de la Varga, M., Schaaf, A., and Wellmann, F.: GemPy 1.0: open-source stochastic geological modeling and inversion, Geosci. Model Dev., 12, 1–32, https://doi.org/10.5194/gmd-12-1-2019, 2019.
De Paor, D. G.: Bézier curves and geological design, in: Computer
methods in the geosciences, Elsevier, 389–417, https://doi.org/10.1016/S1874-561X(96)80031-9, 1996.
DeRose, T., Kass, M., and Truong, T.: Subdivision surfaces in character
animation, Proceedings of the 25th annual conference on Computer graphics
and interactive techniques, 19–24 July 1998, Orlando, Florida, United States of America, 85–94, https://doi.org/10.1145/280814.280826, 1998.
Farin, G. and Hamann, B.: Current trends in geometric modeling and selected
computational applications, J. Comput. Phys., 138, 1–15,
https://doi.org/10.1006/jcph.1996.5621, 1997.
Freymark, J., Scheck-Wenderoth, M., Bär, K., Stiller, M., Fritsche,
J.-G., Kracht, M., and Gomez Dacal, M. L.: 3D-URG: 3D gravity constrained
structural model of the Upper Rhine Graben, GFZ Data Services [data set], https://doi.org/10.5880/GFZ.4.5.2020.004, 2020.
Halstead, M., Kass, M., and DeRose, T.: Efficient, fair interpolation using
Catmull-Clark surfaces, Proceedings of the 20th annual conference on
Computer graphics and interactive techniques, 1–6 August 1993, Anaheim, California, United States of America, 35–44, https://doi.org/10.1145/166117.166121, 1993.
Hoppe, H., DeRose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J.,
Schweitzer, J., and Stuetzle, W.: Piecewise smooth surface reconstruction,
Proceedings of the 21st annual conference on Computer graphics and
interactive techniques, 24–29 July 1994, Orlando, Florida, United States of America, 295–302, https://doi.org/10.1145/192161.192233, 1994.
Jacquemyn, C., Jackson, M. D., and Hampson, G. J.: Surface-based geological
reservoir modelling using grid-free NURBS curves and surfaces, Math.
Geosci., 51, 1–28, https://doi.org/10.1007/s11004-018-9764-8, 2019.
Kälberer, F., Nieser, M., and Polthier, K.: Quadcover-surface
parameterization using branched coverings, Computer graphics forum, 26, 375–384,
https://doi.org/10.1111/j.1467-8659.2007.01060.x, 2007.
Kennedy, J. and Eberhart, R.: Particle swarm optimization, Proceedings of
ICNN'95-international conference on neural networks, 27 November–1 December 1995, Perth, WA, Australia, 1942–1948, https://doi.org/10.1109/ICNN.1995.488968, 1995.
Lavoué, G., Dupont, F., and Baskurt, A.: A framework for quad/triangle
subdivision surface fitting: Application to mechanical objects, Computer
Graphics Forum, 26, 1–14, https://doi.org/10.1111/j.1467-8659.2007.00930.x, 2007.
Lévy, B. and Mallet, J.-L.: Discrete smooth interpolation: Constrained
discrete fairing for arbitrary meshes, ACM Transactions on Graphics, 8, 121–144, https://doi.org/10.1145/62054.62057, 1999.
Loop, C.: Smooth subdivision surfaces based on triangles, Department of Mathematics, University of Utah, 1987.
Ma, X., Keates, S., Jiang, Y., and Kosinka, J.: Subdivision surface fitting
to a dense mesh using ridges and umbilics, Comput. Aided Geom. D.,
32, 5–21, https://doi.org/10.1016/j.cagd.2014.10.001, 2015.
Mallet, J.-L.: Geomodeling, Oxford University Press, Oxford University Press Inc, ISBN-10 0195144600, ISBN-13 978-0195144604, 2002.
Marinov, M. and Kobbelt, L.: Optimization methods for scattered data
approximation with subdivision surfaces, Graphical Models, 67, 452-473,
https://doi.org/10.1016/j.gmod.2005.01.003, 2005.
Miranda, L. J.: PySwarms: a research toolkit for Particle Swarm Optimization
in Python, J. Open Source Softw., 3, 433, https://doi.org/10.21105/joss.00433, 2018.
Moulaeifard, M., Wellmann, F., Bernard, S., de la Varga, M., and Bommes, D.:
Subdivide and Conquer: Adapting Non-Manifold Subdivision Surfaces to
Surface-Based Representation and Reconstruction of Complex Geological
Structures, Math. Geosci., 55, 81–111, https://doi.org/10.1007/s11004-022-10017-x, 2023.
Paluszny, A., Matthäi, S. K., and Hohmeyer, M.: Hybrid finite
element–finite volume discretization of complex geologic structures and a
new simulation workflow demonstrated on fractured rocks, Geofluids, 7,
186–208, https://doi.org/10.1111/j.1468-8123.2007.00180.x,
2007.
Peters, J.: Point-augmented biquadratic C1 subdivision surfaces, Graphical
models, 77, 18–26, https://doi.org/10.1016/j.gmod.2014.10.003,
2015.
Powell, M. J.: An efficient method for finding the minimum of a function of
several variables without calculating derivatives, Computer J., 7,
155–162, https://doi.org/10.1093/comjnl/7.2.155, 1964.
Reif, U.: A unified approach to subdivision algorithms near extraordinary
vertices, Comput. Aided Geom. D., 12, 153–174, https://doi.org/10.1016/0167-8396(94)00007-F, 1995.
Rossignac, J. and Cardoze, D.: Matchmaker: Manifold Breps for non-manifold
r-sets, Proceedings of the fifth ACM symposium on Solid modeling and
applications, 1 June 1999, Ann Arbor Michigan USA, 31–41, https://doi.org/10.1145/304012.304016, 1999.
Sederberg, T. W., Finnigan, G. T., Li, X., Lin, H., and Ipson, H.:
Watertight trimmed NURBS, ACM Transactions on Graphics (TOG), 27, 1–8,
https://doi.org/10.1145/1360612.1360678 2008.
SimBe-hub and MohammadCGRE:SimBe-hub/PySubdiv: PySubdiv (v1.0.0), Zenodo [code and data set], https://doi.org/10.5281/zenodo.6878051, 2022.
Stam, J.: Evaluation of loop subdivision surfaces, SIGGRAPH'98 CDROM
Proceedings, 19–24 July 1998, Orlando, Florida, United States of America, Corpus ID: 8420692, 85–94, 1998.
Sullivan, C. and Kaszynski, A.: PyVista: 3D plotting and mesh analysis
through a streamlined interface for the Visualization Toolkit (VTK), J. Open Source Softw., 4, 1450, https://doi.org/10.21105/joss.01450, 2019.
Suzuki, H., Takeuchi, S., and Kanai, T.: Subdivision surface fitting to a
range of points, Proceedings. Seventh Pacific Conference on Computer
Graphics and Applications (Cat. No. PR00293), 158–167, https://doi.org/10.1109/PCCGA.1999.803359, 1999.
Van Der Walt, S., Colbert, S. C., and Varoquaux, G.: The NumPy array: a
structure for efficient numerical computation, Comput. Sci.
Eng., 13, 22–30, https://doi.org/10.1109/MCSE.2011.37,
2011.
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T.,
Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., and Bright, J.:
SciPy 1.0: fundamental algorithms for scientific computing in Python, Nature
Methods, 17, 261–272, https://doi.org/10.1038/s41592-019-0686-2, 2020.
Wellmann, F. and Caumon, G.: 3-D Structural geological models: Concepts,
methods, and uncertainties, Adv. Geophys., 59, 1–121,
https://doi.org/10.1016/bs.agph.2018.09.001, 2018.
Wu, X., Zheng, J., Cai, Y., and Li, H.: Variational reconstruction using
subdivision surfaces with continuous sharpness control, Computational Visual
Media, 3, 217–228, https://doi.org/10.1007/s41095-017-0088-2, 2017.
Ying, L. and Zorin, D.: Nonmanifold subdivision, Proceedings Visualization,
VIS'01, 21–26 October 2001, San Diego California, 325–569, https://doi.org/10.1109/VISUAL.2001.964528,
2001.
