1. Chapter 3 2D AND 3D SPATIAL DATA REPRESENTATIONS 2008-09-25 김 정 준

2. 차례  Introduction  Classes of Object Representations  GIS Applicability of the Representations  The Selection Criteria  Vector and Raster Representations

3. Introduction  The Chapter aims  Review some of the pertinent spatial data representations  Adopt suitable structures for a geoinformation system capable of handling 2D and 3D spatial data  Geospatial data  2D : X, Y axes  2.5D : 2D + attribute value(Z coordinate)  3D : X, Y, Z axes  Real-world spatial objects  Regular objects(buildings, houses, etc)  Irregular objects(terrain surfaces, forests, trees, etc)

4. Classes of Object Representations  Objects representaitons may be described as surface-based and volume-based  Surface-based representations  Grid, shape model, facet model and boundary representation(b-rep)  Volume-based representations  3D array, octree, constructive solid geometry(CSG) and 3D TIN(or TEN)

5. Classes of Object Representations Surface-based  Grid  Method for surface representation in GIS, digital mapping and digital terrain modelling(DTM)  Advantages  It is simple to generate, and topology information is implicitly defined  Drawbacks  It is not helpful for surfaces of multiple heights, e.g. vertical walls or overhangs Need extra geometric computations and interpolations with ghe grid points

6. Classes of Object Representations Surface-based  Shape Model  Describes an object surface by using surface derivatives(e.g. slopes) of surface points  Each grid point has slope value instead of Z value  Slopes of grid points are determined by using image processing technique

7. Classes of Object Representations Surface-based  Facet Model  Describes an object’s surface by planar surface cells which can be of different shapes and sizes  Uses triangle facets, sometimes known as a triangular irregular network(TIN)  Advatages  The original observation data are preserved, that is, all surface points are used for surface represenation

8. Classes of Object Representations Surface-based  Boundary Representation(B-rep)  Represents an object by a combination of predefined primitives of point, edge, face, and volume  Only suitable for regular and planar objects  Although b-rep is popular in a computer-aided design/computer-aided manufacturing(CAD,CAM)  Due to computational complexity and inefficient Boolean operations

9. Classes of Object Representations Volume-based  3D Array  The most simple data structure in the 3D domain  Advatages  Easy to understand and to implement  Disadvatages  Many array elements are occupied with the same values, it creates a huge but unnecessary demand for computer storage space and memory

10. Classes of Object Representations Volume-based  Octree  Refers to a hierarchical data structure that specifies the occupancy of cubic regions of the object space  It is simply a three-dimensional generation of a quadtree  Each node is terminal or has eight descendants(octants)  Advantages  Simplicity for boolean operation and visualization rendering algorithms  Drawback  A large amount of storage space and more processing power are needed  Vector octree Face node, edge node and vertex node

11. Classes of Object Representations Volume-based  Constructive Solid Geometry(CSG)  Represents an object by a combination of predefined simple primitives called geometric primitives  Spheres, cubes, cylinders, cones, or rectangular solid  Combined by using geometric trasformation and boolean operations Translation, rotation and scaling Union, intersection and substraction  Considered not well suited for irregular objects

12. Classes of Object Representations Volume-based  3D TIN(Tetrahedral network, TEN)  An extension of 2D TIN, sometimes called TEN  A TEN is made of tetrahedra of four vertices, six edges, and four faces  Advantages  The simplest data structure that can be reduced to point, line, area and volume representations  Supports fast topological processing  Convenient for rapid visualizaion

13. GIS Applicability of the Representations  Grid, shape models, and facet models are suitable for describing irregular object surfaces  B-rep model is more for exact surface geometry of regular shapes  3D array, octree, and 3D TIN can be used for irregular objects  Irregular object can best be represented by 3D TIN and octrees  The ability to represent object primitives, e.g. points, lines, surfaces, and areas  The ability to integrate topological and attribute so that geospatial database queries and data retrieval can be performed

14. The Selection Critera  Representation of Object Primitives  Real world objects are all irregular and three dimensional and can all be adequately represented  Using either the TEN or octree approaches  For reasons of efficiency or convenience  Octree  Need to be decomposed into point, line, surface, and solid primitives if they are to be used in a GIS  Focussed on visualization  TEN  More promising model for 3D spatial objects than octree

15. The Selection Critera  Topology of Spatial Objects:Simplexes and Complexes  Topology has a vital role in spatial information system  Used to determine the connection relationships of objects in space  Use the term complex and simplex for describing the topological relationships of planar objects  Complexes are built from simplices  In the 2D case  TIN structures can be regarded as simplicial complexes  Simplicial complex theory is extendable to n-dimension, then we could also represent TEN primitives using the same principle

16. Vector and Raster Representation  Vector  They are represented by one of the basic discrete entities such as points, lines, and areas  Offers better accuracy than raster  Raster  They can be decomposed into pixels(row and column positions)  Geometric data processing such as coordinate transformation is difficult(requiring resampling)  Simplicity of raster data processing  The choice between the two repersentations depends on factors such as processing speed, level of difficulty, etc