Ali Mahdavi-Amiri

A Survey of Digital Earth

The creation of a digital representation of the Earth and its associated data is a complex and difficult task. The incredible size of geospatial data and differences between data sets pose challenges related to big data, data creation, and data integration. Advances in globe representation and visualization have made use of Discrete Global Grid Systems (DGGSs) that discretize the globe into a set of cells to which data are assigned. DGGSs are well studied and important in the GIS, OGC, and Digital Earth communities but have not been well-introduced to the computer graphics community. In this paper, we provide an overview of DGGSs and their use in digitally representing the Earth, describe several current Digital Earth systems and their methods of Earth representation, and list a number of applications of Digital Earths with related works. Moreover, we discuss the key research areas and related papers from computer graphics that are useful for a Digital Earth system, such as advanced techniques for geospatial data creation and representation. Graphical abstractDisplay Omitted HighlightsWe provide definitions of Digital Earths and discrete global grid systems.We discuss different data sets that are represented on Digital Earths, the methods of their acquisition, and the techniques for rendering and processing them.We discuss each component of discrete global grid system such as refinement, indexing, and projection.We provide some state of the art techniques to provide a discrete global grid system.Finally, we study applications of Digital Earths in different areas such as environmental monitoring and education.

Hexagonal connectivity maps for Digital Earth

Geospatial data are gathered through a variety of different methods. The integration and handling of such datasets within a Digital Earth framework are very important in many aspects of science and engineering. One means of addressing these tasks is to use a Discrete Global Grid System and map points of the Earths surface to cells. An indexing mechanism is needed to access the data and handle data queries within these cells. In this paper, we present a general hierarchical indexing mechanism for hexagonal cells resulting from the refinement of triangular spherical polyhedra representing the Earth. In this work, we establish a 2D hexagonal coordinate system and diamond-based hierarchies for hexagonal cells that enables efficient determination of hierarchical relationships for various hexagonal refinements and demonstrate its usefulness in Digital Earth frameworks.

Special Section on Graphics Interface: Atlas of connectivity maps

Semiregular models are now ubiquitous in computer graphics. These models are constructed by refining a model with an arbitrary initial connectivity. Due to the regularity enforced by the refinement, the vertices of semiregular models are mostly regular. To benefit from this regularity, it is desirable to have a data structure specifically designed for such models. We discuss how to design such a data structure, which we call the atlas of connectivity maps (ACM) for semiregular models. In an ACM, semiregular models are divided into regular patches. The connectivity between patches is captured at the coarsest resolution. In this paper, we discuss how to find these patches in a given semiregular model and how to set up the ACM. We also show some of the benefits of this data structure in applications such as the multiresolution framework. ACM can support a variety of different multiresolution frameworks including compact and smooth reverse subdivision methods. The efficiency of ACM is also compared with a standard implementation of half-edge.

Hierarchical grid conversion

Hierarchical grids appear in various applications in computer graphics such as subdivision and multiresolution surfaces, and terrain models. Since the different grid types perform better at different tasks, it is desired to switch between regular grids to take advantages of these grids. Based on a 2D domain obtained from the connectivity information of a mesh, we can define simple conversions to switch between regular grids. In this paper, we introduce a general framework that can be used to convert a given grid to another and we discuss the properties of these refinements such as their transformations. This framework is hierarchical meaning that it provides conversions between meshes at different level of refinement. To describe the use of this framework, we define new regular and near-regular refinements with good properties such as small factors. We also describe how grid conversion enables us to use patch-based data structures for hexagonal cells and near-regular refinements. To do so, meshes are converted to a set of quadrilateral patches that can be stored in simple structures. Near-regular refinements are also supported by defining two sets of neighborhood vectors that connect a vertex to its neighbors and are useful to address connectivity queries. Refinements and simple grid conversions are combined.Grid conversions are obtained by modifying the connectivity of vertices.Transformations imposed by grid conversions and refinements are computed.We employ Grid Conversion to define new regular and semiregular refinements.We also employ it for extending patch-based data structures. Display Omitted

Multiresolution on spherical curves

We develop multiresolution for spherical curves directly in spherical space.The multiresolution scheme is of arbitrary degree.All constituent operations are implemented using line interpolation operations.The results of our subdivision generalize those of spherical Lane-Riesenfeld. Display Omitted In this paper, we present an approximating multiresolution framework of arbitrary degree for curves on the surface of a sphere. Multiresolution by subdivision and reverse subdivision allows one to decrease and restore the resolution of a curve, and is typically defined by affine combinations of points in Euclidean space. While translating such combinations to spherical space is possible, ensuring perfect reconstruction of the curve remains challenging. Hence, current spherical multiresolution schemes tend to be interpolating or midpoint-interpolating, as achieving perfect reconstruction in these cases is more straightforward. We use a simple geometric construction for a non-interpolating and non-midpoint-interpolating multiresolution scheme on the sphere, which is made up of easily generalized components and based on a modified Lane-Riesenfeld algorithm.

Adaptive Atlas of Connectivity Maps

The Atlas of Connectivity Maps (ACM) is a data structure designed for semiregular meshes. These meshes can be divided into regular, grid-like patches, with vertex positions stored in a 2D array associated with each patch. Although the patches start at the same resolution, modeling objects with a variable level of detail requires adapting the patches to different resolutions and levels of detail. In this paper, we describe how to extend the ACM to support this type of adaptive subdivision. The new proposed structure for the ACM accepts patches at different resolutions connected through one-to-many attachments at the boundaries. These one-to-many attachments are handled by a linear interpolation between the boundaries or by forming a transitional quadrangulation/triangulation, which we call a zipper. This new structure for the ACM enables us to make the ACM more efficient by dividing the initial mesh into larger patches.

Optimization of Inverse Snyder Polyhedral Projection

Modern techniques in area preserving projections used by cartographers and other glossarial researchers have closed forms when projecting from the sphere to the plane, as based on their initial derivations. Inversions, from the planar map to the spherical approximation of the Earth which are important for modern 3D analysis and visualizations, are slower, requiring iterative root finding approaches, or not determined at all. We introduce optimization techniques for Snyders inverse polyhedral projection by reducing iterations, and using polynomial approximations for avoiding them entirely. Results including speed up, iteration reduction, and error analysis are provided.

Offsetting spherical curves in vector and raster form

In this paper, we present techniques for offsetting spherical curves represented in vector or raster form. Such techniques allow us to efficiently determine and visualize the region within a given distance of a spherical curve. Our methods additionally support multiresolution representations of the underlying data, allowing the initial coarse offsets to be provided quickly, which may then be iteratively refined to the correct result. An example application of offsetting is also specifically explored in the form of improving the performance of inside/outside tests in the vector case.

Physical Visualization of Geospatial Datasets

Geospatial datasets are too complex to easily visualize and understand on a computer screen. Combining digital fabrication with a discrete global grid system (DGGS) can produce physical models of the Earth for visualizing multiresolution geospatial datasets. This proposed approach includes a mechanism for attaching a set of 3D printed segments to produce a scalable model of the Earth. The authors have produced two models that support the attachment of different datasets both in 2D and 3D format.

Landscaper: A Modeling System for 3D Printing Scale Models of Landscapes

Landscape models of geospatial regions provide an intuitive mechanism for exploring complex geospatial information. However, the methods currently used to create these scale models require a large amount of resources, which restricts the availability of these models to a limited number of popular public places, such as museums and airports. In this paper, we have proposed a system for creating these physical models using an affordable 3D printer in order to make the creation of these models more widely accessible. Our system retrieves GIS relevant to creating a physical model of a geospatial region and then addresses the two major limitations of affordable 3D printers, namely the limited number of materials and available printing volume. This is accomplished by separating features into distinct extruded layers and splitting large models into smaller pieces, allowing us to employ different methods for the visualization of different geospatial features, like vegetation and residential areas, in a 3D printing context. We confirm the functionality of our system by printing two large physical models of relatively complex landscape regions.