A 3D GIS spatial data model based on conformal geometric algebra

Peng-cheng

et al. 2016

IJGI

Three-dimensional (3D) cadastral data models that are based on Euclidean geometry (EG) are incapable of providing a unified representation of geometry and topological relations for 3D spatial units in a cadastral database. This lack of unification causes problems such as complex expression structure and inefficiency in the updating of 3D cadastral objects. The inability of current cadastral data models to express cadastral objects in a unified manner can be attributed to the different expressions of dimensional objects. Because the hierarchical Grassmann structure corresponds to the hierarchical structure of dimensions in conformal geometric algebra (CGA), geometric objects in different dimensions can be constructed by outer products in a unified expression form, which enables the direct extension of two-dimensional (2D) spatial representations to 3D spatial representations. The multivector structure in CGA can be employed to organize and store different dimensional objects in a multidimensional and unified manner. With the advantages of CGA in multidimensional expressions, a new 3D cadastral data model that is based on CGA is proposed in this paper. The geometries and topological relations of 3D spatial units can be represented in a unified form within the multivector structure. Detailed methods for 3D cadastral data model design based on CGA and data organization in CGA are introduced. The new cadastral data model is tested and analyzed with experimental data. The results indicate that the geometry and topological relations of 3D cadastral objects can be represented in a multidimensional manner with an intuitive topological structure and a unified dimensional expression.

Section: Geometrically and Topologically Unified Representation In Cgamentioning

confidence: 99%

Section: Case Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

3D Cadastral Data Model Based on Conformal Geometry Algebra

Peng-cheng

et al. 2016

IJGI

“…Its formal representation enables symbol-ic-like computations so that rule-based reasoning and judgment can be made. Last, when numeric calculations are required (here the numeric calculation could be of general form, possibly a geometric equation or a representation of geometric objects), these operations can be easily performed on demand that sharply simplify the inherent complexity of the computation [22,23].…”

Section: Geoobjmv Obj Points Obj Lines Lines Pointsindexmentioning

confidence: 99%

Geometric algebra method for multidimensionally-unified GIS computation

Yuan

Luo

et al. 2011

Chin. Sci. Bull.

Self Cite

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 GAbased 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. The representation and arrangement of complex geographical objects and scenes are identified as important in the application and usability of geographic information systems (GIS) [1][2][3][4]. Object expression and code construction of operations is an important step in advancing GIS research from static characteristics to a more comprehensive research on temporal and spatially distributed structures, and modeling and forecasting of dynamic processes and mechanisms. It is also an indispensable process in achieving model integration and comprehensive use in GIS and professional areas [5][6][7][8]. There still exist many limitations within traditional GIS, based on Euclidean geometry, in maintaining complex representations of geographical objects, multidimensional spatial relations, and topographical analysis [9]. Constructing models that support multidimensionally-unified geographical object representations and operations based on new mathematical theories is one possible way to reduce the multidimensional complexity of current GIS and to improve architectural efficiencies in its operations and analysis [10,11]. Geometric algebra (GA), known as a unifying descriptive language, can integrate algebra with geometry, mathematics with physics. By defining the spatial operation sets (e.g. geometry, measurement, topology) with GA operators, Euclidean, homogeneous, and conformal spaces can be described and converted among each other, this provide a unification and representation of varied algebraic structures and geometric systems [12,13]. Calculus, geometry, and signal processing (e.g. neural network and wavelet) methods can be reconstructed and expanded under the GA framework [14,15], which then provides a foundation for expansion and reconstruction of topological models. Here, based on GA's multivectors and operators, we construct a geometric framework that enables multidimensionallyunified computation modeling of multiple geometric objects

“…The real world, however, is three-dimensional or even four-dimensional, for example, there exist not only 3D static objects like houses, buildings, geological bodies, but man-made or natural dynamic objects such as vehicles, ships, unmanned aerial vehicles, satellites, typhoon, landslides, etc. Consequently, it is inevitable to expand the 2D GIS into 3D GIS and temporal GIS (Yuan et al, 2011). Although current static, symbolic 2D GIS, and 3D GIS mainly stemming from the former, have made much progress in various aspects, particularly in geo-visualiza-tion, the confliction between the virtual space of traditional cartographic GIS and the real world space, as well as the cognitive space of human beings, is increasingly protruding (Zhu, 2014).…”

Section: Introductionmentioning

confidence: 99%

A ubiquitous knowledgeable data representation model (UKRM) for three-dimensional geographic information systems (3D GIS)

Zhou

et al. 2016

Sci. China Earth Sci.

In the face of complicated, diversified three-dimensional world, the existing 3D GIS data models suffer from certain issues such as data incompatibility, insufficiency in data representation and representation types, among others. It is often hard to meet the requirements of multiple application purposes (users) related to GIS spatial data management and data query and analysis, especially in the case of massive spatial objects. In this study, according to the habits of human thinking and recognition, discrete expressions (such as discrete curved surface (DCS), and discrete body (DB)) were integrated and two novel representation types (including function structure and mapping structure) were put forward. A flexible and extensible ubiquitous knowledgeable data representation model (UKRM) was then constructed, in which structurally heterogeneous multiple expressions (including boundary representation (B-rep), constructive solid geometry (CSG), functional/parameter representation, etc.) were normalized. GIS's ability in representing the massive, complicated and diversified 3D world was thus greatly enhanced. In addition, data reuse was realized, and the bridge linking static GIS to dynamic GIS was built up. Primary experimental results illustrated that UKRM was overwhelmingly superior to the current data models (e.g. IFC, CityGML) in describing both regular and irregular spatial objects.