We propose a fast intersection-free remeshing of triangular meshes that robustly and efficiently generates high-quality non-intersecting meshes. Conducting intersection checks on all local operations during remeshing to prevent intersections represents the principal efficiency bottleneck. Our method is based on a key observation: intersections primarily occur in structurally complex regions. Accordingly, we develop an adaptive method to identify these key regions and perform intersection checks only for local operations within these regions during remeshing, significantly improving the algorithmic efficiency. Our method is an order of magnitude faster than traditional approaches that perform intersection checks on all local operations. Furthermore, we introduce a flip-aware extension mechanism that effectively avoids triangle flipping by constraining the optimization space of local operations, thereby avoiding the formation of irregular sharp edges. We also employ an adaptive iterative size field to eliminate banding phenomenon and propose a quasi-geometric size field adjustment method to quickly achieve smooth size transitions, thereby improving mesh quality. Compared to state-of-the-art methods, our method consistently and quickly generates higher quality non-intersecting meshes. In addition, we have validated the robustness and efficiency of our method, using all 5,469 non-intersecting valid models from the Thingi10K dataset.

This paper presents a new algorithm, Weighted Squared Volume Minimization (WSVM), for generating high-quality tetrahedral meshes from closed triangle meshes. Drawing inspiration from the principle of minimal surfaces that minimize squared surface area, WSVM employs a new energy function integrating weighted squared volumes for tetrahedral elements. When minimized with constant weights, this energy promotes uniform volumes among the tetrahedra. Adjusting the weights to account for local geometry further achieves uniform dihedral angles within the mesh. The algorithm begins with an initial tetrahedral mesh generated via Delaunay tetrahedralization and proceeds by sequentially minimizing volume-oriented and then dihedral angle-oriented energies. At each stage, it alternates between optimizing vertex positions and refining mesh connectivity through the iterative process. The algorithm operates fully automatically and requires no parameter tuning. Evaluations on a variety of 3D models demonstrate that WSVM consistently produces tetrahedral meshes of higher quality, with fewer slivers and enhanced uniformity compared to existing methods.

By introducing an open-sourced CAD abstraction component common geometry module (CGM) as the integration middleware, a three-layer scheme is implemented to integrate our CAE software high end digital prototyping (HEDP) with mainstream CAD software. The major advantages of a layered software design are two-folded for CAE software developers. One is to provide unified interfaces with the differences of currently available CAD products hided. The other is to encapsulate common services relevant to geometry in the integration middleware. Both advantages could help alleviate development burdens greatly. Moreover, this paper will introduce three important functionalities for CAE systems built on the integration middleware, i.e. data transfer, defeaturing and virtual geometry operations with some practical examples. The above work consists of our preliminary efforts for the research of a third-party CAD/CAE integration middleware neutral for any CAD and CAE products.

In this paper, we present our efforts to parallelize an unstructured quadrilateral mesh generator. Its serial version is based on the divider-and-conquer idea, and mainly includes two stages, i.e. geometry decomposition and mesh generation. Both stages are parallelized separately. A highly efficient fine-grain level parallel scheme is presented to parallelize the stage of geometry decomposition. A SubDomain Graph (SDG), which represents the connections of subdomains, is constructed. The task of parallel mesh generation is then reduced to that of the SDG partitioning. Since the number of elements in subdomains could be pre-computed before meshing, a static load balancing scheme to partition the SDG performs well with the aid of Metis tools. Numerical results show that scalable timing performance could be achieved by using the parallel mesh generator with resulting meshes nicely partitioned among processors, which enables a fast parallel simulation environment by eliminating the traditional I/O-busy process of mesh repartitioning.