# MeshODE: A Robust and Scalable Framework for Mesh Deformation

arXiv: https://arxiv.org/abs/2005.11617 · HTML: https://mlsanity.com/paper/2005.11617/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2020.

## Built on by (most cited first, 6 of 6)

- [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022)
- [Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes](https://mlsanity.com/paper/2205.02904/) (2022)
- [CLOAF: CoLlisiOn-Aware Human Flow](https://mlsanity.com/paper/2403.09050/) (2024)
- [TutteNet: Injective 3D Deformations by Composition of 2D Mesh Deformations](https://mlsanity.com/paper/2406.12121/) (2024)
- [Preconditioned Deformation Grids](https://mlsanity.com/paper/2509.18097/) (2025)
- [Neu-PiG: Neural Preconditioned Grids for Fast Dynamic Surface Reconstruction on Long Sequences](https://mlsanity.com/paper/2602.22212/) (2026)

## Abstract (arXiv)

We present MeshODE, a scalable and robust framework for pairwise CAD model deformation without prespecified correspondences. Given a pair of shapes, our framework provides a novel shape feature-preserving mapping function that continuously deforms one model to the other by minimizing fitting and rigidity losses based on the non-rigid iterative-closest-point (ICP) algorithm. We address two challenges in this problem, namely the design of a powerful deformation function and obtaining a feature-preserving CAD deformation. While traditional deformation directly optimizes for the coordinates of the mesh vertices or the vertices of a control cage, we introduce a deep bijective mapping that utilizes a flow model parameterized as a neural network. Our function has the capacity to handle complex deformations, produces deformations that are guaranteed free of self-intersections, and requires low rigidity constraining for geometry preservation, which leads to a better fitting quality compared with existing methods. It additionally enables continuous deformation between two arbitrary shapes without supervision for intermediate shapes. Furthermore, we propose a robust preprocessing pipeline for raw CAD meshes using feature-aware subdivision and a uniform graph template representation to address artifacts in raw CAD models including self-intersections, irregular triangles, topologically disconnected components, non-manifold edges, and nonuniformly distributed vertices. This facilitates a fast deformation optimization process that preserves global and local details. Our code is publicly available.