Eric L. Mestreau

Q-TRAN: A New Approach to Transform Triangular Meshes into Quadrilateral Meshes Locally

Q-Tran is a new indirect algorithmto transform triangular tessellation of bounded three-dimensional surfaces into all-quadrilateralmeshes. The proposed method is simple, fast and produces quadrilaterals with provablygood quality and hence it does not require a smoothing post-processing step. The method is capable of identifying and recovering structured regions in the input tessellation. The number of generated quadrilaterals tends to be almost the same as the number of the triangles in the input tessellation. Q-Tran preserves the vertices of the input tessellation and hence the geometry is preserved even for highly curved surfaces. Several examples of Q-Tran are presented to demonstrate the efficiency of the proposed method.

A three dimensional parametric mesher

A parametric meshing technique is presented. Its distinctive feature relies on approximating the CAD geometry through a hierarchical process where information is gradually gathered. It leads to a robust and high quality mesh for CAD geometries. Emphasis is put on the use of three dimensional information. Limitations of parametric plane meshing is also highlighted. Zero and first order surface approximations are commented, and parametric mesh generation techniques are compared. In the context of the DOD CREATE-MG project, different CAD kernels and meshers communicate through application programming interfaces (API) as plugins. The parametric mesher is coupled to the CAD through the Capstone API’s and is independent of a particular CAD kernel. Numerous examples illustrate the method ’s capabilities.

Singularities in Parametric Meshing

A parametric meshing technique is presented with special emphasis to singularities in the parametric mapping. Singularities are locations where the parametric mapping is highly distorted or even singular. In a NURBS context, this arises when control points are clustered into the same location in three dimensions. Limitations of parametric plane meshing in this context are highlighted, and zero- and first-order surface approximations are commented. In the context of the DOD CREATE-MG project, different CAD kernels and mesh generators communicate as plugins through application programming interfaces (API). The parametric mesh generator is coupled to the CAD through the Capstone APIs and is independent of a particular CAD kernel. Some CAD kernels do not allow these geometrical constructions while some tolerate it. It is therefore a necessity to handle these degenerate cases properly. Examples illustrate the method’s capabilities.

Mesh Insertion of Hybrid Meshes

A mesh insertion method is presented to merge a tool mesh into a target mesh. All the entities of the tool mesh are preserved in the output mesh while some of the entities of the target mesh are modified or eliminated in order to obtain a topologically conforming mesh. The algorithm can handle non-manifold surfaces formed of quadrilaterals and/or triangles as well as volumetric meshes based on hexahedra, prisms, pyramids and/or tetrahedra. Lower order elements such as beams can also be taken into consideration. A robust 2-steps advancing front algorithm is introduced to fill the narrow gap between the two mesh objects to obtain a complete crack-free connection. An efficient mesh data structure is developed to optimize the search operations and the intersection tests needed by the algorithm. Several application examples are provided to show the strength of the presented algorithm.

Entropy solution at concave corners and ridges

Boundary layer volume mesh generation applied to generic non smooth surfaces gives rise to various challenges. The mesh should present a strong anisotropy normal to the surface, should smoothly transition to the isotropic region, and should take into account complex ridges and corners. A theoretical tool to attack this problem consists in relying on the Eikonal equation, which is a non linear hyperbolic equation capable of generating shocks at concave regions and expansion waves close to convex regions. Typically, expansion waves are discretized with multiple normals. In this work, emphasis is given to the the reversible phenomenon, where shocks appear. This represents the extension to the three dimensional space of. Only few strategies have been advocated for concave situations. In, negative elements are removed, therefore stopping the front progression close to these locations. However, since typically a small jump between layers is enforced, stopping the front prematurely will spread from this location outwards. In, the normal direction is limited. However, this may violate the prescribed size, or generate extremely small cells close to concave corners. Another approach consists in using smoothed normals as extruded directions, or even a blend of both, trading normality for postponed front abortion. As mentioned previously, Athanasiadis et al. is one of the few references to consider special procedures for concave situations, where characteristics coalesce. It is mentioned that a quad surface mesh is expected to be able to collapse the prisms along concave ridges in a structured manner. However, this represents only a particular configuration of a more generic approach. The Voronoi diagram is the key building block of this construction. Considering the boundary layer mesh as a subpart of the three dimensional generalized Voronoi diagram, where triangle faces, edges and vertices are taken into account, the Voronoi bisectors are important spatial locations that ideally would be discretized in the mesh. This would require however the computation of the full three dimensional generalized Voronoi diagram. For triangle surface meshes, concavity and convexity are two important notions because they implicitly give informations on the distance field generated by the triangles in space. Convexity means that, as seen before, the distance field will present expansion waves, while concavity brings shock waves. Regarding the Voronoi diagram, convexity is associated with multiple normals, while concavity implies Voronoi bisectors. Therefore, concave edges will provide the birth of Voronoi faces while concave corners will generate Voronoi edges in three dimensions.