![]() ![]() ![]() In addition to implicit and parametric surface-based models, previous studies have investigated hybrid methods (Hassanpour et al. In contrast to grid-based implicit geomodelling, one of the key advantages of parametric surface-based methods is that most of the critical details of the model, such as heterogeneity, will be well maintained since there is no need to consider the “averaged value” within the cells (Jacquemyn et al. ![]() 2019 De Kemp 1999 Wellmann and Caumon 2018). Similar to applications in computer graphics, parametric surface-based geological and reservoir representations are defined by the surrounding surfaces (Caumon et al. A parametric representation has advantages over an implicit representation in the direct representation of surfaces and it can present details in a more compact and modifiable form but at the cost of requiring more effort for calculating spatial queries (Botsch et al. (2010), implicit and parametric representations can be considered as the two main types of surface representations, where in both types, the surface is defined by a specific function: implicit surfaces are defined by a scalar-valued function, and the aim is to find a zero level set, whereas a parametric surface is defined by a vector-valued function, and the aim is to convert the three-dimensional to two-dimensional models in the parametric domain. Surface representation is one of the common concepts between geology and computer graphics. Also, the fitted model can reduce the cost of modelling and simulation by using a reduced number of vertices in comparison with the complex geological structure. The fitted surfaces are watertight, controllable with control points, and topologically similar to the main geological structure. Finally, solving inverse problems by fitting the smooth surfaces to complex geological structures is investigated with a case study. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modelling, are explored, and the subdivision surface method, which is compatible with non-manifold topology, is described. Investigating subdivision schemes with semi-sharp creases is therefore an important part of this paper, as semi-sharp creases characterise the resistance of a mesh structure to the subdivision procedure. Many complex geological structures require a combination of smooth and sharp edges. It is worth mentioning that watertight models are an important basis for subsequent process simulations. ![]() Although NURBS surfaces have been used in geological modelling, subdivision surfaces as a standard method in the animation and gaming industries have so far received little attention-even if subdivision surfaces support arbitrary topologies and watertight boundary representation, two aspects that make them an appealing choice for complex geological modelling. Specifically, we investigate the use of NURBS (non-uniform rational B-splines) and subdivision surfaces, as two main parametric surface-based modelling methods, and compare the strengths and weaknesses of the two approaches. In this work, we therefore review surface-based geological modelling methods from both a geological and computer graphics perspective. However, as many of these methods have been developed for other types of applications, some of the requirements for the representation of geological features may not be considered, and the capacities and limitations of different algorithms are not always evident. Methods from the field of computer graphics are the foundation for the representation of geological structures in the form of geological models. ![]()
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