Geometric modelling and processing of geometric data deals with the mathematical description of realistic shapes for computer graphics, engineering graphics, engineering design, manufacturing technologies, numerical analysis, and scientific computing. Geometric modelling is mathematical in nature but is specifically geared towards its use in engineering and manufacturing fields. The major goal is the pursuit of the use of geometric modelling technology for improving collaboration among the above-mentioned different areas, and to tackle challenges in modelling.

Engineering analysis of models needs innovative use of tools in particular applications. The degree of their detail depends on the procedure of analysis that utilises the geometry. Mathematically, it is difficult to find the “good shapes” among the number of shapes. Intelligent decision making on the types of entities is necessary to use in particular models to meet certain geometric requirements, such as curvature. Hölder regularity is the only criteria to find “good shapes.” However, this technique does not capture the essence of what is subjectively regarded as “good shape”. A more practical measure than Hölder regularity would be useful in curve modelling. Curvature based colour shading, reflection lines, or isophotes are used in surface modelling and are sometimes thought to be necessary to assess the fairness of a surface model. The problem is that all these tools need human interpretation and are not suitable for automated optimisation. The creation of new tools and the modification of old tools of analysis and modelling are the main challenges faced in this field.

This Special Issue intends to bring together mathematicians, engineers, computer scientists, and industry professionals to report recent developments in state-of-the-art strategies in the modelling industry, and to resolve numerous mathematical issues related to geometric modelling. We welcome both original research and review articles.

Potential topics include but are not limited to the following:

• Computational and discrete geometry
• Subdivision curves, surfaces, and solids
• 3D printing and computational manufacturing
• Numerical and graphical analysis of geometric shapes
• Physical based modelling and simulation
• Reverse engineering/reconstruction of surfaces and solids
• Meshing and mesh optimisation
• Shape modelling
• CAGD/CAD/CAM systems
• Fractal geometry for engineers
• Subdivision-based, B-splines, and finite element methods for solving partial differential equations
• Cryptography schemes and cryptanalysis techniques