A frontal Delaunay quad mesh generator using the L^∞norm

Abstract

SUMMARYIn a recent work, a new indirect method to generate all‐quad meshes has been developed. It takes advantage of a well‐known algorithm of the graph theory, namely the Blossom algorithm, which computes in polynomial time the minimum cost perfect matching in a graph. In this paper, we describe a method that allows to build triangular meshes that are better suited for recombination into quadrangles. This is performed by using the infinity norm to compute distances in the meshing process. The alignment of the elements in the frontal Delaunay procedure is controlled by a cross field defined on the domain. Meshes constructed this way have their points aligned with the cross‐field directions, and their triangles are almost right everywhere. Then, recombination with the Blossom‐based approach yields quadrilateral meshes of excellent quality. Copyright © 2013 John Wiley & Sons, Ltd.

Cardiovascular and lung mesh generation based on centerlines

“…Those meshes are based on the generation of a new quadrangular surface mesh of the input geometry. The presented algorithm of quadrangular mesh generation is an original approach that is a combination of a structured elliptic mesh generation approach [5] and an indirect approach [6] that uses distances in the L 1 norm as a base for inserting new points and generates right triangles that are then recombined into quadrangles [7]. From the quadrangular surface mesh, we generate an extruded boundary layer mesh as well as an unstructured tetrahedral mesh of the lumen with pyramids as transition elements [8].…”

Unstructured Grids and the Multigroup Neutron Diffusion Equation

“…If the mesh needs to be based on quadrangles instead, a recombination algorithm can be used to transform two adjacent triangles in one quadrangle, whenever is possible. However, for geometries which are based on rectangular shapes there exist other algorithms [25] both for meshing and for recombining the triangles that give rise to elementary entities with right angles almost everywhere, which may be a desired property of the resulting grid. For finite elements, the steps needed to build the matrices depend on the selection of triangles or quadrangles as the basic elementary geometry because the shape functions change.…”

“…As asked in item (8), how results depend not only on the mesh spacing but also on the meshing algorithm, on the grid's elementary geometric shape, and on the discretization scheme may shed lights on the subject which may be even more interesting than the numerical results themselves. Taking advantage of milonga's capability of reading and parsing command-line arguments, the selection of the core geometry (quarter or eighth), the meshing algorithm (delaunay [16] or delquad [25]), the shape of the elementary entities (triangles or quadrangles), the discretization scheme (volumes or elements), and the characteristic length ℓ of the mesh can be provided at run time. Fixing five values for ℓ = 4, 3, 2, 1, 0.5 gives 2 × 2 × 2 × 2 × 5 = 80 possible combinations, which we solve with successive invocations to milonga with the same input file but with different arguments from a simple script.…”

Sequential decision-making approach for quadrangular mesh generation

“…7). The initial triangular mesh has been generated with the delquad algorithm [17] and contains 34,562 triangles (Fig. 7a).…”

“…Indeed, triangular mesh algorithms usually aim at producing close to equilateral triangles, which is not optimal for recombination [17]. One recent original approach relies on Delaunay-frontal algorithms in L 1 -norm to generate close to right-angled triangles, facilitating the construction of high quality quadrangulations [12,17].…”