize using a combination of attractive geometric losses, and a physics-inspired barrier loss that prevents surface intersections. We then obtain a final deformation of the object, assisted by a diffusion prior. Our method successfully fits accessories of various materials over a breadth of target regions, and is designed to fit directly into existing digital artist workflows. We demonstrate the robustness and accuracy of our pipeline by comparing it with generative approaches and traditional registration algorithms.