A 3-DIMENSIONAL DATA MODEL FOR VISUALISING CLOVERLEAF JUNCTION IN A CITY MODEL* Min SUN,1, 2 Jun CHEN2 and Qiming ZHOU3 1
Survey Institute, Central South University Technology Changsha, Hunan Province, 410083, E-mail:
[email protected] 2
National Geomatics Center of China No.1 Beishengcun Zizhuyuan Beijing, 100044, E-mail:
[email protected] 3
Department of Geography, Hong Kong Baptist University Kowloon Tong, Hong Kong, E-mail:
[email protected] KEYWORDS: 3-Dimensional City Model (3DCM), GIS, Cloverleaf Junction, Data Structure, Database
ABSTRACT Seldom research work has been done about cloverleaf junction expression in a 3-dimensional city model (3DCM). The main reason is that the cloverleaf junction is often in a complex and enormous construction. Its main body is bestraddle in air, and has aerial intersections between its parts. This complex feature made cloverleaf junction quite different from buildings and terrain, therefore, it is difficult to express this kind of spatial objects in the same way as for buildings and terrain. In this paper, authors analyzed spatial characteristics of cloverleaf junction, proposed an all-constraint points TIN algorithm to partition cloverleaf junction road surface, and developed a method to visualize cloverleaf junction road surface using TIN. In order to manage cloverleaf junction data efficiently, the authors also analyzed the mechanism of 3DCM data management, extended BLOB type in relational database, and combined R-tree index to manage 3D spatial data. Based on this extension, an appropriate data structure for cloverleaf junction in 3DCM is proposed.
1. INTRODUCTION Road network is the framework of the whole city with very important functions (Sun and Liu, 1997). Cloverleaf junctions are the most complex part of the city road network. They are often composed of a number of bridges, occupy a large area with many adjacent buildings, and have several levels of road surface. Therefore, it is critical to define an appropriate way for the expression of such a complex object. However, at the present time, the main focus of research in 3-dimensional city model (3DCM) is the objects such as buildings, and it seldom relates to the expression of cloverleaf junction. Haala, et al. (1997) reported the use of airborne laser scanner to obtain digital surface model (DSM) of ground objects, and reconstructed objects such as buildings from DSM. This method, however, is only suitable for reconstructing objects which could be enveloped by a spatial convex body. Koehl (1996) demonstrated a method to express city buildings and terrain using predefined geometry primitives while combining with a digital terrain model (DTM). Because cloverleaf junction main body bestraddle in air, it is difficult to build DTM together with terrain. On the other hand, if one used predefined primitives, cloverleaf junction expression would be very complex, since it would need numerous primitives with many shapes. Besides, it is also difficult to set up spatial relationship between them.
pointed out that the model of the irregular shape objects could be built using DTM algorithms. However, Koehl did not give a specific solution to road network. Ooi, et al. (1998) proposed a simplified road network model using road middle line, road width and assumed thickness to calculate other 3D points which are used to represent road body in a 3D model. This method is simple and efficient, but it does not meet the requirements to represent complex cloverleaf junction. With the development of the modern city, urban road network is gradually developed from the ground to the air. It becomes more and more complex. Cloverleaf junctions are the most complex part in the road network (Figure 1), characterized by their nature of both building and terrain. The resemblance between cloverleaf junction and terrain is that both are a kind of continuous surface, while the resemblance between cloverleaf junction and a building is that both have a regular body. Through the analysis to actual cloverleaf junctions, some spatial natures of the cloverleaf junction can be summarized as follows:
Koehl (1996) once divided city 3D objects into two types: regular shape objects and irregular shape objects. He *
In Proceedings of International Workshop on Urban 3D/Multi-media Mapping, Shibasaki, R. and Shi, Z. (eds.), 30 September – 2 October, Tokyo: 203-208.
the 2D network model from (x, y) to (x, y, z). For a cloverleaf junction road surface is smooth. Two sidelines usually parallel to each other. For the map scale of this study, the road surface can be represented by line segments and points on the sidelines.
Figure 1. Compose of cloverleaf junction.
• • •
The main body of a cloverleaf junction is bestraddle in air. Its road surface is usually smooth, appears to be a band area with a relative fixed width, and has aerial intersections. It has a well-defined topological connectivity.
Because of these characteristics, it is difficult to use predefined primitives, so as to use surface DTM to express a cloverleaf junction. In order to simplify the question, we divided cloverleaf junction into a ground part and an aerial part. For the ground part, it is almost the same as common road segments, so that the ground part can be combined with terrain and represented using DTM. Therefore, in this paper we focus our research only on the aerial part. Cloverleaf junction is an object in 3D space with a regular shape. Its upper face (road surface) is different from side face and lower face its thickness is often ignored. Following Koehl’s (1996) idea, we can firstly partition road surface into TIN, and then use this TIN to represent upper face and lower face of the Cloverleaf junction. Side face can be calculated according to an assumed constant value (Figure 2).
For the purpose of visualization, texture information is demanded in 3DCM. Realistic texture can present much more information than a symbol and often answer the management questions much more directly than text query. Generally speaking, different object types, even different individual object may have different texture. However, road texture is much simpler than building and other 3D objects that have complex and various textures. Through analysis, we found that: •
•
•
Figure 3. A road image.
According to above characteristics, road surface texture can be presented with approximate color, this results in two advantages:
Upper surface (Road surface)
•
Side surface
•
Lower surface
Figure 2. Multi-surface of cloverleaf junction.
2. CLOVERLEAF JUNCTION'S TIN PARTITION
Cloverleaf junction texture is mainly its road surface texture. Its texture is decided by the surface material (such as cement and gravel), therefore road surface texture is usually with minimal variation (Figure 3); Different types of road may use different surface material, thus show different textures. On the other hand, same type of road usually use the same materials so that to present the same texture. Road surface texture usually has no complex pattern, besides special color.
There is no need to capture and manage extra texture data. Thus the amount of data needed for visualization can be largely decreased.
Based on the above analysis, road network can be fully expressed if posses following data: 3D road middle line and two sidelines, crossing nodes or intersection points, road type, color or surface material, and assumed road thickness.
2.1 Cloverleaf Junction Spatial Data
2.2 Cloverleaf Junction Road Surface TIN Partition Using All-Constraint Point Algorithm
In 2DGIS, elements of road network are presented as points (node) and lines (link) on a 2-dimensional plane. The information on the third dimension, e.g. elevation, may only be presented as an attribute value. Thus, it is impossible to represent the 3-dimensional topological relations using the 2-dimensional network model. When considering a 3-dimensional space, a 3-dimensional topological relations need to be established by expanding
Zhu (1997) once specially constructed constraint TIN to express various irregular roofs in 3DCM. However, different from a roof, cloverleaf junction road surface contains aerial intersections (i.e. lines intersect without a node) between its parts, thus a traditional TIN used in 2DGIS cannot be used. Since road surface is smooth, using road two sidelines, we can accurately describe road
surface in a small-enough area, therefore there is no need to collect discrete points or interpose point on the road surface in order to refine the description. All spatial points used to describe the road surface are on the two sidelines. Note that different from the discrete points used in the traditional TIN, these points are considered as point sequences, not as discrete point sets. Therefore, even on a 2-dimensional plane face, we can construct TIN for aerial road surface. Comparing with traditional TIN, which is composed of a set of unrelated discrete points, the constraint TIN is composed of several constraint lines and a set of unrelated discrete points. Since during the TIN construction, only the plane coordinates of the points were considered, it would be difficult to construct TIN for 3D surface that has aerial intersection parts, because these would overlap to each other when they were projected onto the plane. However, when all discrete points lie on the constraint lines, even though the overlapping still exists, the TIN can be constructed for this kind 3D surface using the constraint lines. Cloverleaf junction road surface can be considered as a 3D surface on which all discrete point lie on constraint lines (Figure 4).
1.
2. 3.
4.
5. 6.
For each Part i link all constraint lines {Line 1, Line 2, …, Line n}, and form a loop Loop i. In the case that Line i forms a loop by itself, we record this as Self_Loopi. Select one un-searched loop Loop i. If there is no un-searched loop, then search process is ended. Select two adjacent points Point a and Point b, which define an edge on Loop i, search edge Line p. Note Point a and Point b must be the end points of the constraint line of Part i. Using the maximum angle algorithm in traditional TIN process, select a point that is adjacent to Point a or Point b (e.g. Point i), then Point i and Line p can form a triangle ABP. A new edge is formed by linking Point i and Point a or b as the new Line p. When ABP is an acute angle triangle, repeat step 3. When ABP is an obtuse angle triangle, select a point (Point s), which is the nearest to Line p with a maximum angle, from all Self_loopi to form new triangle with Line p. If there is no Self_loopi, then select Point s from present Loop i according to the same principle. If there is no Point s that could form triangle better than ABP, then go to step 2. When Point s and Line p form a new triangle, both two new edges can be used as start edge for search. When all points on Loop i have joined into triangles, return to step 2. Cloverleaf junction
Part 1
Part 2
…
Line 1
Line 2
…
Line n
Point 1 (x, y, z)
Point 2 (x, y, z)
…
Point n (x, y, z)
Figure 4. Digitised cloverleaf junction.
When all discrete points lie on the constraint lines, they have follow geometric characteristics: • • •
Every point is the point on constraint line, and all point can be regard as ordered. By linking the end points of adjacent constraint lines, all point sequences can be linked into a loop. Adjacent points on a constraint line must belong to one triangle.
In order to partition cloverleaf junction road surface, we propose the algorithm as below. Because all points used in this algorithm are on the constraint lines, we call this algorithm All-Constraint Point Method.
Part n
Figure 5. Cloverleaf junction data compose level.
Figure 6 shows the partitioned surface of Lotus Cloverleaf Junction in Beijing.
Assume one cloverleaf junction is composed of several parts that are not connected to each other: Cloverleaf junction = {Part 1, Part 2, …, Part n}, and every part is composed of a set of edges (lines): Part i = {Line 1, Line 2, …, Line n}, each edge is composed of a set of 3D points: Line i = {Point 1, Point 2, …, Point n}, and Point i = {x, y, z}. Figure 5 shows the geometric data structure of a cloverleaf junction. Figure 6. TIN partition to cloverleaf junction.
3. CLOVERLEAF JUNCTION DATA MANAGEMENT 3.1 Weakness of Present 3DCM Data Management 3DCM is considered as one kind of CAD model (Ranzinger and Gleixner, 1997). The main reason is that CAD can present powerful visualization functions. Many 3DCM systems compile 3D data into files that are compatible with CAD systems. Some 2DGIS also has functional components that can be used to establish 3DCM and provide some simple analysis functions. However, for the majority of 3DCM systems, their spatial data management relies on the proprietary file structure, while their attribute data are managed using a relational database. This dual-database, geo-relational model at least causes problems as follows (Oracle 1997): • • •
• •
It is difficult to maintain data integrity between the spatial and attribute databases. Hybrid solutions cannot take full advantage of the capabilities of RDBMS technologies. Proprietary architectures and file formats complicate or prohibit the exchange of data between applications, resulting in non-sharable data in a number of incompatible storage formats. Changes to the data structure often require rebuilding the database and making major changes to existing processes. Methods for analyzing and expressing data with more than two or three dimensions are inadequate.
Although some commercial products such as Oracle 8 Spatial Cartridge remedies above weakness, and support integrity management of spatial data and attribute, their support is limited to 2D space. On the other hand, Products such as Oracle Olap support multi-dimensional data management, but they do not extend the support to the multi-dimensional spatial data. Although many 3DCM system use a CAD system to organize and display data by taking the advantage of its powerful graphical interface, this utilization is restricted because of lack of support on spatial analysis and query. At the present time, a 3DCM system which based on CAD visualization has limited support on functions other than browse (including animation, circumrotation and zoom) and simple query. 3.2 Spatial 3D Data Management – Relational Database Type Extension and R-tree Index Relational database management system (RDBMS) is the most successful database management system applied to many application areas because of its simple structure and complete theory. Present relational database provides the BLOB type, permitting image and spatial data management. However, the BLOB type is not convenient to query and search, and also not suitable for managing large range geometric objects. Even so, BLOB offers significant advantages for advanced program developer, who would only need to manage input to and output from
BLOB, and establish a good index to process and manage any data types. BLOB is actually a kind of binary stream, which can save image and data structure. Different from other data types, the relational database only treats BLOB as an object, without knowing its contents. Thus, if we want to use BLOB to manage 3D spatial objects, it is necessary to define the idiographic input and output operations. Moreover, in order to query it easily, an index system must be built. Therefore, we define the following 3D spatial object types as the extension of BLOB: Type define C3Dpoint { float x, float y, float z; Write_toBLOB(); Read_fromBLOB(); Index_ID point_ID; } Type define C3Dline { C3Dpoint pointlist[]; Write_toBLOB(); Read_fromBLOB(); Index_ID line_ID; } Type define CTIN { Table (trangle_ID, C3Dpoint1, C3Dpoint2, C3Dpoint3); Wrire_toBLOB(); Read_fromBLOB(); Index_ID TIN_ID; }
These self-defined types are placed as the ‘middleware’. In order to query and search the objects saved in BLOB conveniently, an R-tree index file is also built and placed as middleware (Figure 7). The R-tree data structure has been proven to be useful for storing and organizing spatial data, compared with other data structure like Quadtree and Octree. This is because that R-tree fits better to organize overlapping objects, such as the rectangular bounding boxes of the 2D or 3D CAD models of buildings, building blocks and larger urban units (Gruber, 1998). Spatial objects
Input/output methods
BLOB type
Query space
Application
R-tree index file
Middleware
RDBMS
Figure 7. Relational database extension.
Since we need to search 3D spatial objects, the R-tree nodes need to be as a closed 3D space, such as cuboid. Therefore, the R-tree that is used to manage 3D spatial objects would appear as that shown in Figure 8 (in order to illustrate clearly, only one level nodes are drawn). When a spatial point or area is selected, it will intersect with the node cuboid in R-tree. If a node cuboid has the intersection with the selected point or area, then this node is selected. The more detailed query would need a higher level index to be built in the R-tree.
Class CTIN_BLOB { Table (trangle_ID, C3Dpoint1, C3Dpoint2, C3Dpoint3); …… };
Figure 9 shows the data structure of a cloverleaf junction, where one cloverleaf junction is composed of several parts. Each part is represented by one TIN object and three line array (or list), namely, left side, right side and middle line array. Each array contains numerous lines, which are in turn composed of 3D points. Both the TIN object and line objects are BLOB types. Cloverleaf junction n
3`
Cloverleaf junction Part
2
3
4
1`
BLOB Object
TIN_Object
Line List n
R-Tree Index BLOB Object
Line Object n
1
2
3
4
C3Dpoint(x, y, z) J
Figure 9. Cloverleaf junction data structure. Figure 8. 3D spatial R-tree.
With the extension to the BLOB type, on the application level, the relational database will support several spatial types. This remedies many weaknesses of the 3DCM with the hybrid file structure. Using above middleware and relational database, the data structure suitable to present cloverleaf junctions is constructed. 3.3 Cloverleaf Junction Data Structure
For this application project, the extended database type and R-tree were used to construct the data model of a cloverleaf junction. Since for this study we only consider the aerial part of a cloverleaf junction, this may cause those originally connected parts becoming unconnected. However, if the cloverleaf junction is partitioned according to the connectivity, then a complex cloverleaf junction can be divided into several parts. Considering one connected part as an object, the following classes can be defined: Class Part { CLine_BLOB surface_Right_side_line_variable[]; CLine_BLOB surface_Left_side_line_variable[]; CLine_BOLB surface_Middle_line_variable[]; CTIN_BOLB Display_TIN_patch_variable; …… Attribute variables. …… }; Class CLine_BLOB { C3Dpoint List (or Array) Attribute variables };
In order to save storage space, The C3Dpoint in the TIN table is referenced by its ID value, requiring one additional table be built to retrieve the 3D coordinates. While the speed of data access is concerned, the C3Dpoint item may use the 3D coordinate values directly. In the relational database, following relational tables are defined for the class Part: Cloverleaf junction Part ID 10005 10006 10007 ……
Right line
Left line
Middle line
Display TIN
BLOB BLOB BLOB ……
BLOB BLOB BLOB ……
BLOB BLOB BLOB ……
BLOB BLOB BLOB ……
In order to manage all cloverleaf junction objects in a road network, an R-tree index file is built for class member Display TIN. Note that R-tree nodes only provide approximate match according to the query and search, while the Display TIN item must be used for the accurate match. 4. EXPERIMENT AND CONCLUSION
The proposed data model for a part of a cloverleaf junction was experimented and implemented using the OpenGL graphic engine (Figure 10). For better visual effect, two sources of light were used and the thickness of the cloverleaf junction was ignored.
Topographic Objects, Vol.32, Part 3-4W2, Stuttgart, September 17-19 1997, 68-75. Koehl, M. and Grussenmeyer, P., 1998, 3D data acquisition and modelling in a topographic information system, ISPRS, Volume 32, Part 4. "GIS-Bewteen Visions and Applications", Stuttgart. P314-320. Koehl, M., 1996, The Modelling of urban landscapes. International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part. B4. Vienna. 460-464. Molenrr, M.A., 1992, Topology for 3D vector maps. ITC Journal, 1: 25-33. Figure 10. 3D visualisation to local part of cloverleaf junction.
The representation of road network is very important in 3DCM. Cloverleaf junctions are the most complex parts of the road network. In this paper, we analyzed the spatial characteristics of the cloverleaf junction, and attempted to establish a data model which can better represent the cloverleaf junction in 3DCM. In order to simplify the expression, a cloverleaf junction is partitioned into two parts: the aerial and ground part. Proven by the experiment of this study, it is argued that the aerial part of the road surface can be better represented using TIN. In order to partition the aerial part, an algorithm named All-Constraint Point Method has been proposed. Meanwhile, in order to manage the cloverleaf junction data efficiently, the relational database BLOB type has been extended and combined with R-tree index, forming the foundation of the dedicated data structure for a cloverleaf junction. The further work will address the integration of the road network with terrain and urban buildings. The experimental system for this study also needs to be improved. REFERENCE
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