Abstract
Seamless multidimensional handling and coordinate-free characteristics of geometric algebra (GA) provide means to construct multidimensionally-unified GIS computation models. Using the multivector representation for basic geometric objects within GA, we are able to construct adaptable unified geometric-topological structural models of a multidimensional geographical scene. Multidimensional operators found within the geometry, topology and GIS analysis are developed with basic GA operators. A unified computational framework is proposed, it unifies expressions and operation structures, as well as supports the analysis of multidimensional complex scenes. Finally, we illustrate modelling a three-dimensional residential district, which shows that GA-based multidimensionally-unified computation models can effectively represent and analyze complex and multidimensional geographical scenes. The development of the proposed GIS multidimensionally-unified representation, analysis, and modeling enhances current GIS algorithms and geographical models.
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References
Longley P A, Goodchild M F, Maguire D J, et al. Geographic Information Systems and Science. 2nd ed. New York: Wiley, 2005. 61–83
Lan H X, Martin C D, Lim C H. RockFall analyst: A GIS extension for three-dimensional and spatially-distributed rockfall hazard modeling. Comput Geosci, 2007, 33: 262–279
Beni L H, Mostafavi M A, Pouliot J, et al. Toward 3D spatial dynamic field simulation within GIS using kinetic Voronoi diagram and Delaunay tetrahedralization. Int J Geogrl Inf Sci, 2011, 25: 25–50
Castrillon M, Jorge P A, Lopez I J, et al. Forecasting and visualization of wildfires in a 3D geographical information system. Comput Geosci, 2011, 37: 390–396
**e M W, Zhou G Y, Tetsuro E. Gis component based 3d landslide hazard assessment system: 3dslopegis. Chin Geogr Sci, 2003, 13: 66–72
Merwade V, Cook A, Coonrod J. GIS techniques for creating river terrain models for hydrodynamic modeling and flood inundation map**. Environ Model Software, 2008, 23: 1300–1311
Naoum S, Tsanis I K, Fullarton M A. GIS pre-processor for pollutant transport modeling. Environ Model Software, 2005, 20: 55–68
Karssenberg D, De Jong K. Dynamic environmental modelling in GIS: 1. Modelling in three spatial dimensions. Int J Geogr Inf Sci, 2005, 19: 559–579
McIntosh J, Yuan M. A framework to enhance semantic flexibility for analysis of distributed phenomena. Int J Geogr Inf Sci, 2005, 19: 999–1018
Goodchild M F, Yuan M, Cova T J. Towards a general theory of geographic representation in GIS. Int J Geogr Inf Sci, 2007, 21: 239–260
Liu Y, Goodchild M F, Guo Q, et al. Towards a general field model and its order in GIS. Int J Geogr Inf Sci, 2008, 22: 623–643
Doran C, Lasenby A. Geometric Algebra for Physicists. Cambridge: Cambridge University Press, 2003. 228–264
Dorst L, Fongijne D, Mann S. Geometric Algebra for Computer Science: An Object-oriented Approach to Geometry. San Francisco: Morgan Kaufmann, 2007. 355–379
Hestenes D, Sobcyk G. Clifford Algebra to Geometric Calculus. Heidelberg: Springer-Verlag, 1984. 1–224
Hildenbrand D. Geometric computing in computer graphics using conformal geometric algebra. Comput Graphics-UK, 2005, 29: 795–803
Perwass C. Geometric Algebra with Applications in Engineering. Heidelberg: Springer-Verlag, 2009. 255–368
Bayro-Corrochano E J, Reyes-Lozano L H, Zamora-Esquivel J. Conformal geometric algebra for robotic vision. J Math Imaging Vision, 2006, 24: 55–81
Yuan L W, Yu Z Y, Chen S F, et al. CAUSTA: Clifford algebra based unified spatio-temporal analysis. Trans GIS, 2010, 14(Suppl): 59–83
Chao W M, Feng H. Geometric Algebra Ways of Biomimetic Pattern Recognition and Signal Processing (in Chinese). Bei**g: Science Press, 2010. 35–36
Li H B. Conformal geometric algebra for motion and shape description (in Chinese). J Comput-Aided Design Comput Graph, 2006, 18: 895–901
Karimipour F, Delavar M, Frank A U. A simplex-based approach to implement dimension independent spatial analyses. Comput Geosci, 2010, 36: 1123–1134
Yuan L W, Yu Z Y, Luo W, et al. A 3D GIS spatial data model based on conformal geometric algebra. Sci China Earth Sci, 2011, 54: 101–112
Yu Z Y. Multi-dimensional unified GIS data model based on geometric algebra (in Chinese). Dissertation for the Doctoral Degree. Nan**g: Nan**g Normal University, 2011. 1–117
Wang S S, Liu J, Wang X Y, et al. Qualitative spatial reasoning for multi-dimensional topology and size relations (in Chinese). J Comput Res Develop, 2009, 46: 1169–1175
Lv G N. Geographic analysis-oriented virtual geographic environment: Framework, structure and functions. Sci China Earth Sci, 2011, 54: 733–743
Friedman Y, Gofman Y. Why does the geometric product simplify the equations of physics? Int J Theoretical Phys, 2002, 41: 1841–1855
Zhang J Y. GIS network analysis based on Clifford algebra (in Chinese). Dissertation for the Master’s Degree. Nan**g: Nan**g Normal University, 2010. 1–53
Luo W. Characteristics analysis and motion expression of temporal-spatial field data based on geometric algebra (in Chinese). Dissertation for the Master’s Degree. Nan**g: Nan**g Normal University, 2011. 1–59
Yi L. Multi-dimensional unified algorithm and application of Voronoi based on conformal geometric algebra (in Chinese). Dissertation for the Master’s Degree. Nan**g: Nan**g Normal University, 2011. 1–50
Yang B S, Li Q Q, Gong J Y. A robust and rapid algorithm for generating and transmitting multi-resolution three-dimensional models. Chin Sci Bull, 2006, 51: 987–993
Li Q Q, Li D R. Research on the conceptual frame of the integration of 3D spatial data model (in Chinese). Acta Geod Cartogr Sin, 1998, 27: 325–330
Fang Y, Zhou C H, **g G F, et al. Research of 4th generation GIS software (in Chinese). J Image Graphics, 2001, 6A: 817–823
Chen J, Li Z L, Jiang J, et al. Dynamic and multi-dimensional spatial data modeling: models and methods (in Chinese). Geom Inf Sci Wuhan Univ, 2004, 29: 858–862
Wu L X, Chen X X, Chen D F, et al. A GTP-based entity model for underground real 3D integral representation (in Chinese). Geom Inf Sci Wuhan Univ, 2007, 32: 331–335
Hu Q W, Ling C F, Yu F, et al. Design and implementation of multi-dimensional GIS-based mineral resource evaluation data management system (in Chinese). Adv Earth Sci, 2010, 25: 990–995
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Yuan, L., Lü, G., Luo, W. et al. Geometric algebra method for multidimensionally-unified GIS computation. Chin. Sci. Bull. 57, 802–811 (2012). https://doi.org/10.1007/s11434-011-4891-3
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DOI: https://doi.org/10.1007/s11434-011-4891-3