Optimal layout embedding for semi-structured quad meshing

The embedding of quadrilateral layouts is a critical step in semi-structured mesh generation, yet existing methods often generate suboptimal embedding either arises from geometric fidelity or numeric feasibility. To address this, we introduce a novel quadrilateral layout embedding optimization method that synergistically combines geometric and numerical optimization perspectives. First, we propose a feature-preserving Laplacian smoothing algorithm to optimize node embedding while ensuring geometric fidelity. Second, we design a field-aligned arc embedding method to obtain arc embeddings with minimal parametric distortion. Finally, we validate our approach on a suite of typical 3D models, demonstrating that the proposed method consistently produces high-quality layout embeddings surpass existing techniques in scaled Jacobian and aspect ratio.