Map Projections

Projections for a Digital Earth

4607.2 - The Thinking about Logical Model of Digital Earth in Global Modeling

Tuesday, July 4
3:10 PM - 3:30 PM
Location: Maryland B

Since Gore proposed the concept of "digital earth", the theories, methods and techniques of global modeling for the Earth have been developed greatly in the field of Surveying and Mapping science.
1)The Conceptual Model of Digital Earth
Physically, the Earth is like an irregular approximate rotating ellipsoid. Researchers and users in Survey, GIS and even the general earth products are unanimously adopted the rotating ellipsoid represented by WGS84, the geodetic coordinate system (B, L, H), to express the geographical phenomena on the Earth's surface and nearby spheres. Naturally, then, the rotating ellipsoid comes to be the most popular infrastructures to define the conceptual model of the Earth, with the operations following from GIS: capturing, representing, processing, and analyzing geographic information on the Earth.
With the development of the positioning system such as GPS, BeiDou system and the high-precision remote sensing technology, the massive geographical data with the accuracy of over centimeter-level has been well captured. The 3D earth visualization systems represented by Google Earth have also improved visualized representation of Earth information to a high level. At the same time, most of global spatial data processing and analysis are still based on the classical Euclidean system, which may lead to some structural framework issues. With the further development of Digital Earth, it’s very important to study the high-precision logical model corresponding to the conceptual model of the Earth not only for visualization, but also for spatial processing and analysis.
2)The logical Model of Digital Earth
For a long time, in the absence of mathematical tools which can directly performs rapid and accurate geometric calculation on the ellipsoidal surface, spatial data processing and analysis rely on zonal projection from the Earth surface to the Euclidean plane, using the mathematical tools of Euclidean Geometry for spatial computation. Its logical model seems like a polyhedron structure similar to an ellipsoid, which consists of dozens of separated planes and may discontinuous at the boundary. Euclidean space calculation using polyhedron as the logical model may obtain high precision result after ignoring the minor change of the surface curvature of earth; however, the projection deformation error and the data integration among different projection planes has been the bottleneck for the large span or global scale spatial problems.
The most popular solution now is Global Discrete Grid System(DGGS). DGGS is to divide 3D continuum which takes the earth ellipsoid as the prototype, and to discretize it into a power set of cells. Goodchild and other experts rated it highly for effectively promoting the 3D visualization. However, the well-known Goodchild standard (1994) which indeed leads the DGGS work paid little attention to the measurement. Also, due to the lack of ellipsoidal calculation tools, most grid meshing schemes have selected the isotropic sphere as the logical model, which inevitably leads to model errors between sphere and ellipsoid.
The Ellipsoidal Distance Fields (EDF) technique based on Map Algebra can provide good theoretical support and a set of numerical geometry tools for spatial analysis at global scale. The (B, L, H) orthogonal surface family subdivision and EDF technique are based on field model while the Euclidean geometry using object model, that makes it possible to proceed geometry computation on a non-Euclidean space as the Earth surface. It now has the ability to scale implement, with O(m) time complexity (m is resolution), on Voronoi diagram, buffer, convex hull, contour interpolation and other basic spatial analysis products with the accuracy of centimeter level. This direct use of the ellipsoid as logical model to describe the Earth will raise the accuracy of global positioning, segmentation, measurement, and spatial analysis.

Hai Hu

Dr.
WuHan University

Hu Hai(1977-), male, associate professor of Geographical Information Sciences at the Department of School of Resource and Environmental Sciences, Wuhan University, China. visitor scholar from University of Kansas. PHD in Geographical Information Science and Map Algebra etc.
Now focus on the space-oriented algorithms of Geographical Distance Field(GDF) based on Map Algebra, which could provide numerical tools for spatial analysis in comparative high accuracy and efficiency, especially in large region and global Geographic applications. Now we have used that in Maritime Delimitation and DEM generation etc.

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Lian You

Professor
Wuhan University

You Lian , female, postgraduate, professor from Wuhan University, majors in Geographical Information Science.

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Peng Hu

Professor
Wuhan University

HU Peng( 1944—) , male, postgraduate, professor, majors in Geographical Information Science and Map Algebra etc.

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Miljenko Lapaine

Professor
University of Zagreb, Faculty of Geodesy

Miljenko Lapaine graduated from the Faculty of Science, University of Zagreb, in the field of Theoretical Mathematics. He obtained his PhD from the Faculty of Geodesy, University of Zagreb with a dissertation entitled Mapping in the Theory of Map Projections. He has been a full professor since 2003. He has published more than 900 papers, several textbooks and monographs. Prof. Lapaine is the Chairman of the ICA Commission on Map Projections, a founder and President of the Croatian Cartographic Society and the Executive editor of the Cartography and Geoinformation journal.

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