Vers un système de projection icosaédral hiérarchique global sans distorsions pour cartographie Web

Les systèmes de projection cartographique adaptés aux services de cartographie web, suscitent encore de nombreuses questions de recherche. La majorité des services de cartographie Web (ex. Google Maps, Bing Maps) utilise la Projection Web Mercator(WMP), mais cette dernière présente de grandes distorsions systématiques notamment dans les régions nordiques. Il nous est alors paru nécessaire de développer une autre méthode permettant de projeter la surface du globe avec un minimum de distorsion. Notre approche s’inspire de la projection myriahedrale qui suppose que chaque face du myriahedron est suffisamment petite de telle sorte que les distorsions soient négligeables. La méthode proposée consiste à explorer une nouvelle approche de tessellation de la surface du globe et qui permet de projeter la surface du globe sur les faces de la tessellation et à plusieurs niveaux de détails. Cela permet de compenser la faiblesse des méthodes de tessellations existantes utilisées dans la cartographie Web. Cette tessellation utilise un icosaèdre comme modèle géométrique de base avec une densité de partitionnement des faces de l’icosaèdre entre les niveaux de récursivité égale à 4.La méthodologie proposée consiste en quatre étapes successives: a) la construction d'une structure hiérarchique qui résulte de la subdivision récursive des faces de l'icosaèdre ; b) la définition d’un système de projection approprié à la tessellation icosaédrique; c) la projection des données géospatiales de la sphère terrestre sur chaque face de l’icosaèdre; d) le dépliage de la tessellation icosaédrique résultante sur un plan en utilisant des algorithmes de calcul du plus court chemin afin de maintenir le voisinage autour du point d’intérêt. Nous présenterons les étapes de développement et d’implémentation du système proposé et les résultats obtenus dans le cadre de ce projet de recherche. L’étude comparative avec d’autres systèmes de projection montre que notre approche minimise mieux les déformations par tout sur le globe et surtout dans les régions nordiques.Map projection systems adapted to web mapping services still raise many research questions. The majority of web mapping services (ex. Google Maps, Bing Maps) use Web Mercator Projection (WMP) which introduces large systematic distorsionsin spatial data especially in polar rigions. Therefore, it is necessary to develop an alternative method for projecting these regions with minimal distortions. Our approach is inspired of myriahedral projections which assume that each face of a myriahedron is small enough so that the distortions are negligible. Here, in this research work we propose a new approach for the tessellation of the surface of the globe and the projectionof the spatial information from the glob to the faces of the tessellation at differentlevels of details. This compensates for the weakness of the methods used for tessellation in the existing web mapping systems. The proposed tessellation is created based on an icosahedron with a partitioning density of the faces equal to 4. The proposed methodology consists of four stages: a) constructing of a hierarchical structure resulting the recursive subdivision of the faces of the icosahedron, while maintaining topological relationships between the triangles in each level of detail; b) defining of an appropriate projection system to the icosahedral tessellation; c) projecting of geospatial data of the terrestrial sphere on each face of the icosahedron; d) unfolding the resulting icosahedral tessellation on a plane around a point of interest. Here we present different stages of development and implementation of the proposed system and the results obtained in the framework of this research project. The comparative study with other projection systems shows that our approach allows to better minimize different distortions every where on the globe and specially in the polar rigions

Towards Q-analysis Integration in Discrete Global Grid Systems: Methodology, Implications and Data Complexity

Spatial data is characterized by rich contextual information with multiple characteristics at each location. The interpretation of this multifaceted data is an integral part of current technological developments, data rich environments and data driven approaches for solving complex problems. While data availability, exploitation and complexity continue to grow, new technologies, tools and methods continue to evolve in order to meet these demands, including advancing analytical capabilities, as well as the explicit formalization of geographic knowledge. In spite of these developments Discrete Global Grid Systems (DGGS) were proposed as a new comprehensive approach for transforming scientific data of various sources, types and qualities into one integrated environment. The DGGS framework was developed as the global data model and standard for efficient storage, analysis and visualization of spatial information via a discrete hierarchy of equal area cells at various spatial resolutions. Each DGGS cell is the explicit representation of the Earth surface, which can store multiple data values and be conveniently recognized and identified within the hierarchy of the DGGS system. A detailed evaluation of some notable DGGS implementations in this research indicates great prospects and flexibility in performing essential data management operations, including spatial analysis and visualization. Yet they fall short in recognizing interactivity between system components and their visualization, nor providing advanced data friendly techniques. To address these limitations and promote further theoretical advancement of DGGS, this research suggests the use of Q-analysis theory as a way to utilize the potential of the hierarchical DGGS data model via the tools of simplicial complexes and algebraic topology. As a proof of concept and demonstration of Q-analysis feasibility, the method has been applied in a water quality and water health study, the interpretation of which has revealed much contextual information about the behaviour of the water network, the spread of pollution and chain affects. It is concluded that the use of Q-analysis indeed contributes to the further advancement and development of DGGS as a data rich framework for formalizing multilevel data systems and for the exploration of new data driven and data friendly approaches to close the gap between knowledge and data complexity