CMN 2026

The Meccano Method for Adaptive Triangulation of 2D Regions with Automatic Topology Identification

  • Socorro-Marrero, Guillermo Valentín (University Institute for Intelligent Systems)
  • Oliver-Serra, Albert (University Institute for Intelligent Systems)
  • Montenegro, Rafa (University Institute for Intelligent Systems)

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This work addresses the automatic generation of triangulations within the Meccano method [1], focusing on the construction of the meccano directly from the geometric description of the domain. The strategy circumvents the requirement of a user-defined meccano and is applicable to two-dimensional regions with non-intersecting boundaries. The procedure starts from a polyline representation of the domain boundaries and constructs an initial coarse quadtree. This quadtree is adaptively refined under a set of topological constraints that ensure the domain topology is correctly identified. The resulting quadtree decomposition provides the initial meccano for the Meccano method. Specifically, this involves defining piecewise bijective mappings between each physical boundary and its counterpart in the meccano, applying Kossaczký refinement to approximate the boundaries with a prescribed tolerance, and performing simultaneous untangling and mesh optimization to obtain a valid mesh with higher element quality. Additional refinement strategies are also considered to improve the robustness of the initial meccano. This approach enables the automatic generation of conforming meshes for arbitrary planar geometries. Compared with standard meshing techniques such as Delaunay triangulation or advancing front methods, the resulting meshes exhibit improved quality for a similar number of elements and remain insensitive to the discretization of the polyline boundary description [2]. Representative numerical examples are included to illustrate the method's performance. REFERENCES [1] J. M. Cascón, R. Montenegro, J. M. Escobar, E. Rodríguez, and G. Montero, The Meccano Method for Automatic Tetrahedral Mesh Generation of Complex Genus-Zero Solids, Proceedings of the 18th International Meshing Roundtable, pp. 463-480,2009. [2] J. M. Cascón, E. Rodríguez, J. M. Escobar, and R. Montenegro, Comparison of the meccano method with standard mesh generation techniques. Engineering with Computers, Vol. 31, no. 1, pp. 161-174, 2013.