Study On The 3D Cadastral Spatial Data Model Based On Geometric Algebra

The construction of 3D cadastral spatial data model is the foundation of the implementation of 3D cadastral management.Almost all the construction of current 3D cadastral spatial data models are based on boundary representation considering the characteristics of current 3D spatial data model and the special representation demand for 3D cadastral spatial data objects.However,the boundary representation model constructed based on Euclidean geometry can not represent the objects‘ geometric information directly.Meanwhile,the geometric computation in Euclidean space depends on specific coordinate system.This leads to a huge difference for geometric computation in different dimensional space.Limitations of Euclidean are the main reasons for the difficulties that boundary representation model have encountered in efficient analyzation and computation for spatial topological relations in 3D cadastral space.Considering its application in multidimensional geographical information system(GIS),the theory of geometric algebra is introduced to the area of 3D cadastral spatial data modeling in this paper.The 3D cadastral spatial data model based on geometric algebra is constructed using advantages of geometric algebra in unified representation for topological relations and geometric information,algebraic computation for geometry,coordinate and dimension independence for geometric computation.The main research contents and results include following aspects.(1)Relative domestic and abroad research results in 3D cadastral management area have been analized and discussed in this paper.We introduced the basic concepts in cadastral management and geometric algebra.The concept of basic registered unit and the partitioning method for 3D cadastral space are proposed in this paper.The basic computation in geometric algebra,frequently-used geometric algebraic system and the representation for basic geometric objects in conformal geometric algebraic space are presented.(2)A 3D cadastral spatial data model based on geometric algebra is proposed on the basis of conclusion for current research status of 3D spatial data modeling and the geometric algebra‘s application in GIS fields.The modeling targets in 3D cadastral space are abstracted and partitioned according their dimensions.And then we put forward the conformal expression methods for the geometric information and topological relations of different dimensional cadastral objects in conformal geometric space.Different dimensional cadastral objects can be represented in a unifed form benefit from the advantages of geometric algebra in dimension extension.Multivector structure,a special mathematical structure in geometric algebra,is employed to organize and represent the complex cadastral parcels.Both topological constructive relations and geometric information of cadastral objects are represented within the multivector structures.(3)The representation and computation for topological relations among different cadastral objects are research in this paper.The topological relations in cadastral space are divided into two categories on the basis of current research status in spatial topological relations fields.We put forward a total of 75 types of topological relations among different cadastral objects based on the characteristics of cadastral data.Topological relations computation rules for basic geometric objects in conformal space are studied and discussed.On basis of topological relations computation rules and conformal expression for cadastral objects,the topological relations computation frameworks for cadastral spatial objects are proposed.(4)The cadastral parcels updating algorithms based on their geometric algebraic expression are studied and designed on basis of computation framework research for 3D cadastral spatial topological relations.The multivector structure‘s advantages in adaptive updating play an important role in the process of 3D cadastral parcels‘ geometric information and topological relations reconstruction.Taking merging and segmentation algoritms for 3D cadastral parcel volume as examples,we put forward the 3D cadastral parcels updating algorithms based on their geometric algebraic expression.(5)A 3D cadastral prototype system based on geometric algebra is designed to verify the main results of this paper.3D cadastral spatial data structures based on geometric algebra are discussed.Functional modules including 3D cadastral objects‘ geometric and topological unified representation,spatial information query in 3D cadastral space,spatial topological relations analyzation and conputation in 3D cadastral space and 3D cadastral parcels updating are realized in the prototype system.All relative key techniques that are studied and proposed in this paper are verified and realized in the 3D cadastral prototype system.