4.1 Static information

Based on the Automotive Intelligent Chart (AIC) 3D Electronic Chart Display and Information System (ECDIS) proposed by Liu et al. (Reference Liu, Zhao and Pan2014), we conduct further improvement research. With the development of programmable rendering pipeline and graphics processing unit (GPU) hardware, we adopt the advanced GPU rendering methods in our project, such as hybrid data representation, order independent transparency and geometry clipmap. We have greatly enhanced the previous project in this paper. In terms of fusion visualisation, we mainly make the following optimisations.

• • For the category of basic scene data, which includes remote sensing images, terrain data, we use the level of detail (LOD) method to organise this type of data. Terrain and riverbed data are used to build the fundamental framework. Texture mapping is used to map remote sensing image tiles onto the fundamental framework. A height map tile that contains the terrain data is also stored in the image format. The GPU-based geometry clipmap method (Losasso and Hoppe, Reference Losasso and Hoppe2004) is used to render the basic scene data. The geometry clipmap structure caches a square window of $n\times n$ samples within each level. These windows correspond to a set of nested regular grids centred about the viewer. The structure maintains triangles that are uniformly sized in screen space. This method provides a number of advantages: simplicity of data structures, smooth visual transitions, steady rendering rate, graceful degradation, efficient compression and runtime detail synthesis. To satisfy the need for texture streaming of large rich environments, we use virtual texture (Mittring and GmbH, Reference Mittring and GmbH2008) to manage the texture memory. Only the actually required portions need to be uploaded. This is very efficient.

• • For the category of terrain following objects, such as country boundaries, highways, etc., we use the texturing method to accelerate the rendering of large-scale vector data. First, vector data are drawn onto texture tiles in the fragment buffer. Then, these texture tiles are mapped onto the terrain by texture mapping. This will avoid the interpolation calculation of vector and terrain and can greatly improve the calculation efficiency.

• • For the category of independent objects, such as labels, 3D entities, etc., we refer to the foveated rendering method (Swafford et al., Reference Swafford, Iglesias-Guitian, Koniaris, Moon, Cosker and Mitchell2016) for rendering this type of data. We use hybrid data representation (triangle mesh and displacement map) and data compression to describe entity objects. This will reduce the memory consumption. The basic idea of foveated rendering is to render high-quality images in the foveated area and low-quality images in the peripheral area to save time and cost. Rendering methods based on gaze point information usually use technologies such as multi-texture and fragment programming to improve rendering performance.

• • For the electronic navigational vector objects, the rendering method has also been improved. The order independent transparency method (DFB algorithm) (Maule et al., Reference Maule, Comba, Torchelsen and Bastos2014) is used to render this data type. The transparency attribute of these vector objects such as depth contour, depth area, anchor zone are realised more efficiently. This method can perform correct compositing for objects with efficient memory management.

In terms of data modelling, we have also made improvements. We make full use of advanced data modelling technologies, such as oblique photography and point cloud modelling technology. We select different modelling methods according to the difficulty of data acquisition. For entities that are difficult to collect laser point cloud information on the ground, oblique photography technology is used for data acquisition, and then modelling processing is performed, such as denoising, singulation and trimming. For entities that are easy to collect laser point cloud information on the ground, selection of the data acquisition method is based on the data accuracy requirements: for entities that affect berthing and unberthing, such as docks, laser point cloud technology is used for data acquisition and post-processing; for other entities, oblique photography technology is adopted. Data obtained by oblique photography and point cloud modelling technology can be reconstructed with mature software such as ContextCapture, Trimble Realworks, and fused in our system based on our algorithms.

The reconstruction effects are shown in Figures 3–5. Figures 3 and 4 show the overwater view effect of the ship traffic accident scene and Figure 5 shows the underwater view effect of the ship traffic accident scene.

Figure 3. Shore view effect

Figure 4. Overwater view effect

Figure 5. Underwater view effect

4.2 Dynamic data

For the dynamic data of ship traffic, such as ship positions and accident information, we fuse these data into the accident scene. The reconstruction of trajectories of the accident ship consists of two parts: trajectory point calculation and pose calculation. Trajectory point calculation is used to reconstruct the linear motion of the ship, and the pose calculation is used to maintain the correct posture of the ship.

1. (1) Trajectory point calculation

The trajectory data of the accident ship stored in the ship traffic accident database are extracted to perform the reconstruction. However, during the trajectory data collection process, there are some problems in the data record of the accident ship such as large collection interval and missing data. Data jumping and unsynchronisation may occur. To achieve the synchronisation of trajectories of accident ships and avoid the impact of missing data, trajectory detection and interpolation are needed. Based on the previous position of the trajectory data, ship heading and speed information stored in the database, a data-fusion-based recursive method is designed to fill in the missing data points of the encrypted data. The calculation method is shown in Equation (1),

(1)\begin{equation} \begin{aligned} & P_i = P_{{\rm bef}(i)} + t * \frac{{(\alpha *v + \beta * r)}}{{\sqrt{\alpha ^2 + \beta ^2 }}},\quad i = 1,\ldots ,N, \\ & \text{such that}\left\{\begin{array}{l} P_{{\rm bef}(1)} = P_{{\rm start}} , \\ P_N = P_{{\rm end}}, \end{array} \right. \end{aligned} \end{equation}

where $P_i$ is the position of the output point; $P_{{\rm bef}(i)}$ is the position of the previous point; $t$ is the interpolation time interval; $v$ denotes the unit vector of the ship speed; $r$ denotes the unit vector of the channel centreline or designed route segment; $P_{{\rm start}}$ and $P_{{\rm end}}$ represent the starting point and ending point of the route segment, respectively; and $\alpha$ and $\beta$ are weight coefficients. As can be seen in Equation (1), this method fuses channel information or route information and turns the reconstruction problem into a constraint calculation problem. Therefore, space and time calibrations of the data are achieved and linear motion of the ship can be realised by dynamically refreshing the 3D spatial position of the ship model according to the calculated trajectory point.

1. (1) Pose calculation

Pose calculation decomposes the transformation of pose change about a certain direction axis into rotation transformations about the three coordinate axes of the local coordinate system of the 3D ship model, that is, this calculation simulates the ship's roll, pitch and yaw by constructing rotation matrices about the three axes. The rotation angles are from the traffic accident database. In our system, pitch corresponds to rotation about the $X$-axis, yaw corresponds to rotation about the $Y$-axis, and roll corresponds to rotation about the $Z$-axis. The rotation transformations can be calculated according to Equations (2), (3) and (4), respectively. The rotation angle is positive when rotating counterclockwise,

(2)\begin{align} R_x & = \left[ {\begin{array}{ccc} 1 & 0 & 0 \\ 0 & {\cos ( {\theta _x } )} & { - \sin ( {\theta _x } )} \\ 0 & {\sin ( {\theta _x } )} & {\cos ( {\theta _x } )} \end{array}}\right], \end{align}

(3)\begin{align} R_y & = \left[ {\begin{array}{ccc} {\cos ( {\theta _y } )} & 0 & {\sin ( {\theta _y } )} \\ 0 & 1 & 0 \\ { - \sin ( {\theta _y } )} & 0 & {\cos ( {\theta _y } )} \end{array}}\right], \end{align}

(4)\begin{align} R_z & = \left[ {\begin{array}{ccc} {\cos ( {\theta _z } )} & {\sin ( {\theta _z } )} & 0 \\ { - \sin ( {\theta _z } )} & {\cos ( {\theta _z } )} & 0 \\ 0 & 0 & 1 \end{array}} \right], \end{align}

where $\theta _x$, $\theta _y$ and $\theta _z$ represent the rotation angles about the $X$, $Y$ and $Z$ axes, respectively.

5.1 Ship boundary calculation

Collision detection is to determine whether there is a collision between two objects. It is an indispensable part of ship accident reconstruction. The basic framework of the collision detection algorithm is to perform preliminary detection first, and then gradually to refine intersection calculations. Object space-based collision detection algorithms often use tree-type retrieval structures and bounding boxes to speed up computation. The collision detection in this paper refers to the process for detecting the collision of 3D models of accident participants in the ship traffic accident scene. Usually, the actual outlines of different objects are different. A ship has a rectangle outline. A buoy has a cylindrical outline. For different outline properties of objects, different bounding boxes are designed to accelerate the calculation of collision detection in this paper, such as rectangular bounding box for ships and bridges, cylindrical bounding box for buoys. There are two types of cuboid bounding box: axis-aligned bounding box (AABB) and oriented bounding box (OBB), as shown in Figure 6.

Figure 6. 2D schematic diagram for the bounding box

The construction of an OBB bounding box relies on the spatial trend of the grid points of 3D model. The OBB bounding box is a better approximation of the object and can provide more accurate results when applied in the collision detection calculation. Moreover, when the pose of 3D model changes, it is not necessary to recalculate the OBB bounding box of the model. In the field of trajectory risk reconstruction, accuracy should be the primary condition. Therefore, we adopt the OBB bounding box to accelerate the ship collision detection calculation. However, the common method of constructing an OBB bounding box is relatively complicated. Covariance matrix, eigenvalue and eigenvector should be calculated to determine the direction of the main axes. Moreover, because the distribution of grid points of the 3D ship model is irregular, it is not accurate to use the eigenvector calculated by the covariance matrix as the main axis.

We design a new method in this paper. By designing simple transformations, the calculation efficiency of the OBB bounding box is greatly improved, especially during the real-time operation of the system. Although there is no complicated mathematical formula, the clever and efficient design is very useful in the actual system operation. Based on the ship's heading angle $a$ recorded in the ship traffic accident database, we calculate the three main axes (the local coordinate system of the ship model, as shown in Figure 7) of the 3D ship model by normalisation, rotation transformation and translation transformation, and use this coordinate system to build the OBB bounding box. The specific calculation process is as follows.

Figure 7. Schematic diagram for the local coordinate system

First, obtain the normal direction of the main axis $Ya$ by unitising the ship position coordinate $A$;

Then, take a small step along the longitude direction to get point $B$, project point $B$ onto the tangent plane at point $A$ to form a vector with point $A$ and unitise this vector to yield vector $X'$. At last, the vector $X'$ is rotated about the main axis $Ya$ to obtain the main axis $Za$ (the rotation angle is the heading angle $a$);

Finally, the main axis $Xa$ is calculated by $Ya$ and $Za$ using the right-handed spiral rule.

Compared with the common eigenvector calculation method of the OBB bounding box, the proposed method is simple and can accurately calculate the local coordinate system characterising the 3D ship model. The calculated coordinate system fully matches the spatial trend of the model. Based on the local coordinate system, the OBB bounding box of the model can be directly calculated according to the calculation method of the AABB bounding box. On the basis of the bounding box calculation, spatial intersection calculation is performed to complete the collision detection.

5.2 Data preprocessing

Before the loading of the 3D ship model, the model needs to be normalised. The normalisation calculation scales the 3D ship model to the correct scale relative to the constructed 3D ship traffic accident scene. In this paper, we use the reference object method. The first 3D ship model is normalised according to the reference object in the scene. The normalisation of subsequent 3D ship models is based on the first 3D ship model and the same reference calculation is carried out. Based on the ship traffic accident scene and the ship size information stored in the traffic accident database, the specific calculation process is as follows.

First, calculate the OBB bounding boxes of the 3D ship model and the reference object selected in the accident scene.

Then, scale the 3D ship model according to the reference condition. The reference condition assumes that the ratio of the diagonals of two OBB bounding boxes should be approximately equal to the ratio of the physical sizes of the two objects.

After the normalisation process, the 3D ship model can be loaded into the accident scene. The rotation and translation transformations also need to be performed according to the fusing method of the entity model in the 3D scene (Liu et al., Reference Liu, Zhao and Pan2016).

5.3 Risk calculation

There are many factors that influence ship collision accidents, and it is necessary to reconstruct meaningful factors for accident risk assessment, especially the factors that affect the crew's cognition of risk and the judgment of the next operation. Research results show that more than 80$\%$ of ship collision accidents are caused by human error (Rothblum, Reference Rothblum2000). We assume that human subjective factors have the same influence in different environments. This paper focuses on the influence of objective factors. We use the fuzzy comprehensive evaluation method to construct a fuzzy evaluation model that fuses multiple factors and 2D and 3D spatial calculations. By analysing the accident data, factor extraction and historical data mining are also used in the reconstruction of the risk of ship collision accidents. This model can be mapped to the crew's cognitive process. In this paper, we have collected a total of 497 relatively complete ship collision accident reports from maritime investigation report websites. The sources of accident reports include: Maritime Safety Administration of the People's Republic of China, Shanghai Maritime Safety Administration, Shandong Maritime Safety Administration, Nanjing Maritime Safety Administration, Jiangsu Maritime Safety Administration, Australian Transport Safety Bureau (ASTB), Marine Accident Investigation Branch (MAIB), The Danish Division for Investigation of Maritime Accidents (DMA), National Transportation Safety Board of United States (NTSB) and New Zealand Maritime Bureau (NZM). Furthermore, the visualisation method of the risk cognition model designed in this paper allows the crew to better visually recognise the risk calculation process.

At present, the fuzzy mathematics methods mostly use five parameters to assess the risk: DCPA, TCPA, orientation of the target ship relative to the own ship, speed ratio of the own ship and the target ship, and distance between the own ship and the target ship. In this paper, we select several factors of which the crew have a deep understanding to reflect the risk degree of the accident and construct more comprehensive influencing factors based on the data fusion. We use five factors to evaluate the risk: DCPA, TCPA, fusion of distance and yawing degree, relative bearing $G$ of the target ship relative to the own ship, and fusion of ship density and speed ratio. Among them, DCPA and TCPA are the most important factors influencing the ship risk, which can reflect the distance, relative speed and azimuth of two ships. Smaller values of DCPA and TCPA will result in a greater collision risk. Most research in the ship collision risk area takes DCPA and TCPA as parameters. Usually, the distance between the own ship and the target ship can give a more intuitive calculation of the collision risk. We take the compound factor of distance and yawing degree as a new parameter, which can not only express the influence of distance on risk, but also the influence of yawing degree on risk. When the distance is smaller and the yawing degree is larger, the value of this factor is higher, which reflects a higher degree of danger; on the contrary, it reflects a lower degree of danger. Incoming ships from different directions pose different danger degrees to the ship. Generally speaking, the hazard degree of the starboard side is greater than that of the port side, and the hazard degree before abeam is greater than that behind. Finally, we use the compound factor of ship density and speed ratio as a new parameter. This factor considers not only the influence of the target ship, but also the influence of surrounding ships. Based on the accident sample data, the independence of the constructed influencing factors is verified through Pearson correlation analysis.

We first need to determine the calculation of risk subordinating degree of each factor in the model. In this paper, we assess the trajectory risk of a ship collision accident, without considering ship manoeuvring factors such as the latest avoidance distance. Based on the ship boundary calculation and ship domain concept, we design the method for calculating the risk subordinating degree of each factor.

1. (1) Risk subordinating degree function of DCPA

The risk caused by DCPA to the ship is obvious. A larger value will mean a smaller degree of risk. Risk subordinating degree function of DCPA is as follows:

(5)\begin{equation} U({\rm DCPA}) = \left\{ \begin{array}{ll} \dfrac{1}{2} - \dfrac{1}{2}\sin \left( {\dfrac{\pi }{D}*\left({\rm DCPA} - \dfrac{D}{2}\right)} \right), & \text{if DCPA} \le D; \\ 0, & \text{if DCPA} > D, \end{array} \right. \end{equation}

where $D$ is the absolutely safe encounter distance. When a large ship meets a small boat, the distance calculation should be more accurate. We design a 3D distance fusion calculation method in this paper. Moreover, accurate distance calculation can provide better support for the calculation of collision risk. The calculation of the distance is divided into two cases based on the classical ship domain model proposed by Fujii and Tanaka (Reference Fujii and Tanaka1971). In the ship domain, the 3D OBB bounding box is used to calculate the distance between two ships. First, 3D OBB bounding boxes of two ships are calculated. Then, the principal axis projection and the minimum distance calculation are performed. Outside the ship domain, we calculate the distance between the centre points of two ships. We stipulate that when $U({\rm DCPA})$ is 1, the trajectory risk is 1.

1. (1) Risk subordinating degree function of TCPA

The risk caused by TCPA to the ship is also obvious. A larger value will mean a smaller degree of risk. Risk subordinating degree function of TCPA is as follows:

(6)\begin{equation} U({\rm TCPA}) = \left\{ \begin{array}{ll} \left( {\dfrac{{T - | {{\rm TCPA}} |}}{T}} \right)^2 , & \text{if}\ | {{\rm TCPA}} | \le T; \\ 0, & \text{if}\ | {{\rm TCPA}} | > T, \end{array} \right. \end{equation}

where $T = {\sqrt {D^2 - {\rm DCPA}^2}}/V_R$, $V_R$ is the relative speed and $D$ is the absolutely safe encounter distance. We stipulate that when $U({\rm TCPA})$ is 1, the trajectory risk is 1. Based on the changing law of this factor and the number of corresponding accidents and the experience of experts, we adopt a quadratic power function.

1. (1) Risk subordinating degree function of the compound factor of distance and yawing degree

At present, most inland rivers adopt the traffic separation scheme (TSS). The impact of the ship's deviation from its navigation channel is significant. Moreover, through careful analysis of the ship's navigation characteristics, the close distance between the two ships does not mean a collision risk in most cases. Our algorithm considers both inland navigation and maritime navigation. The deviation of the ship from the routing or the centreline of the channel often indicates anomalies.

The regularity of accident attributes can be found by mining and analysing a large amount of accident data. Based on the collected 497 investigation reports of ship collision accidents, we conduct an analysis of the accident distance factor and the risk degree through data correlation analysis and data fitting analysis. Through statistical analysis of investigation reports, it is found that among 497 ship collision accidents, 350 ship collision accidents relate to close distance (accounting for 70${\cdot }$4%). It can be seen that the distance factor has a significant impact on the risk of ship collision. We classify the distance and count the number of accidents within each interval, as shown in Table 1.

Table 1. Distance classification

Through data fitting, the relationship between the distance and the collision risk is as follows:

(7)\begin{equation} U(d) = 1{\cdot}001*e^{ - 1{\cdot}228*d}, \end{equation}

where $d$ represents the distance between ships and $U(d)$ represents the collision risk degree. The fitting function type is an exponential function. The variance and mean square error obtained are 0${\cdot }$009 and 0${\cdot }$055, respectively. The goodness of fitting and modified goodness of fitting are 0${\cdot }$9864 and 0${\cdot }$9818. It is a good fitting function.

Two ships can be very safe even if they are relatively close in the same inland waterway lane. Based on the electronic navigational chart data, we fuse the distance between two ships with yawing degree and construct a compound factor. The risk subordinating degree function is as follows:

(8)\begin{equation} U(d,w) = \left\{ \begin{array}{ll} \alpha *(w/W)^2 + \beta *U(d), & \text{if}\ w \le W,d \le D; \\ 0, & \text{if}\ d > D, \end{array} \right. \end{equation}

where $W$ represents the width of the prescribed waterway; $w$ denotes the distance between the ship and centreline of the lane; $D$ is the absolutely safe encounter distance; and $d$ is the distance between two ships. Here, $\alpha$ and $\beta$ are the normalised weight coefficients. For offshore cases, $\alpha$ is larger, while for inland cases, $\beta$ is larger. We stipulate that when $U(d,w)$ is 1, the trajectory risk is 1.

1. (1) Risk subordinating degree function of relative bearing

Under the same conditions, incoming ships from different directions pose different danger degrees. When the relative bearing of the incoming ship is $19^\circ$ (the most dangerous situation), the risk subordinating degree is set to 1. When the relative bearing of the incoming ship is $199^\circ$ (the safest situation), the risk subordinating degree is set to 0. The risk subordinating degree function (Zhou and Wu, Reference Zhou and Wu2004) is as follows:

(9)\begin{equation} U(G) = \frac{1}{2}\left( {\cos (G - 19^\circ ) + \sqrt{\frac{{440}}{{289}} + \cos ^2 (G - 19^\circ )}} \right) - \frac{5}{{17}},\quad 0^\circ\le G < 360^\circ, \end{equation}

where $G$ represents the relative bearing.

1. (1) Risk subordinating degree function of the compound factor of ship density and speed ratio

Through statistical analysis of the investigation reports, it is found that among the 497 ship collision accidents, 134 ship collision accidents relate to the ship density factor (accounting for 27$\%$). It can be seen that the ship density factor also has a significant impact on the risk of ship collision. We classify the ship density and count the number of accidents within each interval, as shown in Table 2.

Table 2. Ship density classification

Through data fitting, the relationship between the ship density and the collision risk is as follows:

(10)\begin{equation} U(q) = 0{\cdot}002448*q^{2{\cdot}542}, \end{equation}

where $q$ represents the ship density and $U(q)$ represents the collision risk degree. The fitting function type is a power function. The variance and mean square error obtained are 0${\cdot }$1197 and 0${\cdot }$1998, respectively. The goodness of fitting and modified goodness of fitting are 0${\cdot }$854 and 0${\cdot }$8053. It is a good fitting function.

We use the ship density $q$ to describe the traffic flow, that is, the number of ships per km$^2$. Based on the calculation method of ${\rm DCPA}$ after the ship turns to avoid collision, the functional relationship between ${\rm DCPA}$ and ship speed ratio can be obtained through appropriate assumptions and simplifications (Zhou and Wu, Reference Zhou and Wu2004). According to this, we design the risk subordinating degree function as follows:

(11)\begin{equation} U(q,k) = \alpha *U(q) + \beta *\frac{1}{{1 + \frac{2}{{k*\sqrt {k^2 + 1 + 2*k*\sin (C)} }}}},\quad 0^\circ \le C < 180^\circ, \end{equation}

where $k$ is the speed ratio; $C$ is the collision angle; and $\alpha$ and $\beta$ are the normalised weight coefficients.

Finally, the ship's trajectory risk is calculated as follows:

(12)\begin{align} V & = a_{{\rm DCPA}} *U({\rm DCPA}) + a_{{\rm TCPA}} *U({\rm TCPA}) + a_{d,w} *U(d,w)\nonumber\\ & \quad + a_G *U(G) +a_{q,k} *U(q,k). \end{align}

Based on the advice of experts, the normalised weight items are initially set to (0${\cdot }$35, 0${\cdot }$35, 0${\cdot }$1, 0${\cdot }$1, 0${\cdot }$1). They are dynamically adjusted based on the case feedback and expert opinions. Based on the data mining, our method is capable of self-learning.

6.1 Visualisation method

The primary task of visualisation is to accurately display and convey the information contained in the data, and to provide effective auxiliary means to help users to understand the data. To present data in an easy-to-understand manner, it is necessary to first convert the data into visual codes that are easy to perceive. A radar chart, also called a spider chart, is one type of visual code that displays multi-dimensional data in 2D form. It can quickly express the comparison of multiple indicators in the same coordinate system. On the basis of the designed risk factors, we use a radar chart to express the contribution of each factor in the assessment calculation and intuitively compare and analyse the factors in the reconstruction process.

6.2 Application results

To demonstrate the application effect of the proposed model and system, we take the typical ship collision accident ‘ship encounter’ as an example to carry out the trajectory risk reconstruction. Based on the ship trajectory and pose data stored in the ship traffic accident database, scene and risk calculations are used to realise the trajectory risk reconstruction of the two-ship collision accident. The location of the case is the Yangtze River waterway. A ship loses control and causes the collision.

Figure 8 shows a large-scale view of the two-ship collision accident scene. The red circle indicates the 3D model of the accident ship and the red arrow indicates the trajectory. When the trajectory is selected, the system will highlight the trajectory in white.

Figure 8. Large-scale view of the scene

Figure 9 shows a view of the trajectory risk reconstruction of a two-ship collision accident. The system calculates the risk in real time. Moreover, the system gives a progress indication of the simulation. It can be seen from the figure that the influence of factors is different under different conditions. As shown in Figure 9(a), the risk subordinating degree of the relative bearing is bigger than the risk subordinating degree of the compound factor of the distance and yawing degree and the risk subordinating degree of the compound factor of the ship density and speed ratio. However, as the target ship loses control and changes direction, the ship deviates from the channel and the risk subordinating degree of the compound factor of the distance and yawing degree becomes increasingly bigger. The weighted risk subordinating degree values of the four nodes in Figure 9 are listed in Table 3.

Figure 9. View of the trajectory risk

Table 3. Risk subordinating degree

The law can also be obtained from the numbers, but it is not as intuitive as the graphical display. Our calculation model can visually present the risk change process and all-round navigation environment to the crew. The system can also give a reconstruction of the falling process, as shown in Figures 10 and 11.

Figure 10. Reconstruction of the falling process

Figure 11. Ending of the falling process

To verify the effectiveness of the system, we also conduct user case experiments. We obtain a total of 100 tests from seafarers and marine technology undergraduates of Shanghai Maritime University. We compare the user risk cognition of a 2D electronic chart system, 3D navigation simulator and our system under the same accident reconstruction situation and collect users’ satisfaction with the system. By averaging the obtained satisfaction scores, the results are listed in Table 4.

Table 4. User satisfaction degree

It can be seen from the experimental results that this system can effectively assist users in risk cognition of ship collision accidents.