![](bg8.png)
the influence of irregularities on mesh quality. We
also show that a transition requires no interior singu-
larities if the size function gradient is constant. With
this knowledge, we can remove irregularities from
meshes generated by remeshing or with Delaunay
refinement without decreasing quality significantly.
Furthermore, we present a technique to estimate the
required number of blocks for correctly representing
a domain while satisfying the constraints imposed by
a size function. In the future, we plan to extend this
concepts to more complex problems.
REFERENCES
Alliez, P., De Verdiere, E. C., Devillers, O., and Isenburg,
M. (2003). Isotropic surface remeshing. In 2003
Shape Modeling International., pages 49–58. IEEE.
Alliez, P., Ucelli, G., Gotsman, C., and Attene, M. (2008).
Recent advances in remeshing of surfaces. In Shape
analysis and structuring, pages 53–82. Springer.
Amenta, N., Bern, M., and Eppstein, D. (1999). Optimal
point placement for mesh smoothing. Journal of Al-
gorithms, 30(2):302–322.
Armstrong, C. G., Fogg, H. J., Tierney, C. M., and Robin-
son, T. T. (2015). Common themes in multi-block
structured quad/hex mesh generation. Procedia En-
gineering, 124:70 – 82. 24th International Meshing
Roundtable.
Armstrong, C. G., Li, T. S., Tierney, C., and Robinson, T. T.
(2018). Multiblock mesh refinement by adding mesh
singularities. In International Meshing Roundtable,
pages 189–207. Springer.
Bank, R. E. and Smith, R. K. (1997). Mesh smoothing using
a posteriori error estimates. SIAM Journal on Numer-
ical Analysis, 34(3):979–997.
B
¨
ansch, E. (1991). Local mesh refinement in 2 and 3 di-
mensions. IMPACT of Computing in Science and En-
gineering, 3(3):181–191.
Beaufort, P.-A., Lambrechts, J., Henrotte, F., Geuzaine, C.,
and Remacle, J.-F. (2017). Computing cross fields
a pde approach based on the ginzburg-landau theory.
Procedia engineering, 203:219–231.
Blacker, T. D. and Stephenson, M. B. (1991). Paving: A
new approach to automated quadrilateral mesh gener-
ation. International Journal for Numerical Methods
in Engineering, 32(4):811–847.
Bommes, D., Lvy, B., Pietroni, N., Puppo, E., Silva, C.,
Tarini, M., and Zorin, D. (2013). Quad-mesh gener-
ation and processing: A survey. Computer Graphics
Forum, 32(6):51–76.
Bommes, D., Zimmer, H., and Kobbelt, L. (2009). Mixed-
integer quadrangulation. ACM Trans. Graph., 28(3).
Botsch, M. and Kobbelt, L. (2004). A remeshing approach
to multiresolution modeling. In Proceedings of the
2004 Eurographics/ACM SIGGRAPH symposium on
Geometry processing, pages 185–192.
Campen, M. (2017). Partitioning surfaces into quadrilat-
eral patches: A survey. Computer Graphics Forum,
36(8):567–588.
Canann, S. A., Tristano, J. R., Staten, M. L., et al. (1998).
An approach to combined laplacian and optimization-
based smoothing for triangular, quadrilateral, and
quad-dominant meshes. In IMR, pages 479–494. Cite-
seer.
Cheng, S.-W., Dey, T. K., and Shewchuk, J. (2012). Delau-
nay mesh generation. CRC Press.
Crane, K., Desbrun, M., and Schr
¨
oder, P. (2010). Trivial
connections on discrete surfaces. In Computer Graph-
ics Forum, volume 29, pages 1525–1533. Wiley On-
line Library.
Engwirda, D. and Ivers, D. (2016). Off-centre steiner
points for delaunay-refinement on curved surfaces.
Computer-Aided Design, 72:157–171.
Erten, H. and
¨
Ung
¨
or, A. (2009). Quality triangulations with
locally optimal steiner points. SIAM Journal on Sci-
entific Computing, 31(3):2103–2130.
Georgiadis, C., Beaufort, P., Lambrechts, J., and Remacle,
J. (2017). High quality mesh generation using cross
and asterisk fields: Application on coastal domains.
CoRR, abs/1706.02236.
Klberer, F., Nieser, M., and Polthier, K. (2007). Quadcover
- surface parameterization using branched coverings.
Computer Graphics Forum, 26(3):375–384.
Kowalski, N., Ledoux, F., and Frey, P. (2013). A pde based
approach to multidomain partitioning and quadrilat-
eral meshing. In Proceedings of the 21st international
meshing roundtable, pages 137–154. Springer.
L
¨
ohner, R. and Parikh, P. (1988). Generation of three-
dimensional unstructured grids by the advancing-front
method. International Journal for Numerical Methods
in Fluids, 8(10):1135–1149.
Peraire, J., Vahdati, M., Morgan, K., and Zienkiewicz,
O. C. (1987). Adaptive remeshing for compressible
flow computations. Journal of computational physics,
72(2):449–466.
Persson, P.-O. (2005). Mesh generation for implicit geome-
tries. PhD thesis, Massachusetts Institute of Technol-
ogy.
Ray, N., Vallet, B., Li, W. C., and L
´
evy, B. (2008). N-
symmetry direction field design. ACM Transactions
on Graphics (TOG), 27(2):1–13.
Remacle, J. F., Henrotte, F., Baudouin, T. C., Geuzaine, C.,
B
´
echet, E., Mouton, T., and Marchandise, E. (2013).
A frontal delaunay quad mesh generator using the L ∞
norm. International Journal for Numerical Methods
in Engineering, 94(5):494–512.
Shewchuk, J. R. (1996). Triangle: Engineering a 2d quality
mesh generator and delaunay triangulator. In Work-
shop on Applied Computational Geometry, pages
203–222. Springer.
Shewchuk, J. R. (1997). Delaunay refinement mesh gener-
ation. Technical report, Carnegie-Mellon Univ Pitts-
burgh Pa School of Computer Science.
¨
Ung
¨
or, A. (2004). Off-centers: A new type of steiner points
for computing size-optimal quality-guaranteed delau-
nay triangulations. In Latin American Symposium on
Theoretical Informatics, pages 152–161. Springer.
Zint, D., Grosso, R., Aizinger, V., and K
¨
ostler, H. (2019).
Generation of block structured grids on complex
domains for high performance simulation. Com-
putational Mathematics and Mathematical Physics,
59(12):2108–2123.
GRAPP 2021 - 16th International Conference on Computer Graphics Theory and Applications
74