Q-Morph: An indirect approach to advancing front quad meshing. $Q$-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.

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  1. Sun, Lu; Zhao, Guoqun; Yeh, Gour-Tsyh: 3D hybrid mesh generation with an improved vertical stretch algorithm for geometric models with pinch-out features (2021)
  2. Karčiauskas, Kȩstutis; Peters, Jörg: Low degree splines for locally quad-dominant meshes (2020)
  3. Xiao, Zhoufang; He, Shouping; Xu, Gang; Chen, Jianjun; Wu, Qing: A boundary element-based automatic domain partitioning approach for semi-structured quad mesh generation (2020)
  4. Sun, Lu; Zhao, Guoqun; Yeh, Gour-Tsyh: An automatic quadrilateral mesh generation algorithm applied to 2-D overland flow simulations (2018)
  5. Sun, Lu; Yeh, Gour-Tsyh; Lin, Fang Pang; Zhao, Guoqun: Automatic quadrilateral mesh generation and quality improvement techniques for an improved combination method (2015)
  6. Oñate, Eugenio: Structural analysis with the finite element method. Linear statics. Volume 2: Beams, plates and shells (2013)
  7. Remacle, J.-F.; Henrotte, F.; Carrier-Baudouin, T.; Béchet, E.; Marchandise, E.; Geuzaine, C.; Mouton, T.: A frontal Delaunay quad mesh generator using the (L^\infty) norm (2013)
  8. Remacle, J.-F.; Lambrechts, J.; Seny, B.; Marchandise, E.; Johnen, A.; Geuzainet, C.: Blossom-Quad: a non-uniform quadrilateral mesh generator using a minimum-cost perfect-matching algorithm (2012)
  9. Schiffer, T.; Aurenhammer, F.; Demuth, M.: Computing convex quadrangulations (2012)
  10. Liu, Yan; Xing, H. L.; Guan, Zhenqun: An indirect approach for automatic generation of quadrilateral meshes with arbitrary line constraints (2011)
  11. Lu, Linfa; Qian, Xiaoyuan; Shi, Xiquan; Liu, Fengshan: Quading triangular meshes with certain topological constraints (2011)
  12. Burgos, Manuel A.; Chia, Juan M.; Corral, Roque; López, Carlos: Rapid meshing of turbomachinery rows using semi-unstructured multi-block conformal grids (2010) ioport
  13. Ghadimi, Parviz; Faizi Chekab, Mohammad A.; Maleki, Farzam Safarzadeh: A novel approach to node distribution for 2D mesh generation and its application in marine and ocean engineering (2010)
  14. Staten, Matthew L.; Kerr, Robert A.; Owen, Steven J.; Blacker, Ted D.; Stupazzini, Marco; Shimada, Kenji: Unconstrained plastering - hexahedral mesh generation via advancing-front geometry decomposition (2010)
  15. Randrianarivony, Maharavo; Brunnett, Guido: Preparation of CAD and molecular surfaces for meshfree solvers (2008)
  16. Hartley, P.; Pillinger, I.: Numerical simulation of the forging process (2006)
  17. Kolk, Karsten; Kuhn, Günther: The advanced simulation of fatigue crack growth in complex 3D structures (2006)
  18. Lee, C. K.; Xu, Q. X.: A new automatic adaptive 3D solid mesh generation scheme for thin-walled structures (2005)
  19. Lo, S. H.; Wang, W. X.: Generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3D domain (2005)
  20. Lo, S. H.; Wang, W. X.: Generation of finite element mesh with variable size over an unbounded 2D domain (2005)

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