A METHOD OF EXTRACTING GEOMETRIC INFORMATION 
FROM THE POINT CLOUD OF BUILDING 
Weian Wang a ,Bo Zheng 3 , Xiang Li a 
3 The Department of Surveying and Geo-informatics Engineering, Tongji University, Shanghai, 200092. 
-weian@ tongji.edu.cn, -bobo_821@126.com, -li_super.bb@163.com 
KEY WORDS: Point cloud; Geometric features extraction; Spatial index; Normal distribution analysis; Triangles Classification; 3D 
model reconstruction 
ABSTRACT: 
The purpose of this article is to extract geometric features and other information for polyhedron, then using these features and 
information to build the model of object. In this essay, polyhedron refers to objects such as buildings. Unlike modelling objects in 
other fields, like reverse engineering, buildings’ surface usually consists of large amount of big and plane surfaces. Among these 
surfaces, there are distinct points and lines of intersection (the edges and vertices of the polyhedron). In this article, Triangles 
classification and Surface extraction, Surface contiguous relations restoration, and Polyhedron Vertices solution and Polyhedron 
model Reconstruction constitute the main research of extracting geometric features and building the model of the object. In this 
contribution, some examples of extracting information from the point cloud are presented to demonstrate the method, which is put 
forward in this essay. Besides, the results prove that when the geometric information of vertices, edges and surfaces, together with 
the topological relations among them, are extracted from the point cloud, the model of polyhedron, representative of building in this 
essay, can be built effectively. Equally important, models generated from this method, while occupy less memory space, they can 
store more comprehensive structural information, and have a better exhibitive effect. 
1. INTRODUCTION 
During the passing years, the computer-assisted technology of 
building 3D surface model, which is based on the surface point 
cloud of 3D entity, has gradually become the foundation of 
virtual reality, decision analysis and computer-assisted design. 
And the sources of point cloud show the trend of diversification. 
The objects of model building in the fields of surveying, urban 
designing, and urban 3D landscape planning are normally 
buildings, which consists of polyhedron in most case. Therefore, 
the research of polyhedron model building, utilizing the 
information extracted from the corresponding point cloud, has 
highly practical merits. 
The main characteristics of these modelling targets are: l.The 
object has many entities. 2. It is composed of vertices, edges 
and planes (or it can be approximately thought as basic and 
sample geometries, such as the simple polyhedrons). The 
characteristics determined that it is necessary to use the 
different method from that in Reverse engineering [I1 and other 
fields f2 l At the same time, extracting geometric features such 
as vertices, edges and planes and getting the topological 
relationships among these elements are determined to one of the 
most critical parts. 
To achieve the goal mentioned above, there are several 
processes must be done: 1. Error Elimination |3 '. 2. Triangle 
mesh model generation [4] . Besides, in the focus of the research, 
extracting basic geometric features such as vertices, edges and 
planes base on the triangle mesh model of 3D object, 
topological information transmission and spatial index methods 
are used to solve the problem of the shortage of the geometric 
and topological information. 
Then after the three main process, Triangles classification and 
Surface extraction, Surface contiguous relations restoration, and 
Polyhedron Vertices solution and Polyhedron model 
Reconstruction, the 3D object can be expressed by the simple 
and abstract geometric features. 
2. MAIN PARTS IN THE RESEARCH OF 
EXTRACTING GEOMETRIC INFORMATION FROM 
THE POINT CLOUD OF BUILDING 
2.1 Triangles classification and Surface extraction 
The process of triangles classification is taken out from the 
triangle mesh of the polyhedron’s surface, as well as the normal 
and the topologic relationship of the triangles. In this paper, the 
method used to achieve this aim is Gfowth Triangles 
Classification—starting with a initial growth triangle, based on 
the share relationship of edge among triangles, this approach 
classify the triangles, whose normal’s differences are small in a 
continuous region, into one class. 
The “Class” here means a surface. To the polyhedron, the 
surface is represented by a mathematic plane. The equation of 
each surface could be calculated, using the vertices’ coordinates 
of the triangles, which belongs to the same class. Due to the 
data loss at the vertices and edges of the polyhedron in the 
sampling process of point cloud, some originally non-existed 
surfaces appear in the model; therefore, these falsely added 
surfaces should be eliminated from the final result. 
2.1.1 Normal distribution analysis: In order to obtain the 
approximate number, normal distribution of the main surfaces 
of the object, Normal distribution analysis is used in this paper. 
First, the Normal distribution analysis counts the weighted 
normal of all the triangles, and the normal vectors are 
normalized. In the statistics, the area of the triangle is