Geoscience Reference
In-Depth Information
For this research B-Reps and irregular decomposition models are the most
relevant. B-Rep represents a solid (e.g. polyhedron) as a union of faces defined
by their boundaries: edges and vertices. In this research it is assumed that faces
are planar and edges are straight line segments. B-Rep models are widely used in
CAD systems but they can be adapted in GIS (De Cambray
1993
).
The well-known B-Rep data structures are: half-edge (Mäntylä
1988
), winged-
edge (Baumgart
1975
) and quad-edge (Guibas and Stolfi
1985
). These data struc-
tures can be used for a single 2-manifold solid representation (2-manifold is a 2D
surface embedded in 3D space, e.g. a surface of a sphere, cube, or torus), but can-
not be used for complex models where, for example, two or more adjacent sol-
ids have linked into one complex. A cell complex is an irregular decomposition
of space or an object into non-overlapping cells of any shape. G-maps (Lienhardt
1991
) and facet-edges (Dobkin and Laszlo
1987
) are examples of data structures
which can be used for construction of irregular decomposition models (e.g. for
constructing a 3D Delaunay tetrahedralization).
In this chapter, the dual half edge (DHE) data structure is used for 3D spatial mod-
elling. This structure resolves some of the modelling issues in 3D GIS and expresses
the geometric structures as a cell complex, in preserving adjacency relationships
between cells, and including semantic information using attributes (Boguslawski
2011
; Boguslawski et al.
2011
). The DHE is based on the quad-edge and its exten-
sion—the augmented quad-edge (Ledoux and Gold
2007
). These structures allow
construction of models and their duals at the same time. Dual space is used to con-
nect cells in a complex and to navigate between them. Other data structures like the
half-edge or winged-edge do not provide for management of the duality.
The construction process using the DHE is based on Euler operators which are
used widely in Computer Aided Design (CAD) systems for B-Rep modelling. They
preserve topological consistency of the model on each step of a construction process.
Euler operators were described by Baumgart (
1975
), Braid et al. (
1980
), Mäntylä
(
1988
). 3D navigation in models is based on navigation described by Ledoux and
Gold (
2007
) for the 3D Voronoi/Delaunay model. In this research 3D data modelling
using the DHE as part of the rapid indoor data acquisition technique is addressed.
4 LADM
Land Administrative Domain Model (LADM) is a concept which consists of the
Party, (RRR's) rights, restriction, and responsibilities, Administrative, and Spatial
Unit packages for a land administration system. For the purpose of this research,
the focus is the Spatial Unit Package. According to Ying et al. (
2011
), cadastral
application should have capabilities of 3D solid objects manipulation which can
manage, operate and analyse 3D parcels. In this chapter, authors have decided to
use DHE data structure. DHE is a topological data structure which store geometry,
topology and attributes of a 3D model. Figure
3
shows prototype system for this
research based on the LADM standards.
