Disclosure of Invention
In order to at least solve the problems in the prior art, the invention provides a three-dimensional modeling method, a three-dimensional modeling device and three-dimensional modeling equipment for an uneven roadway, so that three-dimensional modeling of the roadway is realized, and simulation of the real condition of an underground wind environment is realized.
The technical scheme provided by the invention is as follows:
in one aspect, a three-dimensional modeling method for uneven roadways comprises the following steps:
acquiring the type and section basic data of a target simulation tunnel and mining statistical data of a preset distance in the target simulation tunnel;
calculating the flatness of the target simulation roadway according to the mining statistical data, and generating fluctuating coordinate data conforming to normal distribution based on the flatness;
obtaining an uneven curve conforming to normal distribution based on preset mapping software and fluctuating coordinate data conforming to flatness;
establishing a tunnel section contour line based on the tunnel section basic data of the target simulation tunnel;
combining the uneven curve with the contour line of the section of the roadway, and acquiring an uneven closed plane based on a roadway connecting line;
and lofting is carried out along the profile direction of the roadway according to the uneven closed plane, and a solid model of the uneven roadway is obtained.
Optionally, the type of the target simulation roadway includes: the shape of the section of the roadway;
the section basic data comprises: the radius of the top circle of the target simulation roadway, the width of a bottom plate, the heights of waist lines at two sides and the overall height of the target simulation roadway; the section basic data is an initial section of the target simulation roadway;
the mining statistical data comprises: overbreak data and underbreak data.
Optionally, the calculating the flatness of the target simulation roadway includes:
and determining the flatness R according to the maximum values of the over-excavation amount and the under-excavation amount of each section of statistical object within the preset distance in the target simulation roadway.
Optionally, the generating of the undulation coordinate data conforming to the normal distribution includes:
determining the abscissa of the fluctuation coordinate according to the length L of the target simulation roadway and the distance p between the fluctuation of the roadway wall surface;
and constructing a normal distribution database B based on a preset standard deviation, and determining the ordinate of the fluctuation coordinate according to the overall respective database B.
Optionally, the determining the abscissa of the undulation coordinate according to the target simulation roadway length L and the distance p between the undulation of the roadway wall includes:
determining the number of points required for generating an uneven curve under the constraint of the simulated roadway length L and the roof fluctuation distance p: n ═ L/p (1);
determining and obtaining a functional relation of a distance p between the roadway wall surface undulations:
p=(p1+p2+p3+…+pn-1)/n (2);
wherein p isn-1Representing the distance between the (n-1) th point and the nth point;
determining the functional relation of the abscissa parameter Xi of the ith point for obtaining the uneven curve as follows:
Xi=Xi-1+p (3);
wherein, XiAnd a parameter formula for the abscissa of the ith point of the unevenness curve when the abscissa of the starting point is 0.
Optionally, the constructing a normal distribution database B based on the preset standard deviation, and determining the ordinate of the undulation coordinate according to the overall difference database B includes:
generating points on a [0, L ] interval by taking p as an interval distance, and storing data of n points into a row matrix A;
establishing a normal distribution database B with the total data amount of n, the expected value of 0 and the standard deviation of R/3;
establishing a cyclic operation, randomly and unreleased extracting data from the database B, and sequentially storing the data into the row matrix C;
and respectively taking the matrixes A and C as an X coordinate and a Y coordinate for generating uneven curve points to obtain roadway wall surface fluctuation data based on normal distribution.
Optionally, the preset standard deviation is a normal distribution standard deviation, and the selection range of the normal distribution standard deviation includes:
the standard deviation of normal distribution is R/3, so that 99.73% of fluctuation data are positioned between (-R, R), and the fluctuation of the target simulation roadway can reach the maximum value required by simulation; or the like, or, alternatively,
the standard deviation of normal distribution is R/2, so that 99.54% of fluctuation data are positioned between (-R, R), and the fluctuation of the target simulation roadway reaches the maximum value required by simulation within a first preset degree; or the like, or, alternatively,
and the standard deviation of the normal distribution is R, so that 62.26% of fluctuation data are positioned between (-R, R), the fluctuation of the target simulation roadway reaches the maximum value required by simulation within a second preset degree, at the moment, part of data are positioned outside a limited interval, and the formed fluctuation has certain randomness.
Optionally, the preset drawing software is CAD drawing software;
the method for obtaining the uneven curve conforming to normal distribution based on the preset mapping software and the fluctuating coordinate data conforming to the flatness comprises the following steps:
customizing a function F for generating an scr script file, and creating the file for data storage;
writing spline, and adding initial point coordinates (0, 0);
writing fluctuation data x (i), y (i), and changing lines when each group of data is recorded;
and after the input is finished, copying the content of the script file to a CAD command frame to generate the uneven curve which is in accordance with the normal distribution.
In another aspect, a three-dimensional modeling apparatus for uneven roadway includes: the device comprises an acquisition module, a generation module, an acquisition module, an establishment module, a plane acquisition module and a model acquisition module;
the acquisition module is used for acquiring the type and section basic data of a target simulation tunnel and mining statistical data of a preset distance in the target simulation tunnel;
the generating module is used for calculating the flatness of the target simulation roadway according to the mining statistical data and generating fluctuating coordinate data which accord with normal distribution based on the flatness;
the obtaining module is used for obtaining an uneven curve which accords with normal distribution based on preset drawing software and fluctuation coordinate data which accords with flatness;
the establishing module is used for establishing a roadway section contour line based on the roadway section basic data of the target simulation roadway;
the plane acquisition module is used for combining the uneven curve and the roadway section contour line and acquiring an uneven closed plane based on a roadway connecting line;
and the model acquisition module is used for lofting along the profile direction of the roadway according to the uneven closed plane to acquire the solid model of the uneven roadway.
In still another aspect, a three-dimensional modeling apparatus for uneven roadways includes: a processor, and a memory coupled to the processor;
the memory is used for storing a computer program, and the computer program is at least used for executing the three-dimensional modeling method of uneven roadway;
the processor is used for calling and executing the computer program in the memory.
The invention has the beneficial effects that:
according to the three-dimensional modeling method, the three-dimensional modeling device and the three-dimensional modeling equipment for the uneven roadway, the type and section basic data of the target simulation roadway and mining statistical data of the preset distance in the target simulation roadway are obtained; calculating the flatness of the target simulation roadway according to the mining statistical data, and generating fluctuating coordinate data which are in accordance with normal distribution based on the flatness; obtaining an uneven curve conforming to normal distribution based on preset mapping software and fluctuating coordinate data conforming to flatness; establishing a tunnel section contour line based on tunnel section basic data of the target simulation tunnel; combining the uneven curve with the contour line of the section of the roadway, and acquiring an uneven closed plane based on the connecting line of the roadway; and lofting is carried out along the profile direction of the roadway according to the uneven closed plane, and a solid model of the uneven roadway is obtained. The three-dimensional modeling of the roadway is realized, and therefore the real condition simulation of the underground wind environment is realized. The invention adopts normal distribution to generate an uneven curve of the wall surface of the roadway, can well simulate the uneven form of the wall surface of the roadway by combining the parameters of the section of the roadway, and can be used for measurement and calibration of sensors in the roadway and analysis of the underground wind environment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be described in detail below. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the examples given herein without any inventive step, are within the scope of the present invention.
In order to at least solve the technical problem provided by the invention, the embodiment of the invention provides a three-dimensional modeling method for an uneven roadway.
Fig. 1 is a schematic flow chart of a three-dimensional modeling method for an uneven roadway according to an embodiment of the present invention, and referring to fig. 1, the method according to the embodiment of the present invention may include the following steps:
and S11, acquiring the type and section basic data of the target simulation roadway and mining statistical data of a preset distance in the target simulation roadway.
In a specific implementation process, an engineering team can select a roadway needing three-dimensional modeling as a target simulation roadway according to actual requirements, so that the three-dimensional modeling method of the uneven roadway provided by the embodiment of the application is applied to three-dimensional modeling of the target simulation roadway, the problem of rough modeling of the wall surface of the roadway is solved to a certain extent, and simulation of the ventilation environment in the roadway and the measurement effect of the sensor is achieved.
In this embodiment, a three-dimensional modeling method of an uneven roadway provided in the embodiment of the present invention is described by taking a three-dimensional modeling of uneven top of a three-arch roadway as an example. It should be noted that the three-arch roadway in the present embodiment is only an example, and is not limited.
In some embodiments, optionally, the target simulates a type of lane, including: the shape of the section of the roadway; section basic data, including: the radius of the top circle of the target simulation roadway, the width of a bottom plate, the heights of waist lines at two sides and the overall height of the target simulation roadway; section basic data which is the initial section of the target simulation roadway; mining statistical data, including: overbreak data and underbreak data.
Fig. 2 is a schematic diagram of acquiring basic data of a roadway and defining flatness R according to an embodiment of the present invention, where (a) is basic data of a section to be acquired; (b) the flatness R of the roadway with the length L is defined.
For example, referring to fig. 2, the roadway basic data includes section basic data, which includes radii R1, R of a top circle of the target simulation roadway, a width w of the bottom plate, a height H of the two side waistlines, and a total height of the roadway (R1+ H), and the section data of the roadway is obtained as an initial section of the roadway model, as shown in fig. 2 (a).
When mining statistical data of a preset distance in a target simulation roadway is obtained, the mining statistical data can be obtained through a measurement statistical method, for example, the process of performing statistical measurement on the overexcavation and underexcavation conditions of the roadway in the preset distance can be as follows: a. determining the length L of a roadway to be measured; b. taking the wall surface of the smooth roadway as a standard, marking the over-excavation part as positive, marking the under-excavation part as negative, and marking the part meeting the standard as 0; c. and measuring and counting the length of each section, the peak point of the over-cut section and the under-cut section and the size of the peak point by taking the continuous over-cut section, the under-cut section and the leveling section as counting objects.
And S12, calculating the flatness of the target simulation roadway according to the mining statistical data, and generating fluctuation coordinate data which accord with normal distribution based on the flatness.
In some embodiments, optionally, calculating the flatness of the target simulation roadway includes: and determining the flatness R according to the maximum values of the over-excavation amount and the under-excavation amount of each section of statistical object within the preset distance in the target simulation roadway.
For example, in the embodiment of the present invention, the standard roadway roof may be used as the center, the maximum degree of the up-and-down fluctuation of the roof in the simulated length is used as the simulated flatness R, and the flatness R is a positive value, that is, the maximum value of the over-excavation amount and the under-excavation amount of each statistical object of the roadway in the distance L measured in the above embodiment is used as the flatness R.
In some embodiments, optionally, generating the normally distributed undulation coordinate data includes: determining the abscissa of the fluctuation coordinate according to the length L of the target simulation roadway and the distance p between the fluctuation of the roadway wall surface; and constructing a normal distribution database B based on a preset standard deviation, and determining the ordinate of the fluctuation coordinate according to the overall respective database B.
In some embodiments, optionally, determining the abscissa of the undulation coordinate according to the target simulation roadway length L and the distance p between the roadway wall undulations includes:
determining the number of points required for generating an uneven curve under the constraint of the simulated roadway length L and the roof fluctuation distance p: n ═ L/p (1);
determining and obtaining a functional relation of a distance p between the roadway wall surface undulations:
p=(p1+p2+p3+…+pn-1)/n (2);
wherein p isn-1Representing the distance between the (n-1) th point and the nth point;
determining the abscissa parameter X of the ith point for obtaining the uneven curveiThe functional relationship of (a) is as follows:
Xi=Xi-1+p (3);
wherein XiAnd a parameter formula showing the abscissa of the ith point of the uneven curve when the abscissa of the starting point is 0.
For example, referring to fig. 2(b), in the present embodiment, several groups of fluctuation coordinate data conforming to the normal distribution are generated, and the abscissa is determined by the three-dimensional roadway length L to be generated and the distance p between the roadway wall surface fluctuations, where p can be defined as the average value of the distances between the adjacent over-cut peak point, under-cut peak point and flat section middle point of the roadway within a certain distance L measured as described in the above embodiment.
In some embodiments, optionally, constructing a normal distribution database B based on a preset standard deviation, and determining the ordinate of the undulation coordinate according to the overall difference database B includes:
generating points on a [0, L ] interval by taking p as an interval distance, and storing data of n points into a row matrix A;
establishing a normal distribution database B with the total data amount of n, the expected value of 0 and the standard deviation of R/3;
establishing a cyclic operation, randomly and unreleased extracting data from the database B, and sequentially storing the data into the row matrix C;
and respectively taking the matrixes A and C as an X coordinate and a Y coordinate for generating uneven curve points to obtain roadway wall surface fluctuation data based on normal distribution.
For example, in this embodiment, the finally obtained normal distribution-based roadway wall surface fluctuation data may be obtained through programming calculation, and the specific process is as follows:
a. generating points on a [0, L ] interval by taking p as an interval distance, and storing data of n points into a row matrix A;
b. establishing a normal distribution database B with the total data amount of n, the expected value of 0 and the standard deviation of R/3;
c. establishing a cyclic operation, randomly and unreleased extracting data from the database B, and sequentially storing the data into the row matrix C;
d. and respectively taking the matrixes A and C as an X coordinate and a Y coordinate for generating uneven curve points to obtain roadway wall surface fluctuation data based on normal distribution.
In some embodiments, optionally, the predetermined standard deviation is a normal distribution standard deviation, and the selection range of the normal distribution standard deviation includes:
the standard deviation of normal distribution is R/3, so that 99.73% of fluctuation data is positioned between (-R, R), and the fluctuation of a target simulation roadway can reach the maximum value required by simulation; or the like, or, alternatively,
the standard deviation of normal distribution is R/2, so that 99.54% of fluctuation data are positioned between (-R, R), and the fluctuation of the target simulation roadway reaches the maximum value of the simulation requirement within a first preset degree; or the like, or, alternatively,
and the standard deviation of the normal distribution is R, so that 62.26% of fluctuation data are positioned between (-R, R), the fluctuation of the target simulation roadway reaches the maximum value required by simulation within a second preset degree, at the moment, part of data are positioned outside a limited interval, and the formed fluctuation has certain randomness.
For example, the first preset degree may be set to 99.54%, so that the standard deviation of the normal distribution is selected to be R/2, and 99.54% of fluctuation data is ensured to be located between (-R, R), so that the roadway fluctuation can substantially reach the maximum value required by the simulation. The second preset degree can be set to be 62.26%, so that the standard deviation of normal distribution is R, 62.26% of fluctuation data are ensured to be positioned between (-R, R), most of fluctuation of the roadway can reach the maximum value required by simulation, at the moment, part of data are positioned outside a limited interval, and the formed fluctuation has certain randomness.
And S13, obtaining an uneven curve conforming to normal distribution based on preset drawing software and the fluctuation coordinate data conforming to flatness.
In some embodiments, optionally, the preset drawing software is CAD drawing software; based on preset mapping software and fluctuation coordinate data conforming to the flatness, an unevenness curve conforming to normal distribution is obtained, and the method comprises the following steps:
customizing a function F for generating the scr script file, and storing data in the newly-built file;
writing spline, and adding initial point coordinates (0, 0);
writing fluctuation data x (i), y (i), and changing lines when each group of data is recorded;
after the input is finished, copying the content of the script file to a CAD command frame to generate an uneven curve which is in accordance with normal distribution.
Fig. 3 is a schematic diagram of a fluctuation curve generated based on normal distribution under different flatness R according to an embodiment of the present invention. Referring to fig. 3, for example, the fluctuation coordinate data corresponding to the flatness R is imported into the CAD, and a plurality of groups of unevenness curves corresponding to the normal distribution are obtained.
Adding a distance s to the starting point of the curve according to the position of the section of the roadway to be combined to obtain an uneven curvej(sj1,sj2……sjn). Wherein s isjnThe height of the top combination point and the horizontal bottom plate and the s of the combination points at two sides at the junction of the nth curvejIs the width of the roadway.
And S14, establishing a roadway section contour line based on the roadway section basic data of the target simulation roadway.
For example, the contour line of the section of the tunnel is established as the starting point section of the three-dimensional model of the uneven tunnel to be established.
And S15, combining the uneven curve with the roadway section contour line, and acquiring an uneven closed plane based on the roadway connecting line.
For example, in this embodiment, the obtained roof unevenness curve and the roadway section contour line may be combined, and a roadway connecting line may be added to form an unevenness closed plane.
The combination point of the roadway wall surface comprises a central arc at the top of the three-arch roadway, the upper parts of arcs on two sides, a top plate of the rectangular roadway, two sides of the three-arch roadway and the rectangular roadway, and a bottom plate of the roadway. The bottom plate is a horizontal plane vertical to the section of the roadway.
Fig. 4 is a schematic diagram of a combination of a top relief curve and a contour line of a roadway section, where (a) is distribution of combination points at the top of the roadway section; (b) is a schematic combination diagram.
Fig. 5 is a schematic diagram of a roadway connecting line and a constructed closed plane according to an embodiment of the present invention, wherein (a) is a schematic diagram of a part of a curved connecting line (including two linear connecting portions); (b) is a closed plane formed.
In the embodiment provided by the invention, referring to fig. 4-5, in the uneven-top three-arch roadway, an uneven closed plane is formed through the top combination point, the uneven curve and the connecting line. Because only the unevenness part to the tunnel top simulates, the tunnel connecting wire that needs to add need contain two group to connect with the straight line, constitute closed wire frame, finally form closed plane entity.
And S16, lofting along the profile direction of the roadway according to the uneven closed plane, and obtaining the solid model of the uneven roadway.
Fig. 6 is a schematic diagram of lofting a closed plane according to an embodiment of the present invention. Fig. 7 is a schematic diagram of a straight roadway entity with uneven top, which is generated by the present invention, wherein (a) is a side view of the roadway entity; (b) is a top view of the roadway entity.
Referring to fig. 6-7, in the embodiment of the present invention, the closed plane needs to be sequentially lofted from one side of the two sides of the roadway along the top of the roadway to be connected to the other side of the two sides of the roadway, and the transition effect of the two closed planes is smooth fitting.
The present invention is not limited to the above-described embodiments, and various changes can be made without departing from the spirit and scope of the present invention by those skilled in the art.
It should be noted that, in the embodiment of the present invention, the steps S11-S16 are only an example of executing steps, and are not limited.
According to the three-dimensional modeling method for the uneven roadway, provided by the embodiment of the invention, the type and section basic data of the target simulation roadway and mining statistical data of a preset distance in the target simulation roadway are obtained; calculating the flatness of the target simulation roadway according to the mining statistical data, and generating fluctuating coordinate data which are in accordance with normal distribution based on the flatness; obtaining an uneven curve conforming to normal distribution based on preset drawing software and fluctuating coordinate data conforming to flatness; establishing a tunnel section contour line based on tunnel section basic data of the target simulation tunnel; combining the uneven curve with the contour line of the section of the roadway, and acquiring an uneven closed plane based on the connecting line of the roadway; and lofting is carried out along the profile direction of the roadway according to the uneven closed plane, and a solid model of the uneven roadway is obtained. The three-dimensional modeling of the roadway is realized, and therefore the real condition simulation of the underground wind environment is realized. The invention adopts normal distribution to generate an uneven curve of the wall surface of the roadway, can well simulate the uneven form of the wall surface of the roadway by combining the parameters of the section of the roadway, and can be used for measurement and calibration of sensors in the roadway and analysis of the underground wind environment.
Based on a general inventive concept, the embodiment of the invention also provides a three-dimensional modeling device for uneven roadways.
Fig. 8 is a schematic structural diagram of a three-dimensional modeling apparatus for uneven roadways according to an embodiment of the present invention, and referring to fig. 8, the apparatus according to the embodiment of the present invention may include the following structures: an acquisition module 81, a generation module 82, an acquisition module 83, an establishment module 84, a plane acquisition module 85, and a model acquisition module 86;
the acquisition module 81 is configured to acquire the type and section basic data of a target simulation tunnel and mining statistical data of a preset distance in the target simulation tunnel;
the generating module 82 is configured to calculate the flatness of the target simulation roadway according to the mining statistical data, and generate fluctuating coordinate data conforming to normal distribution based on the flatness;
an obtaining module 83, configured to obtain an uneven curve conforming to normal distribution based on preset mapping software and undulation coordinate data conforming to flatness;
the establishing module 84 is used for establishing a roadway section contour line based on the roadway section basic data of the target simulation roadway;
the plane acquisition module 85 is used for combining the uneven curve and the roadway section contour line and acquiring an uneven closed plane based on a roadway connecting line;
and the model obtaining module 86 is used for lofting along the contour direction of the roadway according to the uneven closed plane to obtain a solid model of the uneven roadway.
With regard to the apparatus in the above-described embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment related to the method, and will not be elaborated here.
According to the three-dimensional modeling device for the uneven roadway, provided by the embodiment of the invention, the type and section basic data of the target simulation roadway and the mining statistical data of the preset distance in the target simulation roadway are obtained; calculating the flatness of the target simulation roadway according to the mining statistical data, and generating fluctuating coordinate data which are in accordance with normal distribution based on the flatness; obtaining an uneven curve conforming to normal distribution based on preset mapping software and fluctuating coordinate data conforming to flatness; establishing a tunnel section contour line based on tunnel section basic data of the target simulation tunnel; combining the uneven curve with the contour line of the section of the roadway, and acquiring an uneven closed plane based on the connecting line of the roadway; and lofting is carried out along the contour direction of the roadway according to the uneven closed plane, and a solid model of the uneven roadway is obtained. The three-dimensional modeling of the roadway is realized, and therefore the real condition simulation of the underground wind environment is realized. The invention adopts normal distribution to generate an uneven curve of the wall surface of the roadway, can well simulate the uneven form of the wall surface of the roadway by combining the parameters of the section of the roadway, and can be used for measurement and calibration of sensors in the roadway and analysis of the underground wind environment.
Based on a general inventive concept, the embodiment of the invention also provides three-dimensional modeling equipment for uneven roadways.
Fig. 9 is a schematic structural diagram of a three-dimensional modeling apparatus for an uneven roadway according to an embodiment of the present invention, and referring to fig. 9, the three-dimensional modeling apparatus for an uneven roadway according to an embodiment of the present invention includes: a processor 91, and a memory 92 connected to the processor.
The memory 92 is used for storing a computer program, and the computer program is at least used for the three-dimensional modeling method of uneven roadway described in any of the above embodiments;
the processor 91 is used to call and execute computer programs in the memory.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily think of the changes or substitutions within the technical scope of the present invention, and shall cover the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
It is understood that the same or similar parts in the above embodiments may be mutually referred to, and the same or similar parts in other embodiments may be referred to for the content which is not described in detail in some embodiments.
It should be noted that the terms "first," "second," and the like in the description of the present invention are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Further, in the description of the present invention, the meaning of "a plurality" means at least two unless otherwise specified.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and alternate implementations are included within the scope of the preferred embodiment of the present invention in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present invention.
It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present invention may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc.
In the description of the specification, reference to the description of "one embodiment," "some embodiments," "an example," "a specific example," or "some examples" or the like means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.