Identifying combinations of tetrahedra into hexahedra: a vertex based strategy

Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra an algorithm that performs this identification and builds the set of all possible combinations of tetrahedral elements of an input mesh T into hexahedra, prisms, or pyramids. All identified cells are valid for engineering analysis. First, all combinations of eight/six/five vertices whose connectivity in T matches the connectivity of a hexahedron/prism/pyramid are computed. The subset of tetrahedra of T triangulating each potential cell is then determined. Quality checks allow to early discard poor quality cells and to dramatically improve the efficiency of the method. Each potential hexahedron/prism/pyramid is computed only once. Around 3 millions potential hexahedra are computed in 10 seconds on a laptop. We finally demonstrate that the set of potential hexes built by our algorithm is significantly larger than those built using predefined patterns of subdivision of a hexahedron in tetrahedral elements.Comment: Preprint submitted to CAD (26th IMR special issue

Distance decay in activity chains analysis. A Belgian case study

This paper aims at measuring and testing the distance decay effect in activity chains. It enables one to show how far distance constrains the length of the trips and if there are borders effects. Two Belgian data bases are used: one conducted at the national level, the other at a regional level. Statistical tests are conducted for (1) several definitions of the trip and chain, (2) several distance measurements (time or kilometers), (3) several purposes of trips, and (4) different categories of travellers. This exploratory data analysis enables one to gain information about the spatial aspects of the activity chains and to get a better fit in the gravity type models.

There are 174 Subdivisions of the Hexahedron into Tetrahedra

This article answers an important theoretical question: How many different subdivisions of the hexahedron into tetrahedra are there? It is well known that the cube has five subdivisions into 6 tetrahedra and one subdivision into 5 tetrahedra. However, all hexahedra are not cubes and moving the vertex positions increases the number of subdivisions. Recent hexahedral dominant meshing methods try to take these configurations into account for combining tetrahedra into hexahedra, but fail to enumerate them all: they use only a set of 10 subdivisions among the 174 we found in this article. The enumeration of these 174 subdivisions of the hexahedron into tetrahedra is our combinatorial result. Each of the 174 subdivisions has between 5 and 15 tetrahedra and is actually a class of 2 to 48 equivalent instances which are identical up to vertex relabeling. We further show that exactly 171 of these subdivisions have a geometrical realization, i.e. there exist coordinates of the eight hexahedron vertices in a three-dimensional space such that the geometrical tetrahedral mesh is valid. We exhibit the tetrahedral meshes for these configurations and show in particular subdivisions of hexahedra with 15 tetrahedra that have a strictly positive Jacobian

Finding Hexahedrizations for Small Quadrangulations of the Sphere

This paper tackles the challenging problem of constrained hexahedral meshing. An algorithm is introduced to build combinatorial hexahedral meshes whose boundary facets exactly match a given quadrangulation of the topological sphere. This algorithm is the first practical solution to the problem. It is able to compute small hexahedral meshes of quadrangulations for which the previously known best solutions could only be built by hand or contained thousands of hexahedra. These challenging quadrangulations include the boundaries of transition templates that are critical for the success of general hexahedral meshing algorithms. The algorithm proposed in this paper is dedicated to building combinatorial hexahedral meshes of small quadrangulations and ignores the geometrical problem. The key idea of the method is to exploit the equivalence between quad flips in the boundary and the insertion of hexahedra glued to this boundary. The tree of all sequences of flipping operations is explored, searching for a path that transforms the input quadrangulation Q into a new quadrangulation for which a hexahedral mesh is known. When a small hexahedral mesh exists, a sequence transforming Q into the boundary of a cube is found; otherwise, a set of pre-computed hexahedral meshes is used. A novel approach to deal with the large number of problem symmetries is proposed. Combined with an efficient backtracking search, it allows small shellable hexahedral meshes to be found for all even quadrangulations with up to 20 quadrangles. All 54,943 such quadrangulations were meshed using no more than 72 hexahedra. This algorithm is also used to find a construction to fill arbitrary domains, thereby proving that any ball-shaped domain bounded by n quadrangles can be meshed with no more than 78 n hexahedra. This very significantly lowers the previous upper bound of 5396 n.Comment: Accepted for SIGGRAPH 201

Carpooling and employers: a multilevel modelling approach

Both public policy-makers and private companies promote carpooling as a commuting alternative in order to reduce the number of Single Occupant Vehicle (SOV) users. The Belgian questionnaire Home-To-Work-Travel (HTWT) is used to examine the factors which explain the share of carpooling employees at a worksite. The modal split between carpooling and rail use was also subject of the analysis. The number of observations in the HTWT database (n=7460) makes it possible to use more advanced statistical models: such as multilevel regression models which incorporate, next to the worksite level, also the company and economic sector levels. As a consequence, a more employer-oriented approach replaces the traditional focus of commuting research on the individual. Significant differences in modal split between economic sectors appeared. The most carpool-oriented sectors are construction and manufacturing, while rail transport is more popular in the financial and public sector. Carpooling also tend to be an alternative at locations where rail is no real alternative. Next to this, regular work schedules and smaller sites are positively correlated with a higher share of carpooling employees. Finally, no real evidence could be found for the effectiveness of mobility management measures which promote carpooling. However, most of these measures are classified in the literature as less effective and a case study approach should complete the research on mobility management initiatives

Le recensement de la population : un requiem ?

Ce numéro de Regards économiques vise à rappeler aux distraits que l’histoire du recensement de la population se termine en Belgique en 2001, et que même si un nouvel outil statistique est en gestation, bien des réalités spatiales et/ou sociales seront désormais à jamais occultées. La Belgique se prive ainsi d’un outil stratégique et scientifique capital.

Geslachtsgemeenschap op jonge leeftijd: wat maakt het een positieve ervaring? Samenvatting van de onderzoeksresultaten en praktische implicaties

Dit is een samenvatting van onderzoeksresultaten waarvan het onderzoek kadert binnen het SAFE II-project (Sexual Awareness for Europe) gecoördineerd door IPPF-EN en gesubsidieerd door de Europese Unie in het kader van het Health Programme. Het onderzoek werd uitgevoerd binnen een samenwerking tussen Sensoa en de Vakgroep Sociologie van de Universiteit Gent

The Economic Impacts of Port Activity in Antwerp: A Disaggregated Analysis

The importance of ports is usually measured by indicators such as added value, employment and investment on a much aggregated level. This paper tries to define the importance of the port of Antwerp for the regional and national economy on a disaggregated level. It attempts to identify, quantify and locate the mutual relationships between the different players in the port and between these players and other industries. Finally, it proposes a method to calculate the effects of changes in port activity at a detailed level. A sector analysis is done by means of a reduced regional input-output table, through a bottom-up approach. The most important customers and suppliers of the port's key players or stakeholders are identified. A geographical analysis is feasible by using data on a disaggregated level. Each customer or supplier can be located by means of their postcode. In this way, the extent of the economic impact of the port of Antwerp is quantified.

How to incorporate the spatial dimension within destination choice models? The case of Antwerpen

This paper considers different alternatives for including spatial aspects within the activity-based approach for modeling destination choices. The study area is the urban agglomeration of Antwerpen (Belgium); the city and its suburbs are considered. Individual travel surveys are used. The paper pays particular attention to the inclusion of space within the decision context by including specific land-use explanatory variables generated by Geographical Information Systems. A preliminary geographical analysis is performed in order to represent the city by a limited set of destinations (n = 33) and to characterize those zones in terms of land use. Discrete choice modelling is used: each individual faces the total set of spatial destination alternatives. Several modelling approaches are explored and compared in terms of utility function (for instance Box-Cox; random coefficients) and in terms of global formulation (multinomial logit versus nested logit). The mixed nested logit formulation is selected as best and the parameter estimations are interpreted; it shows the importance of space within destination choices. This paper provides a useful background for decision-makers and planners of transportation policy related to individual mobility patterns. Keywords Discrete choice model, activity-based approach, GIS, land use, urban mobility, Antwerpen