We analyze the joint efforts made by the geometry processing and the numerical analysis communities in the last decades to define and measure the concept of “mesh quality”. Researchers have been striving to determine how, and how much, the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depends on the particular mesh adopted to model the problem, and which geometrical features of the mesh most influence the result. The goal was to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. We overview the most common quality indicators, measures, or metrics that are currently used to evaluate the goodness of a discretization and drive mesh generation or mesh coarsening/refinement processes. We analyze a number of local and global indicators, defined over two‐ and three‐dimensional meshes with any type of elements, distinguishing between simplicial, quadrangular/hexahedral, and generic polytopal elements. We also discuss mesh optimization algorithms based on the above indicators and report common libraries for mesh analysis and quality‐driven mesh optimization.

The definition of a molecular surface which is physically sound and computationally efficient is a very interesting and long standing problem in the implicit solvent continuum modeling of biomolecular systems as well as in the molecular graphics field. In this work, two molecular surfaces are evaluated with respect to their suitability for electrostatic computation as alternatives to the widely used Connolly-Richards surface: the blobby surface, an implicit Gaussian atom centered surface, and the skin surface. As figures of merit, we considered surface differentiability and surface area continuity with respect to atom positions, and the agreement with explicit solvent simulations. Geometric analysis seems to privilege the skin to the blobby surface, and points to an unexpected relationship between the non connectedness of the surface, caused by interstices in the solute volume, and the surface area dependence on atomic centers. In order to assess the ability to reproduce explicit solvent results, specific software tools have been developed to enable the use of the skin surface in Poisson-Boltzmann calculations with the DelPhi solver. The results indicate that the skin and Connolly surfaces have a comparable performance from this last point of view.

A urban digital twin is the virtual representation of real assets, processes, systems and subsystems of a city. It uses and integrates heterogeneous data to learn and evolve with the physical city, providing support to monitor the current status and predict/anticipate possible future scenarios. In this paper, we focus on the issues and potential related to the geometric layer of the city digital twin. On the one hand, detailed 3D data to reconstruct the urban morphology very accurately might not be available, and planning a new survey is costly in terms of money and time. On the other hand, the more the geometry adheres to the real counterpart, the more accurate measures and simulations related to the urban space will be. We describe our approach to develop the geometric layer of the digital twin of the city of Matera, in Italy, using only pre-existing public data. Specifically, our method exploits available digital elevation models from a previous regional aerial survey and integrates them with data coming from OpenStreetMap to generate an as-precise-as-possible 3D model, annotated with heterogeneous semantic information. We demonstrate the potential of the geometric layer by developing two geometric characterisation services, namely route slope extraction and light/shadow maps according to a specific date and time. In the next steps, the computed attributes will help to answer specific objectives which could be of interest for the Municipality, such as personalised optimal routes taking into account user preferences including slope and perceived environmental comfort.

The digital twin (DT) paradigm provides a purpose-built digital representation of a physical system. DTs are often composed by several interconnected models, which need to be specifically tailored to fit the DT purposes. The objective of this work is the development of an urban digital twin (UDT) for the city of Matera, following urban intelligence (UI) paradigm. The latter leverages the multi-disciplinary integration and optimization of the city systems and subsystems to develop purpose-driven DTs and support the decision-making process. The UDT is intended to support governance, stakeholders, and citizens, integrating morphological data for the city representation, reliable simulation tools and data-driven methods for the city state prediction (e.g., traffic, solar irradiation), optimization algorithms for planning and emergency response, sensors for vehicle and pedestrian traffic volumes and environmental monitoring (e.g., pollutant distributions), and a participatory data collection process from the citizens. A Data Lake is used to make available to the UDT modules the data produced by the morphological representation, simulations/data-driven methods, sensors, and the participatory data. The Data Lake provides a standardized approach for the aggregation and extraction of information. Finally, an Urban Sensing Engine supports the decision-making process with artificial intelligence forms of reasoning, to effectively combine the information produced by the UDT components.