HexOpt: Efficient and robust hexahedral mesh optimization using Rectified Hybrid Quadratic Jacobian and geometry-aware mapping
Hua Tong, Jessica Zhang · Computer-Aided Design · 2026
We present HexOpt , a novel software package designed to optimize hexahedral mesh quality through a Rectified Hybrid Quadratic Jacobian energy functional and geometry-aware mapping. HexOpt accepts a triangular surface mesh and a volumetric hexahedral mesh as inputs. To overcome critical challenges such as element size-dependent gradient biases, prolonged optimization times, and erroneous boundary projection, we formulate a constrained optimization problem. The Rectified Hybrid Quadratic Jacobian energy is set as the objective function, while equality constraints enforce precise alignment between the quadrilateral boundary and the input geometry. These constraints fix vertices at geometric corners, restrict edge points to edges, and map face points to triangular faces. The optimization is solved via the Augmented Lagrangian method, with the Limited-Broyden–Fletcher–Goldfarb–Shanno method and the Armijo line search method driving the iterative process. The geometry-aware mapping employs normal-guided closest-point projection and mean value Tutte embedding to ensure geometric fidelity. HexOpt demonstrates robust performance across diverse 3D models and hexahedral meshes generated by various methods. It achieves consistent quality improvements without requiring manual intervention or parameter tuning compared with the initial state. Experimental results validate its computational efficiency and robustness in complex geometries, underscoring its utility as a reliable post-processing tool for hexahedral mesh optimization. We provide the HexOpt source code, input/output meshes (around 100 examples), and statistical data in the repository: https://github.com/CMU-CBML/HexOpt .