WO2022203455A1

WO2022203455A1 - Method and apparatus for simulating trajectory of elastic body, and computer program

Info

Publication number: WO2022203455A1
Application number: PCT/KR2022/004234
Authority: WO
Inventors: 진대제; 진상국; 김경태앤드류
Original assignee: 친버디 주식회사
Priority date: 2021-03-26
Filing date: 2022-03-25
Publication date: 2022-09-29
Also published as: KR102484980B1; KR20220134287A; JP2024511482A

Abstract

The present invention is characterized by comprising the steps of: acquiring an initial position of an elastic body, and an initial velocity of the elastic body formed by inertia applied to the elastic body; determining a flight trajectory from the start of flight of the elastic body due to inertia applied to the elastic body to landing on the M-th plane mesh included in a mesh model by applying, to a predefined flight trajectory model, the initial position and the initial velocity of the elastic body as flight trajectory calculation factors, wherein the mesh model is formed by emulating, with the first to N-th plane mesh, a field that becomes a movement space of the elastic body; and determining a rolling trajectory, in which the elastic body rotates and moves on the K-th plane mesh after the flight of the elastic body is complete, by applying, to a predetermined rolling trajectory model, the elastic body's rolling start position and rolling start speed, and external force acting on the elastic body on the K-th plane mesh as rolling trajectory calculation factors.

Description

Elastomer trajectory simulation method and apparatus, computer program

The present invention relates to a trajectory simulation method and apparatus for an elastic body, and a computer program, and more particularly, to a trajectory simulation method and apparatus for an elastic body, which simulates a flight trajectory and a rolling trajectory formed by inertia applied to an elastic body, and a computer program. it's about

Golf is a game of hitting a golf ball from the tee box on the course and finally putting it into the hole cup on the green. Golf players study the topography of the course in order to put the golf ball into a given hole with the minimum number of strokes, and whenever the golf ball is hit, they shoot while imagining the trajectory of the golf ball flying and rolling according to the speed and direction of the golf ball in their head. do. Once the public imagines the trajectory depending on the experience of each individual, the actual movement trajectory and the final landing position of the golf ball often have a significant difference from the trajectory and position predicted by the golfer.

As equipment for simulating and providing the trajectory of a conventional golf ball, simulation equipment applied to indoor screen golf is widely applied. It works by displaying the trajectory of the golf ball. However, the golf simulation equipment as described above is expensive equipment that is commercially available and requires a large-scale facility, so there is a limit that an individual cannot use it in an actual field.

Accordingly, there is a need for an efficient method and system in which an individual can easily grasp the trajectory of a golf ball on the field using a portable device such as a mobile phone possessed by the individual.

An object according to an aspect of the present invention is to simulate the trajectory of an elastic body formed when a striking force is applied to an elastic body such as a golf ball by a striking device such as a golf club, expensive equipment and large-scale facilities, etc. An object of the present invention is to provide a method and apparatus for simulating the trajectory of an elastic body, and a computer program, which can simulate the trajectory of an elastic body more quickly, accurately and at low cost by eliminating dependence.

The present invention is a trajectory simulation method of an elastic body, which is performed by a computing device and simulates a movement trajectory of an elastic body, comprising the steps of obtaining an initial position of the elastic body and an initial velocity of the elastic body formed by an inertia force applied to the elastic body ; The flight trajectory from when the elastic body starts flying by the applied inertia force to landing in the M-th plane mesh included in the mesh model is calculated in advance as the initial position and initial velocity of the elastic body as a flight trajectory calculation factor. As a step of determining by applying the defined flight trajectory model, the mesh model is a field in which the movement space of the elastic body is emulated with a first to N-th plane mesh (N is a natural number of 2 or more, M is N the following natural numbers); and a rolling trajectory in which the elastic body rotates on the K-th plane mesh after the flight of the elastic body is finished, and as a rolling trajectory calculation factor, the rolling start position of the elastic body in the K-th flat mesh, and rolling start speed and determining by applying an external force acting on the elastic body to a predefined cloud trajectory model (K is a natural number greater than or equal to M and less than or equal to N).

In the present invention, as the first to N-th plane meshes are sequentially arranged with a predefined inclination, respectively, the mesh model is configured such that the field is emulated in a three-dimensional space defined by a three-axis coordinate system, and the elastic body The flight trajectory and cloud trajectory of is determined as a three-dimensional trajectory in the mesh model.

In the present invention, in the step of determining the flight trajectory, from the mathematical model defining the M-th plane mesh and the flight trajectory model, the flight time until the elastic body starts to fly and then lands in the M-th plane mesh to determine the landing position of the elastic body in the M-th plane mesh from the determined flight time, the initial position of the elastic body, a flight segment determined by the flight trajectory model during the determined flight time, and the elastic body It is characterized in that the path connecting the landing positions of the flight trajectory is determined.

Calculating the repulsion speed of the elastic body from the landing speed of the elastic body with respect to the M-th flat mesh and a predefined coefficient of restitution with respect to the M-th flat mesh; and comparing the calculated repulsion speed of the elastic body with a preset threshold value; further comprising, wherein the determining of the rolling trajectory is performed when the repulsion speed of the elastic body is less than the threshold value.

In the present invention, when the rebound speed of the elastic body is equal to or greater than the threshold value, the landing position and the repulsion speed of the elastic body are applied as the flight trajectory calculation factors, and the step of determining the flight trajectory is repeatedly performed.

In the present invention, the external force acting on the elastic body as the rolling trajectory calculation factor includes gravity and frictional force acting on the elastic body on the K-th plane mesh, and in the step of determining the rolling trajectory, the K-th plane mesh It is characterized in that the cloud trajectory is determined using a flow line vector defined by a normal vector and a slope of

In the present invention, in the step of determining the cloud trajectory, the elastic body counts the rolling time that has elapsed after starting the cloud, and reflects the cloud section determined by the cloud trajectory model during the counted cloud time. It is characterized in that the cloud trajectory is determined.

In the step of determining the cloud trajectory in the present invention,

When the elastic body moves from the Kth planar mesh to the K+1th planar mesh, a continuous rolling trajectory determining operation is performed, wherein the continuous rolling trajectory determining operation comprises:

From the mathematical model defining the boundary line of the K-th flat mesh and the K+1-th flat mesh and the rolling trajectory model, the time required from the rolling start position of the elastic body in the K-th flat mesh to reaching the boundary line to determine the rolling start position and the rolling start speed of the elastic body in the K+1th flat mesh using the determined required time, and the normal vector of the K+1th flat mesh, and the determined Kth Using the rolling start position and rolling start speed of the elastic body in the +1 flat mesh and the gravity and friction forces acting on the elastic body on the K+1 flat mesh as the rolling trajectory calculation factors, It is characterized in that the rolling trajectory of the elastic body is determined.

In the present invention, the continuous rolling trajectory determining operation is characterized in that it is repeatedly performed until the elastic body stops.

In the present invention, after the step of determining the rolling trajectory, when an environmental external force emulated by an environmental factor of the field is applied to the elastic body in a state in which the elastic body is stopped, the frictional force of the flat mesh in which the stationary elastic body is located and the Calculating the displacement of the elastic body from the environmental external force, and reflecting the calculated displacement of the elastic body to the rolling trajectory; characterized in that it further comprises.

The present invention further comprises; displaying the determined flight trajectory and cloud trajectory.

In the present invention, the elastic body is a golf ball, the field is a golf course, the mesh model is a model emulated by the golf course, and the flight trajectory and the rolling trajectory are the movement trajectories of the golf ball according to the swing of the elastic body. , The computing device is implemented as a portable device carried by the user, characterized in that it displays the movement trajectory of the golf ball to the user.

An elastic body trajectory simulation apparatus according to an aspect of the present invention includes a processor; and a memory that is executed through the processor and stores at least one command for simulating a movement trajectory of the elastic body, wherein the at least one command executed through the processor includes an initial position of the elastic body, and the elastic body A command to obtain the initial velocity of the elastic body formed by the inertia applied to Trajectory) as a command to determine the initial position and initial velocity of the elastic body as a flight trajectory calculation factor by applying a pre-defined flight trajectory model, wherein the mesh model includes the first to second fields as the movement space of the elastic body. A command (N is a natural number greater than or equal to 2, M is a natural number less than or equal to N), which is emulated with an N plane mesh, and a rolling trajectory in which the elastic body rotates on the K-th plane mesh after the flight of the elastic body is finished, Command to determine the rolling start position, rolling start speed, and external force acting on the elastic body in the K-th plane mesh as a trajectory calculation factor by applying an external force acting on the elastic body to a predefined rolling trajectory model (K is M or more and N or less) natural number).

A computer program according to an aspect of the present invention is combined with hardware, comprising: obtaining an initial position of the elastic body, and an initial velocity of the elastic body formed by the inertia force applied to the elastic body; The flight trajectory from when the elastic body starts flying by the applied inertia force to landing in the M-th plane mesh included in the mesh model is calculated in advance as the initial position and initial velocity of the elastic body as a flight trajectory calculation factor. As a step of determining by applying the defined flight trajectory model, the mesh model is a field in which the movement space of the elastic body is emulated with a first to N-th plane mesh (N is a natural number of 2 or more, M is N the following natural numbers); and the rolling trajectory in which the elastic body rotates on the K-th planar mesh after the flight of the elastic body is finished, as a rolling trajectory calculation factor, the rolling start position of the elastic body in the K-th flat mesh, the rolling start speed and the elastic body. It is characterized in that it is stored in a computer-readable recording medium to execute; determining an external force acting by applying it to a predefined cloud trajectory model (K is a natural number greater than or equal to M and less than or equal to N).

According to one aspect of the present invention, the present invention determines a flight trajectory formed by an external force applied to the elastic body by applying the initial position and initial velocity of the elastic body to a flight trajectory model defined by a predetermined mathematical model, and after landing of the elastic body By simulating the trajectory of an elastic body by applying a method of determining the rolling trajectory of an elastic body by applying the cloud starting position and rolling speed to the cloud trajectory model defined by a predetermined mathematical model, it is faster and more accurate without expensive equipment and large-scale facilities The trajectory of the elastic body can be simulated at a low cost, and the trajectory simulation method of the elastic body is mounted on a portable device such as a smartphone possessed by the golfer, so that before hitting the golf ball from the golfer's point of view, It is also advantageous in that the predicted trajectory can be provided.

1 is a block diagram showing a trajectory simulation apparatus of an elastic body according to an embodiment of the present invention.

2 is a flowchart illustrating a trajectory simulation method of an elastic body according to an embodiment of the present invention.

3 and 4 are exemplary views showing an example of the trajectory of the elastic body moving in the 3D mesh model in the trajectory simulation method of the elastic body according to an embodiment of the present invention.

5 is an exemplary diagram illustrating a state in which a trajectory of an elastic body is displayed on a portable device in a trajectory simulation method of an elastic body according to an embodiment of the present invention.

Hereinafter, an embodiment of a method and apparatus for simulating the trajectory of an elastic body and a computer program according to the present invention will be described with reference to the accompanying drawings. In this process, the thickness of the lines or the size of the components shown in the drawings may be exaggerated for clarity and convenience of explanation. In addition, the terms to be described later are terms defined in consideration of functions in the present invention, which may vary according to intentions or customs of users and operators. Therefore, definitions of these terms should be made based on the content throughout this specification.

1 is a block diagram showing a trajectory simulation apparatus of an elastic body according to an embodiment of the present invention, FIG. 2 is a flowchart illustrating a trajectory simulation method of an elastic body according to an embodiment of the present invention, FIGS. 3 and FIG. 4 is an exemplary diagram illustrating an example of a trajectory of an elastic body moving within a three-dimensional mesh model in a trajectory simulation method of an elastic body according to an embodiment of the present invention, and FIG. 5 is a trajectory simulation method of an elastic body according to an embodiment of the present invention. It is an exemplary view showing a state in which the trajectory of the elastic body is displayed on the portable device.

Referring to Figure 1, the trajectory simulation apparatus 10 of the elastic body according to an embodiment of the present invention (hereinafter, the present device) is a processor 100, a memory 200, a positioning unit 300, a communication unit 400 and It may include a display unit 500 . The apparatus 10 including each of the above components 100 to 500 may be implemented as a computing device possessed by a user, and the computing device may be implemented as a portable device such as a smartphone or tablet.

The processor 100 is a subject that simulates the trajectory of the elastic body in this embodiment, and may be implemented as a central processing unit (CPU) or a system on chip (SoC), and operates an operating system or application to drive the processor ( 100) can control a plurality of hardware or software components connected to each other, and perform various data processing and operations. The processor 100 may be configured to execute at least one command stored in the memory 200 , and store the execution result data in the memory 200 .

The positioning unit 300 may correspond to a Global Positioning System (GPS) positioning module that acquires the current location of the device 10 and transmits it to the processor 100 , and the communication unit 400 is the wireless device of the device 10 . It may function as a communication module (eg, an LTE or WiFi communication module) to support wireless communication between the device 10 and an external system. The display unit 500 may be implemented as a display panel of the device 10, for example, a touch screen panel, and the trajectory of the elastic body simulated by the processor 100 is displayed through the display unit 500 and provided to the user. can

The memory 200 may store at least one command executed by a process for simulating the movement trajectory of the elastic body. The memory 200 for storing a command for simulating the movement trajectory of the elastic body may be implemented as a volatile storage medium and/or a non-volatile storage medium, for example, a read-only memory (ROM) and/or random It may be implemented as a random access memory (RAM).

At least one command stored in the memory 200 and executed by the processor 100 may include the following commands.

- A command to obtain the initial position of the elastic body and the initial velocity of the elastic body formed by the inertia force applied to the elastic body means that a predetermined force is applied to the elastic body).

- A flight trajectory from when the elastic body starts flying due to the applied inertia force to landing in the M-th plane mesh included in the mesh model, and the initial position and initial velocity of the elastic body are predefined as flight trajectory calculation factors A command to be determined by applying it to the flight trajectory model.

- A command to calculate the rebound speed of the elastic body from the landing speed of the elastic body with respect to the M-th planar mesh and a predefined coefficient of restitution for the M-th planar mesh.

- A command to compare the calculated rebound velocity of the elastic body with a preset threshold value.

- When the repulsion speed of the elastic body is greater than or equal to the threshold, the landing position and repulsion speed of the elastic body are applied as flight trajectory calculation factors so that the process of determining the flight trajectory is repeatedly performed.

- When the repulsion velocity of the elastic body is less than the threshold value, the rolling trajectory in which the elastic body rotates on the K-th plane mesh is used as a rolling trajectory calculation factor, and the rolling start position of the elastic body in the K-th plane mesh, the rolling start speed and A command to determine the external force acting on the elastic body by applying it to a predefined cloud trajectory model.

- When an environmental external force emulated by an environmental factor in the field is applied to the elastic body in a state where the elastic body is stationary, the displacement of the elastic body is calculated from the frictional force and environmental external force of the flat mesh in which the stationary elastic body is located, and the calculated displacement of the elastic body command to be reflected in the cloud trajectory.

- A command to display the flight trajectory and the cloud trajectory determined through the above process.

Prior to a detailed description of the process of simulating the trajectory of the elastic body, first, a mesh model on which the present embodiment is based will be described. In this embodiment, it will be described that the elastic body corresponds to a golf ball, a field to a golf course, and a flight trajectory and a rolling trajectory correspond to the movement trajectory of the golf ball according to the user's swing.

As shown in FIG. 3 , the mesh model is defined as a model in which a field (ie, a golf course (golf course terrain)) that is a movement space of an elastic body is emulated with a first to N-th plane mesh (N is a natural number of 2 or more, FIG. 3 shows an example in which the mesh model is composed of first to fourth planar meshes MS1 - MS4 as N is assumed to be 4).

Each planar mesh consists of a triangular planar structure, and metadata for each planar mesh (physical property data such as the inclination and restitution coefficient of the planar mesh, and vertex coordinate data of each planar mesh (P _m ....P _k) ), mathematical attribute data such as normal vector (n) and flow vector (p), and regulation data such as fairway, green, hazard, and OB (Out of Bound) according to the corresponding golf course rule) are added to the mesh model. may be defined. Accordingly, the plurality of planar meshes (that is, the first to Nth planar meshes) are sequentially arranged with a gradient defined according to the above-described metadata, and accordingly, the mesh model has a field with a three-axis coordinate system (x-axis, y-axis). axis, z-axis) is configured to be emulated in a three-dimensional space defined by 3 shows that the elastic body is struck at the initial position B _i and lands on the B _k point of the first planar mesh MS1, repels by the repulsive force at the B _k point and B _k+1 point to perform a subsequent flight, and the second The cloud movement starts from the point B _k+2 of the planar mesh (MS2), and the passing point B _k+3 on the boundary line 'P _m+1 - P _m+2 ' and the boundary line 'P _m+2 - P _m+4 ' An example of stopping at B _s after entering the fourth planar mesh MS4 through the passing point B _k+4 is shown.

The mesh model configured as described above is a basis for mathematically defining a flight trajectory model and a cloud trajectory model used to calculate a flight trajectory and a cloud trajectory of an elastic body, as will be described later. The process described below assumes that the processor 100 receives the mesh model defined as above from the external system through the communication unit 400 and stores it in the memory 200 .

Based on the above description, a process of simulating the trajectory of the elastic body will be described in detail below with reference to FIGS. 2 to 5 .

Referring to FIG. 2 , first, the processor 100 obtains an initial position of the elastic body and an initial velocity of the elastic body formed by the inertia applied to the elastic body from the memory 200 ( S100 ).

The initial position of the elastic body means the initial position of the elastic body placed in the field before an inertial force is applied to the elastic body, and is stored in advance in the memory 200 as three-dimensional position coordinates based on the three-axis coordinate system of the aforementioned mesh model. can The initial velocity of the elastic body refers to the initial velocity of the elastic body formed immediately after an inertia force is applied to the elastic body, and the initial velocity of the elastic body has a three-axis component based on a three-axis coordinate system. The memory 200 may store in advance a range of an initial speed that can be formed in the elastic body, and when a specific value within the range of the initial speed is selected by the user, the processor 100 sets the selected specific value to the initial speed of the elastic body. It can be obtained as speed.

When the initial position and initial velocity of the elastic body are obtained through step S100, the processor 100 calculates the flight trajectory from when the elastic body starts flying by inertia to landing in the M-th plane mesh included in the mesh model, the flight trajectory It is determined by applying the initial position and initial velocity of the elastic body as calculation factors to a predefined flight trajectory model (S200). A flat mesh on which the elastic body first lands is denoted as an M-th planar mesh (M is a natural number less than or equal to N), and FIGS. 3 and 4 show an example in which the M-th planar mesh is the first planar mesh MS1.

External forces such as gravity, air friction force, and wind force and internal force due to the self-spin of the elastic body act on the elastic body in flight. In this embodiment, only gravity is considered as a force acting on the elastic body in flight to reduce the computational load. Accordingly, the acceleration acting on the elastic body in flight is expressed according to Equation 1 below.

[ Equation 1 ]

In Equation 1, a _x , a _y , and a _z are accelerations in the x-axis, y-axis, and z-axis directions, respectively, and g is the gravitational acceleration.

The flight trajectory model applied in step S200 is defined as Equation 2 below by the constant acceleration motion equation.

[ Equation 2 ]

In Equation 2, v(t) is the velocity of the elastic body after t time from the start of flight, V _i is the initial velocity of the elastic body, a is the acceleration acting on the elastic body, B(t) is the position of the elastic body after t time, B _i is the initial position of the elastic body. v(t), V _i , a, B(t), B _i have three-axis components according to the three-axis coordinate system.

On the other hand, the normal vector of the M-th plane mesh on which the elastic body first lands is n(n _x , n _y , n _z ) = n(cosα, cosβ, cosθ) (here, α, β, θ are the normal vectors on the x-axis, respectively. , y-axis, angle formed with the z-axis, n is vector notation), and when the coordinates of one vertex of the M-th plane mesh are defined as (X _m , Y _m , Z _m ), defining the M-th plane mesh The equation of the plane as a mathematical model is expressed by Equation 3 below.

[ Equation 3 ]

In Equation 3, the variables x, y, and z are coordinates of points on the M-th plane mesh.

Accordingly, the processor 100, from the mathematical model (Equation 3) and the flight trajectory model (Equation 2) defining the M-th plane mesh, the elastic body from the start of flight to the flight until landing in the M-th plane mesh The time and landing location may be determined (S210).

Specifically, if the initial position of the elastic body B _i = (x _i , y _i , z _i ), the flight time T _L , and the landing position of the elastic body B _L = (x _L , y _L , z _L ), Equation 1 And 2, the landing position of the elastic body is expressed as in Equation 4 below.

[ Equation 4 ]

In Equation 4, V _ix , V _iy , and V _iz are the x-axis, y-axis, and z-axis components of the initial velocity of the elastic body.

Since the landing position of the elastic body is on the M-th plane mesh according to Equation 3, Equation 5 below is derived.

[ Equation 5 ]

When

Equations

4 and 5 are combined, the flight time T _L of the elastic body is derived as shown in Equation 6 below.

[ Equation 6 ]

As the flight time T _L is determined, the landing speed and landing position of the elastic body according to Equation 4 may also be determined, and the landing speed V _L and the landing position B _L are derived as shown in Equation 7 below.

[ Equation 7 ]

Through the above process, the process may determine the path connecting the initial position of the elastic body, the flight section determined by the flight trajectory model during flight time, and the landing position of the elastic body as the flight trajectory (S220).

After step S200, the processor 100 calculates the repulsion speed of the elastic body from the landing speed of the elastic body with respect to the M-th flat mesh and the coefficient of restitution predefined for the M-th flat mesh (S300). When the coefficient of restitution of the M-th planar mesh is defined as e (eg, 0.6), the following Equation 8 is derived according to the velocity relation before and after the collision.

[ Equation 8 ]

In Equation 8, R(T _L ) is the repulsion rate.

Next, the processor 100 compares the repulsion speed of the elastic body calculated by Equation 8 with a preset threshold value (R _c ) (S400). The threshold value is a reference value for determining whether the elastic body will fly again due to the repulsion after landing, or roll, and may be stored in advance in the memory 200 as a specific value based on the designer's intention and experimental results. Yes (eg 1.0 mm/s).

If it is determined in step S400 that the rebound speed of the elastic body is equal to or greater than the threshold value, the processor 100 applies the landing position and the rebound speed of the elastic body as a flight trajectory calculation factor, and then repeats step S200 of determining the flight trajectory. That is, in the first performed step S200, the initial position and initial speed of the elastic body are used as flight trajectory calculation factors, and when the elastic body starts flying again because the repulsion speed after landing of the elastic body is equal to or greater than the threshold value, the processor 100 performs flight After updating the flight trajectory calculation factor for determining the trajectory to the landing position and repulsion velocity of the elastic body derived according to Equation 7, step S200 of determining the flight trajectory is repeatedly performed. The above process is repeated until the rebound velocity of the elastic body becomes less than the threshold value.

When it is determined that the repulsion speed of the elastic body is less than the threshold value in step S400 (including the case where it is determined that the rebound speed of the elastic body is less than the threshold value after step S200 is repeatedly performed), the processor 100 determines that the elastic body is a K-th plane The rolling trajectory that rotates on the mesh is determined by applying the rolling start position, rolling start speed, and external force acting on the elastic body in the K-th plane mesh as a rolling trajectory calculation factor to a predefined rolling trajectory model (S500) . K is a natural number greater than or equal to M and less than or equal to N, that is, when the elastic body landing on the M-th flat mesh starts rolling, the K-th flat mesh is the same as the M-th flat mesh, and the elastic body repeats the flight several times to form an adjacent flat mesh. When moved, the Kth planar mesh may correspond to any one of the K+1th to Nth planar meshes. Hereinafter, the step S500 will be described assuming that the K-th planar mesh and the M-th planar mesh are the same.

In step S500 , the processor 100 determines the cloud trajectory using the flow line vector defined by the normal vector and the slope of the K-th plane mesh as a mediator. As is well known, a flow line is a line on which an object on a plane moves by gravity in the vertical direction and a plane inclination. _x , p _y , p _z ) = p(n _x n _z /sinθ, n _y n _z /sinθ, -sinθ).

The external force acting on the elastic body as the rolling trajectory calculation factor may include gravity and frictional force acting on the elastic body on the K-th plane mesh. Since the elastic body rolls on the K-th plane mesh having a predetermined inclination, the gravitational acceleration acting on the elastic body must be corrected by the flow line vector described above. Considering the frictional deceleration acting on , the acceleration acting on the elastic body in rolling motion is expressed according to Equation 9 below.

[ Equation 9 ]

In Equation 9, g _p is the corrected gravitational acceleration (g·sinθ), μ is the frictional deceleration of the K-th plane mesh (m/s ² ), and u is the unit vector of the rolling start speed.

The cloud trajectory model applied in step S500 is defined as Equation 10 below by the constant acceleration motion equation.

[ Equation 10 ]

In Equation 10, v(t) is the velocity of the elastic body after t time from the start of rolling, V _i is the rolling start speed, a is the acceleration acting on the elastic body, B(t) is the position of the elastic body after t time, B _i is the cloud start position. v(t), V _i , a, B(t), and B _i have triaxial components according to the triaxial coordinate system (for convenience, they are expressed with the same notation as Equations 1 to 7 for calculating the flight trajectory of the elastic body, Each factor of Equations 1 to 7 according to step S200 and each factor of Equation 9 to 17 according to step S500 and S600 are clearly distinguished).

In step S500, the processor 100 counts the rolling time that has elapsed since the elastic body starts rolling (S510), and during the counted cloud time, the cloud section determined by the cloud trajectory model (that is, B in Equation 10) t))), the cloud trajectory is determined (S520, S530).

On the other hand, there may occur a case in which the elastic body moves from the Kth flat mesh to the K+1th planar mesh through rolling movement, and in this case, the processor 100 may perform a continuous rolling trajectory determination operation. The continuous cloud trajectory determination operation is defined as the following process.

- From the mathematical model and the cloud trajectory model defining the boundary of the K-th flat mesh and the K+1 mesh, the elapsed time from the rolling start position of the elastic body in the K-th flat mesh to the boundary line (expressed as transit time) to decide).

- The process of determining the rolling start position and the rolling start speed of the elastic body in the K+1th planar mesh using the transit time and the normal vector of the K+1th planar mesh.

- Using the determined rolling starting position and rolling speed of the elastic body in the K+1th planar mesh and the gravity and frictional forces acting on the elastic body on the K+1th planar mesh as rolling trajectory calculation factors, The process of determining cloud trajectories.

Specifically for each process, the coordinates of both ends of the boundary line of the Kth plane mesh and the K+1th plane mesh are defined as P ₂ (X2,Y2,Z2) and P ₃ (X3,Y3,Z3), respectively. When, the boundary line is defined by the following Equation 11 (see FIG. 4 ).

[ Equation 11 ]

In Equation 11, x _c , y _c are the x-coordinates and y-coordinates of a point at which the elastic body passes through the boundary line (hereinafter, the passing point).

If the transit time from the rolling start position of the elastic body until reaching the passing point is T _c , the passing point is expressed by the following Equation 12 by Equation 10.

[ Equation 12 ]

When Equations 11 and 12 are combined, the transit time T _c from the rolling start position of the elastic body to the passing point is derived as shown in Equation 13 below.

[ Equation 13 ]

When the transit time T _c until reaching the passing point is determined through the above process, the processor 100 determines the passing time in the K+1th planar mesh using the determined transit time and the normal vector of the K+1th planar mesh. Determine the rolling start position and rolling start speed of the elastic body. Since the cloud start position corresponds to the passing point, the processor 100 determines the rolling start speed, but in this case, when moving from the Kth plane mesh to the K+1th plane mesh, the inclination is changed, and accordingly, each plane mesh Since the normal vector of is also changed, the processor 100 determines the rolling start speed of the elastic body using the normal vector of the K+1th planar mesh (that is, of the elastic body at T _c calculated based on the Kth planar mesh). The rolling start speed of the elastic body in the K+1th planar mesh is determined by correcting the speed using the normal vector of the K+1th planar mesh).

When the velocity of the elastic body at T _c calculated based on the K-th plane mesh is V _i (V _cx , V _cy , V _cz ), it can be derived by applying T _c to v(t) in Equation 10. Yes), the rolling start speed in the K+1th planar mesh can be expressed as Equation 14 below.

[ Equation 14 ]

In Equation 14, n _x ', n _y ', and n _z ' are normal vector components of the K+1th plane mesh.

The processor 100 uses the rolling start position and the rolling start speed of the elastic body in the K+1th planar mesh determined as described above and the gravity and friction forces acting on the elastic body on the K+1th planar mesh as rolling trajectory calculation factors. +1 Determine the rolling trajectory of the elastic body on the planar mesh. The continuous rolling trajectory determination operation according to Equations 11 to 14 is repeatedly performed until the elastic body stops.

Next, when explaining the process of calculating the stop position of the elastic body (assuming that the elastic body stops on the K-th plane mesh), the time required for the elastic body to stop after starting rolling (expressed as a stop time) is T _s , the following Equation 15 is derived according to Equations 9 and 10.

[ Equation 15 ]

When Equation 15 is divided and organized by each axis component, the following Equation 16 is obtained.

[ Equation 16 ]

The processor 100 determines a maximum value among T _sx , T _sy , and T _sz determined through Equation 16 as a final stop time T _s , and applies the determined T _s to B(t) of Equation 10 to final Determine the static stopping position B _s .

On the other hand, it is normal that the elastic body does not move any more when it is stopped. However, when the force applied to the elastic body by the wind or the movement of the ground becomes greater than the static friction force, the elastic body can move. Accordingly, the processor 100 after step S500, when an external external force (wind force or movement of the ground) emulated by an environmental factor of the field in a state where the elastic body is stopped is applied to the elastic body, the stationary elastic body is located in the flat mesh It is also possible to calculate the displacement of the elastic body from the friction force and environmental external force, and reflect the calculated displacement of the elastic body to the rolling trajectory (S600).

When the static friction force defined according to the static friction coefficient is F _L , and the external force defined according to the acceleration according to Equation 9 is F, the velocity and position of the elastic body formed by the environmental external force can be expressed by Equation 17 below. (The mass of the elastic body is constant, so it is assumed to have a value of 1).

[ Equation 17 ]

The process of reflecting the displacement according to the environmental external force to the cloud trajectory may be repeatedly performed until the elastic body finally stops (eg, when the stationary state of the elastic body is maintained for a predetermined period of time).

When the flight trajectory and the rolling trajectory of the elastic body are finally determined through steps S100 to S600 , the processor 100 displays the flight trajectory and the rolling trajectory of the elastic body through the display unit 500 ( S700 ). In this case, as shown in FIG. 5 , the processor 100 performs the elastic body on a geometric model (eg, a contour model) in which the topography of the golf course is modeled, not a mesh model, so that the user can more intuitively check the trajectory of the elastic body. can display the trajectory of

On the other hand, the trajectory simulation method of the elastic body according to the present embodiment may be written as a computer program for executing steps S100 to S700 described above in combination with hardware, and is stored in a computer-readable recording medium to operate the computer program. can be implemented in a general-purpose digital computer. The computer-readable recording medium includes magnetic media such as ROM, RAM, hard disk, floppy disk, and magnetic tape, optical media such as CD-ROM and DVD, and floppy disk. A hardware device specially configured to store and execute program instructions, such as a magneto-optical media, such as a flash memory, may correspond.

As such, in this embodiment, the initial position and initial velocity of the elastic body are applied to the flight trajectory model defined by a predetermined mathematical model to determine the flight trajectory formed by the external force applied to the elastic body, and the rolling start position and cloud after landing of the elastic body By applying the starting velocity to the rolling trajectory model defined by a predetermined mathematical model to determine the rolling trajectory of the elastic body, the trajectory of the elastic body is simulated. The trajectory can be simulated, and by mounting the trajectory simulation method of the elastic body in a portable device such as a smartphone possessed by the golfer, the golfer can be provided with the expected trajectory according to the hitting in a simpler way before hitting the golf ball. There are also advantages to being

Implementations described herein may be implemented in, for example, a method or process, an apparatus, a software program, a data stream, or a signal. Although discussed only in the context of a single form of implementation (eg, discussed only as a method), implementations of the discussed features may also be implemented in other forms (eg, as an apparatus or program). The apparatus may be implemented in suitable hardware, software and firmware, and the like. A method may be implemented in an apparatus such as, for example, a processor, which generally refers to a computer, a microprocessor, a processing device, including an integrated circuit or programmable logic device, or the like. Processors also include communication devices such as computers, cell phones, portable/personal digital assistants ("PDA") and other devices that facilitate communication of information between end-users.

Although the present invention has been described with reference to the embodiment shown in the drawings, this is merely exemplary, and it is understood that various modifications and equivalent other embodiments are possible by those of ordinary skill in the art. will understand Accordingly, the true technical protection scope of the present invention should be defined by the following claims.

Claims

A trajectory simulation method of an elastic body, which is performed by a computing device and simulates a movement trajectory of the elastic body, the method comprising:

obtaining an initial position of the elastic body and an initial velocity of the elastic body formed by inertia applied to the elastic body;

The flight trajectory from when the elastic body starts flying by the applied inertia force to landing in the M-th plane mesh included in the mesh model is calculated in advance as the initial position and initial velocity of the elastic body as a flight trajectory calculation factor. As a step of determining by applying the defined flight trajectory model, the mesh model is a field in which the movement space of the elastic body is emulated with a first to N-th plane mesh (N is a natural number of 2 or more, M is N the following natural numbers); and

A rolling trajectory in which the elastic body rotates on the K-th plane mesh after the flight of the elastic body is finished, as a rolling trajectory calculation factor, the rolling start position of the elastic body in the K-th plane mesh, rolling start speed, and determining an external force acting on the elastic body by applying a predefined cloud trajectory model (K is a natural number greater than or equal to M and less than or equal to N);

A trajectory simulation method of the elastic body, characterized in that it comprises a.
According to claim 1,

As the first to N-th plane meshes are sequentially arranged with a predefined inclination, respectively, the mesh model is configured to emulate a three-dimensional space in which the field is defined by a three-axis coordinate system,

The trajectory simulation method of the elastic body, characterized in that the flight trajectory and the rolling trajectory of the elastic body are determined as three-dimensional trajectories in the mesh model.
According to claim 1,

In the step of determining the flight trajectory,

From the mathematical model defining the M-th plane mesh and the flight trajectory model, determining the flight time from when the elastic body starts to fly to landing in the M-th plane mesh,

Determine the landing position of the elastic body in the M-th plane mesh from the determined flight time,

A trajectory simulation method of an elastic body, characterized in that the flight trajectory determines a path connecting the initial position of the elastic body, the flight section determined by the flight trajectory model during the determined flight time, and the landing position of the elastic body.
4. The method of claim 3,

calculating the repulsion speed of the elastic body from the landing speed of the elastic body with respect to the M-th flat mesh and a predefined coefficient of restitution with respect to the M-th flat mesh; and

Comparing the calculated repulsion speed of the elastic body with a preset threshold value; further comprising,

The step of determining the rolling trajectory is a movement simulation method of the elastic body, characterized in that performed when the repulsion speed of the elastic body is less than the threshold value.
5. The method of claim 4,

When the repulsion speed of the elastic body is equal to or greater than the threshold value, the landing position and the repulsion speed of the elastic body are applied as the flight trajectory calculation factors and the step of determining the flight trajectory is repeatedly performed.
According to claim 1,

The external force acting on the elastic body as the rolling trajectory calculation factor includes gravity and frictional force acting on the elastic body on the K-th plane mesh,

In the determining of the rolling trajectory, the trajectory simulation method of an elastic body, characterized in that the rolling trajectory is determined using a flow line vector defined by a normal vector and a slope of the K-th plane mesh as a mediator.
7. The method of claim 6,

In the step of determining the cloud trajectory,

The trajectory of the elastic body, characterized in that the elapsed rolling time is counted after the elastic body starts rolling, and the rolling trajectory is determined in a way that reflects the cloud section determined by the cloud trajectory model during the counted rolling time simulation method.
8. The method of claim 7,

In the step of determining the cloud trajectory,

When the elastic body moves from the Kth planar mesh to the K+1th planar mesh, a continuous rolling trajectory determining operation is performed, wherein the continuous rolling trajectory determining operation comprises:

From the mathematical model defining the boundary line of the K-th flat mesh and the K+1-th flat mesh and the rolling trajectory model, the time required from the rolling start position of the elastic body in the K-th flat mesh to reaching the boundary line to decide,

Determine the rolling start position and the rolling start speed of the elastic body in the K+1th flat mesh using the determined required time and the normal vector of the K+1th flat mesh,

Using the determined rolling start position and rolling start speed of the elastic body in the K+1th flat mesh and the gravity and friction forces acting on the elastic body on the K+1th flat mesh as the rolling trajectory calculation factors, the K+1th A trajectory simulation method of an elastic body, characterized in that the rolling trajectory of the elastic body is determined on a planar mesh.
9. The method of claim 8,

The trajectory simulation method of an elastic body, characterized in that the operation of determining the continuous rolling trajectory is repeatedly performed until the elastic body stops.
10. The method of claim 9,

After determining the cloud trajectory,

When an environmental external force emulated by an environmental factor of the field is applied to the elastic body in a state in which the elastic body is stationary, the displacement of the elastic body is calculated from the frictional force of the flat mesh in which the stationary elastic body is located and the environmental external force; Reflecting the calculated displacement of the elastic body to the rolling trajectory; trajectory simulation method of the elastic body, characterized in that it further comprises.
According to claim 1,

Displaying the determined flight trajectory and the cloud trajectory; trajectory simulation method of the elastic body characterized in that it further comprises.
12. The method of claim 11,

The elastic body is a golf ball, the field is a golf course, the mesh model is a model emulated by the golf course, and the flight trajectory and the rolling trajectory are the movement trajectories of the golf ball according to the swing of the elastic body,

The computing device is implemented as a portable device possessed by a user, and the trajectory simulation method of an elastic body, characterized in that it displays the movement trajectory of the golf ball to the user.
processor; and

It is executed through the processor, and at least one instruction for simulating the movement trajectory of the elastic body is stored in a memory;

The at least one instruction executed through the processor includes:

a command to obtain an initial position of the elastic body and an initial velocity of the elastic body formed by the inertia force applied to the elastic body;

The flight trajectory from when the elastic body starts flying by the applied inertia force to landing in the M-th plane mesh included in the mesh model is calculated in advance as the initial position and initial velocity of the elastic body as a flight trajectory calculation factor. As a command to be determined by applying to the defined flight trajectory model, the mesh model is a command (N is a natural number of 2 or more, M is a natural number less than or equal to N), and

After the flight of the elastic body ends, the rolling trajectory in which the elastic body rotates on the K-th planar mesh is calculated as a rolling trajectory calculation factor, and the rolling start position of the elastic body in the K-th flat mesh, the rolling start speed, and the elastic body act on the elastic body. A trajectory simulation apparatus of an elastic body, characterized in that it includes a command (K is a natural number greater than or equal to M and less than or equal to N) for determining by applying an external force to a predefined cloud trajectory model.
combined with hardware,

obtaining an initial position of the elastic body and an initial velocity of the elastic body formed by inertia applied to the elastic body;

The flight trajectory from when the elastic body starts flying by the applied inertia force to landing in the M-th plane mesh included in the mesh model is calculated in advance as the initial position and initial velocity of the elastic body as a flight trajectory calculation factor. As a step of determining by applying the defined flight trajectory model, the mesh model is a field in which the movement space of the elastic body is emulated with a first to N-th plane mesh (N is a natural number of 2 or more, M is N the following natural numbers); and

After the flight of the elastic body ends, the rolling trajectory in which the elastic body rotates on the K-th planar mesh is calculated as a rolling trajectory calculation factor, and the rolling start position of the elastic body in the K-th flat mesh, the rolling start speed, and the elastic body act on the elastic body. determining by applying an external force to a predefined cloud trajectory model (K is a natural number greater than or equal to M and less than or equal to N);

A computer program stored in a computer-readable recording medium to execute the