## Theoretical Discussion  
### Study Scope and Method  
There are three methods of acquiring 3D shape information using laser scanning: Phase-based measurement method used to measure short distances of 60 m or less. Second, there is the time-of-flight (ToF) measurement method, which can measure up to several kilometers; and lastly the triangulation method, which is mainly used for inspection or reverse engineering [3].  
Among them, the first two methods are used in construction and civil engineering areas because of the problem of size and distance. Table 1 below describes the characteristics of the different laser scanning techniques according to the aforementioned three 3D shape information acquisition methods classified by the measurement principles.  
The continuous scan data acquired from specified objects go through a registration process which is related to registration relative to space and the geo-referencing process which, in turn, is related to converting data to absolute coordinates. Registration is a process of theoretically calculating the relative position that makes the difference in distance between figuratively common parts closer to 0 based on the scan data measured at different locations. This is a coordinate conversion process so that the scan data will form the same coordinate system and is determined by the moving and rotating elements in space. Here, three matching points are required in one registration process. That is, registering in the process of connecting two sub-projects, according to the space configuration [4].  
Studies using point clouds in construction have been conducted in various fields. [PERSON] (2009) approached the acquisition of 3D shapes of buildings through a method of extracting 3D shape  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Measuring Principle** & **Distance(m)** & **Accuracy(mm)** & **Measuring Speed** \\ \hline ToF method & \textgreater{}1000 & \textless{}20 & slow \\ Phase method & \textless{}60 & \textless{}10 & fast \\ Triangulation method & \textless{}5 & \textless{}1 & fast \\ \hline \hline \end{tabular}
\end{table}
Table 1: The Characteristics of the laser scanning techniques in relation to the measurement principles.  
data from the contour of a polygon [2]. [PERSON] et al. (2013) produced a 3D city model through point cloud data collected from a ground laser scanner [5].  
[PERSON] (2014) constructed a civil engineering site model using point cloud data and assigned safety grades according to height to use them as basic data for safety enhancement of the area [6]. Previously, [PERSON] (2012) compared accuracy by grid size after calculating the volume of 3D point clouds through the triangular grid method [7]. Both were followed by [PERSON] (2015) who calculated forest volume by applying variations caused by wind through the triangular grid method [8]. That same year, [PERSON] (2015) improved the economy and efficiency of 3D interior modeling by comparatively analyzing total station by laser scanner [9].  
In addition to the aforementioned studies, other studies using point cloud in various directions such as fitting and matching [1], recognition [10; 11], texture mapping [12], feature extraction [13; 14; 15], reconstruction and modeling [16; 17; 18], data comparison [19; 20], analysis and robotics [21], and etc., are being conducted. These studies focus on improving productivity using point cloud data in construction-related areas and acquiring required data in research and management areas. However, there are no studies that compare the volume and shape of two objects to secure a matching space by such means.