The massspring model has been typically employed in physicalbased simulators for clothes or patches. The massspring model frequently utilizes equal mass and the gravity factor. The model structure of masses supports a shape applicable to fishing nets. Therefore, to create a simulation model of a fishing net, we consider the massspring model and adopt the tidalcurrent and buoyancy effects in underwater environments. These additional factors lead to a more realistic visualization of fishingnet simulations. In this paper, we propose a new massspring model for a fishingnet and a method to simplify the calculation equations for a realtime simulation of a fishingnet model. Our 3D massspring model presents a meshstructure similar to a typical massspring model except that each intersection point can have different masses. The motion of each mass is calculated periodically considering additional dynamics. To reduce the calculation time, we attempt to simplify the mathematical equations that include the effect of the tidalcurrent and buoyancy. Through this research, we expect to achieve a realtime and realistic simulation for the fishing net.
1. INTRODUCTION
A 3D fishingnet simulation has been used to check the efficient spread of a net and also train a fisherman. The structure of a fishingnet is very similar with those of general mass spring models to show the motion of the cloth or patches. This similarity makes a 3D fishingnet simulation use a mass spring model
[1]

[3]
,
[9]
.
In general fishingnet simulation programs, the calculation speed is one of the critical issues for the realtime simulation
[4]

[8]
. There have been developed many researches to get the higher calculation speed. Ko proposed the method to reduce the integration time
[5]
. Lee simplified the equations to solve the motion of fishingnet using constant term
[6]
. These previous researches basically consider the only gravity factor to simulate the motion of massspring model. However, the fishingnet has to understand the undersea factors such as tidalcurrent and buoyancy to imitate its realistic motion
[7]
,
[11]
. And also it needs to consider the nonuniform mass distribution of a fishingnet because a fishingnet can be formed with several netting twines with different weights
[9]

[12]
. These additional factors make the simulation system difficult to get the realtime simulation because we have to create the model to consider the factors such as the density of fluid, the density of objects, the volume of objects, and the vector field of tidal current. Therefore, we try to implement a simulation system for the fishingnet whose motion also can be affected by the tidalurrent, buoyancy, and the gravity factor
[12]

[14]
. In order to reduce the calculation time, we will simplify some equations to determine the motion of a fishingnet. The massspring model to imitate the motion of the fishingnet will be modified so that the mass at each vertex can have a different weight.
In this paper, we propose a practice system for 3D fishingnet simulation from general massspring background. We may obtain an accurate motion of fishingnet using a twostep approach: The first step is an
Input Data Control
based on actual fishingnet data with different masses. The second step is the
Physics Processor
which decides the motion of the fishingnet by a tidalcurrent factor, a buoyancy factor, and a gravity factor in an undersea environment.
Our approach has the following advantages. First, we may generate a realistic simulation in specific undersea environment. This is because
Physics Process
can generate better results than simple gravity. We also increase the calculation speed through the simplification of some equations.
2. SYSTEM OVERVIEW
Our system consists of four steps as shown in
Fig. 1
. Because our net is suggested in a form with unequal mass, we first give an input directly for each mass point in
Input Data Control
step. In this step, the properties of masses or springs are also added into a structural fishingnet data. The second step,
Interactive User Interface
, determines the external force such as the lift force of tidalcurrent, the density of objects, the volume of objects. It also initializes a position vector of fishingnet by user’s mouse control. The third step is the
Physics Processor
which calculates the motion of our fishingnet model using the environmental characteristics such as tidalcurrent and buoyancy. To obtain a realtime motion of fishingnet model, we will simplify several calculation equations to get the motion of our models.
System Overview
The last step,
3D Simulation Manager
, shows the natural motion on the display monitor using computed values.
3. INPUT DATA CONTROL FOR FISHINGNET DATA
Since our fishingnet model considers the various environmental effects, this model has to define the various types of mass. We will collect the actual data of real fishingnet in order to define the mass types for our fishingnet model. After the tuning of these actual data, we use the tuning data as input data of our fishingnet model. To express the fishingnet simulation with unequal masses, we consider the following data structure.
As shown in
Table 1
, each mass point has its mass properties, 3D position, and link attributes implying its connectivity structures. Through investigation of actual fishingnets, we designed our massspring model for fishingnet as expressed in
Fig. 2
. Most of mass points have link connections of a diamond shape among its neighboring mass points. Periodically, vertical links are added to the link connection of a diamond shape.
Input Data of FishingNet
Input Data of FishingNet
MassSpring Model of FishingNet
A fishingnet model consists of a finite number of mass points and its mass points are connected with several spring links. As depicted in
Fig. 2
, each point can have different densities, and it divide into three regions. For example, the buoys, the sinker, and the general points are located at the topline, the bottom line, the middle region, respectively.
4. PHYSICS PROCESSOR
 4.1 Initialization of FishingNet
In the second process of
Fig. 1
, the initial fishingnet model can be structured by input step come from both actual net information of
Input Data Control
, and a position of fishingnet through
Interactive User Interface
. In general, for each mass point, we calculate the initial position using mathematical equations. Mass and link connection between mass points are chosen among the userdefined basic forms which are derived from real fishingnet structures. For special masses around the top line and bottom line of a fishingnet, we input different masses and properties through the
Interactive User Interface
dialog box. In
Interactive User Interface
, it is possible that we directly move each point after picking vertex.
A fishingnet has a lot of intersection points which correspond to the mass point. If we use all intersection points in fishingnet, this simulation system is not possible to get a realtime fishingnet simulation system. So, we have chosen some representative intersection points that is enough to show the simulation of fishingnet. The selected points are shown as large circle points in
Fig. 3
. To express the net structure with unselected points, we use the texture mapping technique with diamond shapes. This texture is given in a checked pattern with black color in
Fig. 3
.
Initial Positions of Mass Points for a FishingNet and its Textures
 4.2 Motion Equation
The mesh structure in an actual fishingnet should be approximated with a small number of mass points to get a rapid calculation. We will try to add the environmental forces to a fishingnet simulation and then consider the environmental forces such as buoyancy and tidal current force. So, at each mass point of the fishingnet, its motion equation includes the gravity, tidalcurrent force, and buoyancy as follow:
where
F_{g}
is a gravity force, (
F_{c}
+
F_{cd}
+
F_{cl}
) is a tidalcurrent force, and (
F_{b}
+
F_{bd}
) is a buoyancy force. Although our method will show the meshstructure similar with the other massspring model based on gravitation, it also has characteristics of tidalcurrent and buoyancy as well as each point can have different mass.
 4.3 TidalCurrent Equation
The Tidalcurrent force is subdivided into
F_{c}, F_{cd}, F_{cl}
forces in the motion equation (1).
F_{c}
means the magnitude and direction vector of the tidalcurrent, and
F_{cd}
is the drag force that the tidalcurrent affects on the object.
F_{cd}
is generally calculated as follows:
where
S
is the projected area of the object,
ν
is the velocity of the object, and
N
is the normal vector of the object. Vector (
F_{c}

ν
) is normalized by
normal()
function.
F_{cl}
is the lift force that the tidalcurrent makes the object afloat.
F_{cl}
can be defined as follows as:
where
S
is the projected area of the object,
V_{L}
is the vector of the lift force,
K_{L}
is the coefficient of the lift force.
V_{L}
and
K_{L}
are given as follows:
where
N
is the normal vector of the object,
ν
is the velocity of the object, and
F_{c}
is the vector of the tidalcurrent. From equation (4), we obtain the vector of the lift force as
V_{L}
.
where
K_{L}
is a very important factor because it determines the scale of lift force. In order to choose the adequate
K_{L}
value, we utilize a lift function
L_{func}( )
. These values are depended on the
N, F_{c}
, and
ν
factors. The
N
is the normal vector of the object,
F_{c}
is the vector of the tidalcurrent, and
ν
is the velocity of the object.
In several experimental observations of fishingnet, we can obtain the experimental coefficients for
L_{func}( )
as given in
Table 2
.
Experimental Coefficients of the Lift Force
Experimental Coefficients of the Lift Force
Using data in
Table 2
,
L_{func}( )
can be represented as curvature graph as shown in
Fig. 4
. This graph for the coefficients of lift forces is skewed slightly in right direction.
Graph of Lift Function, L_{func}( )
We can recognize that this coefficient graph is very similar with a cosine function.
Fig. 5
shows the difference between the graph of
L_{func}( )
and general cos().
comparison of the L_{func}( ) with Cos () Graph
Since the coefficients shows a small gap between two curves, it is possible to approximate the
K_{L}
value with a general cosine function. Therefore, we can simplify the
K_{L}
value as follows:
In order to reduce the computational calculation time of cos(), we compensate the cosine value using Taylor series function
Taylor()
. Therefore,
K_{L}
can be converted as follow as:
Tidalcurrent force make mass point move to adequate position according to the tidalcurrent force.
If the tidal current force is adapted in a perpendicular direction with fishingnet, the fishingnet are moved into the curved shape as shown in
Fig. 6
because two or more end points are attatched to the fixed position such as a ship. According to the magnitude of tidal current force, the curvature of fishingnet will be smaller.
Net Deformations by a Tidalcurrent
 4.4 Buoyancy Equations
Buoyancy force is defined as combination of
F_{b}
and
F_{bd}
in the motion equation (1). If
F_{b}
is the buoyancy force,
D_{o}
is the density of the object,
D_{f}
is the density of the fluid,
Dt
is the density by the temperature,
D_{p}
is the density by the pressure,
V
is the volume of the object, and
W
is the weight of the object, the buoyancy force can be defined as
Since
D_{f}, Dt
, and
D_{p}
are relatively expensive to compute, Eq. (8) should be simplified. Through the various experiments, we can observe that two density factors,
Dt
and
D_{p}
, do not show the great graphical effects in the simulation of a fishingnet. So, we decide to eliminate two factors in the equation (8) and then the equation to calculate the effect of buoyancy can be simplified in one term as follows:
The drag force occurred by the buoyancy force is define as follows:
where
D_{f}
is the density of the fluid,
S
is the projected area of the object, and
K_{b}
is the cofficient of the drag force.
Finally, fishingnet motion is generated using
implicit Euler integration
as follows:
where
m
is mass of particle,
T
is a timestep of simulaion.
The fishingnet in trawler should be positioned in an adequate height in undersea and also can be opened in a vertical form. This buoyancy factor make the fishingnet form a vertical shape.
Fig.7
shows the fishingnet opened vertically.
FishingNet shape by Buoyancy Effect
5. EXPERIMENTAL RESULTS
We implemented the 3D fishingnet simulator using simplified equations that are described in section 4. We make a test the net shape according to the buoyancy force and tidalcurrent force. At this time, both ends of the fishingnet are always fixed similar with real fishingnets.
Fig. 8
(a) shows the fishingnet without buoyancy and tidalcurrent forces. The middle point of this net are drooped under the weight of fishingnet. The buoyancy mitigates the drooping of fishingnet because the mass points get the upward force.
Fig. 8
(b) represents the effects of buoyancy force. Buoys attached along the above line of fishingnet cause the different buoyancy force between the above line and the bottom line. These differences give the good opened shape of a net. It is similar with the shape of a net in real world.
Fig. 8
(c) shows the effects for only tidalcurrent force and so the net have moved along the direction of tidalcurrent.
Fig. 8
(d),
8
(e), and
8
(f) is net shapes considering the buoyancy and tidalcurrent. The top line of fishingnet is floating on the sea while its bottom line goes under by sinker attachments. They present the shapes from various camera views in the fishingnet simulation employing buoyancy and tidalcurrent force.
Simulation Results
From these simulation results, we can observe that our simulation system employing buoyancy and tidalcurrent forces is very similar with the real fishingnet.
6. CONCLUSION
In this paper, we have developed a 3D fishingnet simulation system considering a tidalcurrent force and buoyancy. In order to get a realtime simulation, we have chosen the physics model and then simplified the equations to describe the physical effects of the tidalcurrent force and buoyancy. This simplification makes the realtime simulation possible. In particular, the cosine function for coefficient value
K_{L}
gave very similar visual results and also caused a huge cutoff in an execution time. In case of buoyancy, we considered only the density of fluid because the other factors do not provide big differences. Through such simplifications, we achieved the realtime simulation and also upgraded the visual effects in the 3D simulation of the fishingnet.
Acknowledgements
This work was supported by Research Grant of Pukyong National University (2013 year).
BIO
Joseph Yoon
He received the B.S., M.S. and completed Doctor course in Computer Science from Pukyong National University, KOREA in 2003, 2005, and 2007 respectively. Since then, he had worked as developer with Sensingmap Co., Ltd. at Pusan National University in KOREA until 2011. Since 2012, he has been studying with Department of IT Converagence and Application Engineering at Pukyong National University in KOREA. His main research interests include Computer Graphics and HumanComputer Interaction.
YoungBong Kim
He received the B.S. in Computer Science from Seoul University, Korea in 1987 and also received the M.S. and Ph.D. in Computer Science from Korea Advanced Institute of Science and Technology, KOREA in 1989, 1994 respectively. Since then, he had worked as a researcher with Samsung Electronics until 1995. Since 1995, he has been a professor with Department of IT Convergence and Application Engineering at Pukyong National Uneversity in KOREA. His main research interests include Computer Graphics and Animation.
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