Q-Morph: an indirect approach to advancing front quad meshing

Abstract

SUMMARYQ-Morph is a new algorithm for generating all-quadrilateral meshes on bounded three-dimensional surfaces. After first triangulating the surface, the triangles are systematically transformed to create an all-quadrilateral mesh. An advancing front algorithm determines the sequence of triangle transformations. Quadrilaterals are formed by using existing edges in the triangulation, by inserting additional nodes, or by performing local transformations to the triangles. A method typically used for recovering the boundary of a Delaunay mesh is used on interior triangles to recover quadrilateral edges. Any number of triangles may be merged to form a single quadrilateral. Topological clean-up and smoothing are used to improve final element quality. Q-Morph generates well-aligned rows of quadrilaterals parallel to the boundary of the domain while maintaining a limited number of irregular internal nodes. The proposed method also offers the advantage of avoiding expensive intersection calculations commonly associated with advancing front procedures. A series of examples of Q-Morph meshes are also presented to demonstrate the versatility of the proposed method.

Geometry and Structural Modeling for High-Fidelity Aircraft Conceptual Design Optimization

“…Blended wing-body Truss-braced wing Two-dimensional quad meshing algorithms fall under three general categories: domain-decomposition [20,21], advancing-front [22], and triangulation-based methods [23]. The first two-recursively splitting the domain through heuristic algorithms and marching out from boundaries-are unsuited to the current problem because of the line constraints imposed by the structural members intersecting the skin.…”

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

“…For instance, [57] is based on an heuristic combination of triangles resulting in a quad-dominant mesh. This technology was improved by considering an advancing-front approach during the triangle combination [58][59][60]. These methods start from the boundary of the domain and advance towards the inner part of the geometry until the fronts collide and no triangles are left.…”

“…The advacing-front approach presented in the Q-morph method [60] were extended to three dimensions in the H-morph algorithm [66]. This algorithm generates hexahedral-dominant meshes for arbitrary volumes.…”

Quad-Dominant Mesh Adaptation Using Specialized Simplicial Optimization

“…Once the target vertex density is achieved, adjacent simplicial elements are merged to form cubical ones. Different merging strategies are possible including advancing fronts [14,15,16], graph theory [17] and quality constraints [18,3,4]. Although, some non-cubical elements may remain, particularly in three dimensions, such cubical-dominant meshes are acceptable in many applications.…”