CN110020401B - Method, device and equipment for calculating curve integral of arc length and storage medium - Google Patents

Abstract

The invention belongs to the technical field of mathematical calculation, and discloses a curve integral calculation method, device, equipment and storage medium for arc length. The method includes: obtaining integral data corresponding to the curve integral of the arc length to be calculated, and extracting at least two first integral elements from the integral data, and a value range corresponding to the first integral elements; according to the The first integral element is used to determine the curve integral model corresponding to the curve integral of the arc length; according to the curve integral model, the integral calculation formula corresponding to the curve integral of the arc length is determined; according to the first integral element Corresponding to the value range and the integral calculation formula, the integral result corresponding to the curve integral of the arc length is calculated. Through the above method, the technical problem in the prior art that the calculation method of the curve integral of the arc length is too simple and cannot meet the actual needs of users is solved.

Description

Method, device, equipment and storage medium for calculating curve integral of arc length

Technical Field

The present invention relates to the field of mathematical calculation technology, and in particular to a curve integral calculation method, device, equipment and storage medium for arc length.

Background Art

The curvilinear integral over arc length is a specific curvilinear integral, often also called the first kind of curvilinear integral.

At present, in order to facilitate the calculation of the curve integral of the arc length, many calculation devices for the curve integral of the arc length have been introduced one after another, such as a double integral counter.

Although these computing devices can be used to quickly and accurately calculate the integral results of the curve integral of the arc length, since the current computing devices can only recognize 14 native curve integral models corresponding to the curve integral of the arc length, the user must provide calculation data according to these 14 native curve integral models in order to obtain the corresponding integral results.

Obviously, the existing calculation scheme for the curve integral of arc length is difficult to meet the needs of users, so it is urgent to provide a new calculation scheme for the curve integral of arc length to solve the above technical problems.

The above contents are only used to assist in understanding the technical solution of the present invention and do not constitute an admission that the above contents are prior art.

Summary of the invention

The main purpose of the present invention is to provide a curve integral calculation method, device, equipment and storage medium for arc length, aiming to solve the technical problem that the curve integral calculation method for arc length in the prior art is too single and cannot meet the actual needs of users.

To achieve the above object, the present invention provides a method for calculating the curve integral of arc length, the method comprising the following steps:

Obtaining integral data corresponding to the curve integral of the arc length to be calculated, and extracting at least two first integral elements and value ranges corresponding to the first integral elements from the integral data;

Determining a curve integral model corresponding to the curve integral of the arc length according to the first integral element;

Determine, according to the curve integral model, an integral calculation formula corresponding to the curve integral of the arc length;

According to the value range corresponding to the first integral element and the integral calculation formula, an integral result corresponding to the curve integral of the arc length is calculated.

Preferably, the step of extracting at least two first integral elements and the value ranges corresponding to the first integral elements from the integral data includes:

According to a preset correspondence table, the integral data is converted into a character string to obtain a character string to be processed;

According to a preset illegal character table, illegal characters in the character string to be processed are filtered to obtain a target character string;

At least two first integral elements and value ranges corresponding to the first integral elements are extracted from the target character string.

Preferably, the step of determining the curve integral model corresponding to the curve integral of the arc length according to the first integral element comprises:

Determining the position of each first integral element in the integral data;

According to the order of the positions of the first integral elements in the integral data, the first integral elements are arranged in order, and a preset interval is set between two adjacent first integral elements to obtain the curve integral model corresponding to the curve integral of the arc length.

Preferably, the first integral element comprises an integral arc element and a coordinate element;

The step of calculating the integral result corresponding to the curve integral of the arc length according to the value range corresponding to the first integral element and the integral calculation formula includes:

Determine the upper and lower limits of the integral according to the value range corresponding to the integral arc segment element;

Determining the arc differential according to the value range corresponding to the coordinate element;

Substitute the integral upper and lower limits and the arc differential into the integral calculation formula to obtain a target integral calculation formula;

According to the target integral calculation formula, the integral result corresponding to the curve integral of the arc length is calculated.

Preferably, before the step of determining the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model, the method further comprises:

Determining whether the curve integration model is available;

If the curve integral model is available, then performing the step of determining the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model;

If the curve integral model is not available, an error prompt is given to the user, so that the user can modify the integral data according to the error prompt;

Wherein, the step of determining whether the curve integral model is available comprises:

Comparing the curve integral model with a preset curve integral model in a pre-built curve integral model library, and determining that the curve integral model is available if there is a preset curve integral model in the curve integral model library that is identical to the curve integral model;

Otherwise, it is determined that the curve integration model is not applicable.

Preferably, before the step of comparing the curve integral model with a preset curve integral model in a pre-built curve integral model library, the method further comprises:

Acquire a predetermined primary curve integral model, and extract a second integral element included in the primary curve integral model;

Adjusting the position of the second integral element in the primary curve integral model to obtain a secondary curve integral model equivalent to the primary curve integral model, wherein the secondary curve integral model includes the primary curve integral model;

The secondary curve integral model is used as the preset curve integral model.

Preferably, before the step of adjusting the position of the second integral element in the primary curve integral model to obtain a secondary curve integral model equivalent to the primary curve integral model, the method further comprises:

Counting the number N of second integral elements included in the primary curve integral model, where N is an integer greater than or equal to 2;

According to the number N, determining the number M of secondary curve integral models equivalent to the primary curve integral model, where M is an integer greater than or equal to N;

Determining an adjustment rule of the primary curve integral model according to the number M and the second integral element;

The step of adjusting the position of the second integral element in the primary curve integral model to obtain a secondary curve integral model equivalent to the primary curve integral model includes:

According to the adjustment rule, the position of the second integral element in the primary curve integral model is adjusted to obtain M secondary curve integral models equivalent to the primary curve integral model.

In addition, to achieve the above-mentioned purpose, the present invention also proposes a curve integral calculation device for arc length, the device comprising:

An extraction module, used to obtain integral data corresponding to the curve integral of the arc length to be calculated, and extract at least two first integral elements and a value range corresponding to the first integral elements from the integral data;

A first determining module, configured to determine a curve integral model corresponding to the curve integral of the arc length according to the first integral element;

A second determination module is used to determine the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model;

A calculation module is used to calculate the integral result corresponding to the curve integral of the arc length according to the value range corresponding to the first integral element and the integral calculation formula.

In addition, to achieve the above-mentioned purpose, the present invention also proposes a curve integral calculation device for arc length, the device comprising: a memory, a processor, and a curve integral calculation program for arc length stored in the memory and executable on the processor, the curve integral calculation program for arc length being configured to implement the steps of the curve integral calculation method for arc length as described above.

In addition, to achieve the above-mentioned purpose, the present invention also proposes a computer-readable storage medium, on which a curve integral calculation program for arc length is stored. When the curve integral calculation program for arc length is executed by a processor, the steps of the curve integral calculation method for arc length as described above are implemented.

The curve integral calculation scheme for arc length provided by the present invention, when calculating the integral result of the curve integral for arc length, obtains the integral data corresponding to the curve integral for arc length, extracts the first integral element related to the curve integral for arc length currently required to be calculated and the value range corresponding to each first integral element from the integral data, and then determines the curve integral model corresponding to the curve integral for arc length currently required to be calculated according to the extracted first integral element, and then determines the integral calculation formula corresponding to the curve integral for the arc length according to the determined curve integral model, and finally automatically calculates the integral result of the curve integral for the arc length according to the value range corresponding to each first integral element and the determined integral calculation formula. Since the process of determining the curve integral model corresponding to the curve integral for the arc length is based on the extracted first integral element, rather than directly based on the integral data provided by the user, the format of the integral data provided by the user is not limited to conform to the 14 existing native curve integral models, so that the user can provide integral data according to his own input habits, thereby greatly facilitating the use of the user, and effectively solving the technical problem that the curve integral calculation method for arc length in the prior art is too single and cannot meet the actual needs of the user.

BRIEF DESCRIPTION OF THE DRAWINGS

1 is a schematic diagram of the structure of a curve integral calculation device for arc length in a hardware operating environment according to an embodiment of the present invention;

FIG2 is a schematic flow chart of a first embodiment of a method for calculating arc length by curve integral according to the present invention;

3 is a schematic flow chart of a second embodiment of a method for calculating arc length by curve integral according to the present invention;

FIG. 4 is a structural block diagram of a first embodiment of a curve integral calculation device for arc length according to the present invention.

The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings.

DETAILED DESCRIPTION

It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

Refer to FIG. 1 , which is a schematic diagram of the structure of a curve integral calculation device for arc length in a hardware operating environment involved in an embodiment of the present invention.

As shown in FIG1 , the curve integral calculation device for the arc length may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to realize the connection and communication between these components. The user interface 1003 may include a display screen (Display), an input unit such as a keyboard (Keyboard), and the optional user interface 1003 may also include a standard wired interface and a wireless interface. The network interface 1004 may optionally include a standard wired interface and a wireless interface (such as a wireless fidelity (WIreless-FIdelity, WI-FI) interface). The memory 1005 may be a high-speed random access memory (Random Access Memory, RAM) memory, or a stable non-volatile memory (Non-Volatile Memory, NVM), such as a disk memory. The memory 1005 may also be a storage device independent of the aforementioned processor 1001.

Those skilled in the art will appreciate that the structure shown in FIG. 1 does not constitute a limitation on the curve integral calculation device for arc length, and may include more or fewer components than shown in the figure, or a combination of certain components, or a different arrangement of components.

As shown in FIG. 1 , the memory 1005 as a storage medium may include an operating system, a network communication module, a user interface module, and a curve integral calculation program for arc length.

In the curve integral calculation device for arc length shown in FIG1 , the network interface 1004 is mainly used for data communication with a network server; the user interface 1003 is mainly used for data interaction with a user; the processor 1001 and the memory 1005 in the curve integral calculation device for arc length of the present invention can be arranged in the curve integral calculation device for arc length, and the curve integral calculation device for arc length calls the curve integral calculation program for arc length stored in the memory 1005 through the processor 1001, and executes the curve integral calculation method for arc length provided in an embodiment of the present invention.

An embodiment of the present invention provides a curve integral calculation method for arc length. Referring to FIG. 2 , FIG. 2 is a flow chart of a first embodiment of a curve integral calculation method for arc length according to the present invention.

In this embodiment, the curve integral calculation method for arc length includes the following steps:

Step S10, obtaining integral data corresponding to the curve integral of the arc length to be calculated, and extracting at least two first integral elements and value ranges corresponding to the first integral elements from the integral data.

It is understandable that the integral data may be from manual input by a user or data outputted from the system and waiting for further processing. In this embodiment, the integral data is from user input.

In addition, the integral data mentioned in this embodiment specifically refers to the relevant data corresponding to the curve integral of the arc length for which the integral result needs to be calculated, mainly including the first integral element used to calculate the curve integral of the arc length and the value range corresponding to the first integral element.

In addition, it should be noted that the first integral element mentioned in this embodiment does not simply refer to the arc length element ds mentioned in the curve integral of the arc length, but also includes coordinate elements, integral arc segment elements, integrand elements, etc., which are not listed one by one here and no limitation is made.

In addition, it is worth mentioning that, according to the existing 14 native curve integral models (hereinafter referred to as: first-level curve integral models), it can be determined that a first-level curve integral model needs to include at least two integral elements and the value ranges corresponding to the two integral elements.

The curve integral model mentioned in this embodiment is actually a curve integral model equivalent to the first-order curve integral model, that is, it contains the same integral elements, but the positions of the integral elements are different.

Therefore, in order to ensure that the operation of determining the curve integral model in step S20 can proceed smoothly, when extracting the first integral element from the integral data, it is necessary to extract at least two first integral elements and the value range corresponding to the first integral element.

For ease of understanding, the following are the 14 existing first-order curve integration models:

(1) y = y(x), a≤x≤b;

(2) x = x(y), c ≤ y ≤ d;

(3)x=x(t), y=y(t), α≤t≤β;

(4)f=f(x,y), y=y(x), a≤x≤b;

(5)f=f(x,y), x=x(y), c≤y≤d;

(6)f=f(x,y), x=x(t), y=y(t), α≤t≤β;

(7)y=y(x), z=z(x), a≤x≤b;

(8)x=x(y), z=z(y), c≤y≤d;

(9)x=x(z), y=y(z), p≤z≤q;

(10)x=x(t), y=y(t), z=z(t), α≤t≤β;

(11)f=f(x,y,z), y=y(x), z=z(x), a≤x≤b;

(12)f=f(x, y, z), x=x(y), z=z(y), c≤y≤d;

(13)f=f(x, y, z), x=x(z), y=y(z), p≤z≤q;

(14) f=f(x, y, z), x=x(t), y=y(t), z=z(t), α≤t≤β.

Correspondingly, if the integral data provided by the user is "y=y(x), a≤x≤b", or "a≤x≤b, y=y(x)", then the first integral element extracted from the integral data is specifically the coordinate element "x" and the coordinate element "y", and the value range corresponding to the coordinate element "x" extracted from the integral data is "a≤x≤b", and the value range corresponding to the coordinate element "x" is "y=y(x)".

It should be understood that the above is only an example and does not constitute any limitation on the technical solution of the present invention. In practical applications, those skilled in the art can make settings as needed, and no limitation is made here.

In addition, it is worth mentioning that in actual applications, when computer equipment processes data input by users, it usually converts the data input by users into a string format internally, and then performs corresponding processing based on the string according to business needs.

Therefore, before executing the operation of extracting the first integral element and the value range corresponding to the first integral element, the integral data can be first converted into a character string, and then the first integral element and the value range corresponding to the first integral element can be extracted from the character string.

For ease of understanding, this embodiment provides a specific implementation method, which is roughly as follows:

(1) According to a preset correspondence table, the integral data is converted into a character string to obtain a character string to be processed.

It should be understood that the corresponding relationship table is constructed before executing the curve integral calculation operation on the arc length mentioned in this example.

In practical applications, in order to be able to identify the content of the integral data as accurately as possible, the integral data of curve integrals of arc length written by different users can be collected in advance from major data platforms, and a large amount of existing integral data can be analyzed and learned based on big data analysis technology and machine learning technology to determine a correspondence table that can identify the integral data provided by different users as much as possible.

For example, it can be set in the correspondence table that if the current information extracted from the integral data is "x∈[a,b]", the content can be converted into a character string of "a≤x≤b".

For another example, it can be set in the correspondence table that if any two first integral elements are separated by a semicolon, a comma, a space, or the like, the current symbol is replaced by a comma.

It should be understood that the above is only an example and does not constitute any limitation on the technical solution of the present invention. In specific applications, technicians in this field can make settings as needed, and the present invention does not limit this.

(2) According to a preset illegal character table, illegal characters in the character string to be processed are filtered to obtain a target character string.

It should be understood that in actual applications, when providing integral data, in addition to inputting the first integral element of the curve integral model that can determine the curve integral of the arc length, and the value range corresponding to each first integral element, the user will also add some illegal characters according to personal writing habits. Therefore, in order to ensure that the computer device can accurately extract the first integral element and the value range corresponding to the first integral element from the integral data, an illegal character table can be pre-set, and illegal characters can be recorded in the illegal character table. In this way, when the illegal character filtering operation is performed on the string to be processed, the string to be processed is directly traversed, and the current character traversed is compared with the illegal characters in the illegal character table. If the current character traversed is the same as the illegal character, the current character traversed is deleted from the string to be processed, and the target string is obtained.

(3) Extracting at least two first integral elements and the value ranges corresponding to the first integral elements from the target character string.

For ease of understanding, the following examples are used to illustrate:

Assume that the integral data input by the user is: "y=y(x) and x∈[a,b].", and the illegal characters recorded in the preset illegal character table B are: B={".", "!", "", "?"}.

Then, through the character string conversion process, the character string to be processed corresponding to the above integral data is {S＝{y＝y(x), a≤x≤b. }.

Next, the character string S to be processed and the illegal character table B are traversed respectively, and the characters traversed from the character string S to be processed are compared with the characters traversed from the illegal character table B, and finally it is determined that the character "." in the character string S to be processed is an illegal character.

Next, the character “.” in the character string S to be processed is filtered out to obtain the target character string _SP = {S = {y = y(x), a≤x≤b}.

Finally, the first integral element extracted from the target string _SP is specifically the coordinate element "x" and the coordinate element "y". The value range corresponding to the coordinate element "x" extracted from the integral data is "a≤x≤b", and the value range corresponding to the coordinate element "x" is "y＝y(x)".

It should be understood that what is given above is only a specific implementation method of extracting the first integral element from the integral data, and the value range corresponding to the first integral element, which does not constitute any limitation on the technical solution of the present invention. In specific applications, technicians in this field can set it as needed, and the present invention does not limit this.

In addition, the "first" in the above-mentioned "first integral element" is only used to indicate that the integral element is extracted from the integral data, and does not limit the integral data itself, and the first integral element can be any integral element in the integral data.

Correspondingly, the "first level" in the "first level curve integral model" does not impose any limitation on the model corresponding to the curve integral of the arc length. In practical applications, the curve integral model can be any first level curve integral model, or any second level curve integral model equivalent to the first level curve integral model.

Correspondingly, the “secondary” in the “secondary curve integral model” does not impose any limitation on the model corresponding to the curve integral of arc length.

Step S20: determining a curve integral model corresponding to the curve integral of the arc length according to the first integral element.

The steps of determining the curve integral model corresponding to the curve integral of the arc length are roughly as follows:

First, determine the position of each first integral element in the integral data;

Then, according to the order of the positions of the first integral elements in the integral data, the first integral elements are arranged in order, and a preset interval, such as a comma, is set between two adjacent first integral elements to obtain the curve integral model corresponding to the curve integral of the arc length.

For ease of understanding, the following examples are used to illustrate:

Assuming that the integral data provided by the user is "y=y(x), a≤x≤b", the first integral element extracted is specifically the coordinate element "x" and the coordinate element "y", and the value range corresponding to the coordinate element "x" extracted from the integral data is "a≤x≤b", and the value range corresponding to the coordinate element "x" is "y=y(x)".

At the same time, the position of the coordinate element "x" is obtained as w _x , and the position of the coordinate element "y" is obtained as w _y .

By comparison, it is found that the value corresponding to w _y is smaller than the value corresponding to w _x , that is, the coordinate element "y" should be located before the coordinate element "x". The curve integral model obtained after this arrangement is "y＝y(x), a≤x≤b".

If the integral data provided by the user is "a≤x≤b, y＝y(x)", although the first integral element extracted is still the coordinate element "x" and the coordinate element "y", the value range corresponding to the coordinate element "x" extracted from the integral data is "a≤x≤b", and the value range corresponding to the coordinate element "x" is "y＝y(x)".

However, by comparing the numerical value corresponding to _wx with the numerical value corresponding to _wy , it can be found that the numerical value corresponding to _wy is greater than the numerical value corresponding to _wx , that is, the coordinate element "y" should be located after the coordinate element "x". The curve integral model obtained after this arrangement is "a≤x≤b, y＝y(x)".

It should be understood that the above is only an example and does not constitute any limitation on the technical solution of the present invention. In specific applications, technicians in this field can make settings as needed, and the present invention does not limit this.

In addition, it is worth mentioning that the curve integral model mentioned in this embodiment specifically includes a primary curve integral model and an equivalent model equivalent to the primary curve integral model.

For the sake of convenience, the primary curve integral model and an equivalent model of the primary curve model are referred to as secondary curve integral models below.

Correspondingly, the curve integral model determined above is any one of the secondary curve integral models.

Step S30: determining an integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model.

Specifically, since the existing 14 first-order curve integral models correspond to four different curve integrals of arc length, the actual corresponding relationship is as follows:

The first-order curve integral models (1) to (3) correspond to the arc length of the plane curve, the first-order curve integral models (4) to (6) correspond to the plane curve of the corresponding arc length, the first-order curve integral models (7) to (10) correspond to the arc length of the space curve, and the first-order curve integral models (11) to (14) correspond to the space curve of the corresponding arc length.

Correspondingly, the derived curve integral model will also correspond to four different curve integrals of arc length.

Therefore, the charging calculation formula corresponding to the curve integral of the arc length determined according to the curve integral model will also be different.

It should be noted that, in practical applications, in order to be able to quickly and accurately determine the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model, the following agreement can be made in advance:

(1) f1 is used to indicate the position where the ternary function mark “f(xyz)=” exists in the curve integral model;

(2) f2 indicates the position where the binary function symbol "f(xy)=" exists in the curve integral model;

(3) f3 represents the position where the mark "x=" exists in the curve integral model;

(4) f4 represents the position where the mark "y=" exists in the curve integration model;

(5) f5 indicates the position where the mark “z=” exists in the curve integral model;

(6) f6 represents the position where the mark “≤x≤” exists in the curve integral model;

(7) f7 represents the position where the mark “≤y≤” exists in the curve integral model;

(8) f8 represents the position where the mark “≤z≤” exists in the curve integral model;

(9) f9 represents the position where the mark “≤t≤” exists in the curve integration model;

(10) ft1 indicates the position where the first “,” exists in the curve integral model;

(11) ft2 indicates the position where the second “,” exists in the curve integral model;

(12) ft3 indicates the position where the third “,” exists in the curve integral model;

(13) ft4 indicates the position where the fourth “,” exists in the curve integral model.

Correspondingly, if in the curve integral model, f2>0, f3>0, f7>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the integral result of the plane curve integral of the arc length. In this case, the integral calculation formula to be selected is:

Integral calculation formula 1:

表示积分弧段，f(x(y)，y)表示被积函数，

表示弧微分。It should be understood that in the above integral calculation formula, I represents the plane curve integral of the arc length,

represents the integral arc, f(x(y), y) represents the integrand,

represents the arc differential.

Furthermore, if in the curve integral model, f2>0, f4>0, f6>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the integral result of the plane curve integral of the arc length. In this case, the integral calculation formula to be selected is:

Integral calculation formula 2:

表示积分弧段，f(x，y(x))表示被积函数，

表示弧微分。It should be understood that in the above integral calculation formula, I represents the plane curve integral of the arc length,

represents the integral arc, f(x, y(x)) represents the integrand,

represents the arc differential.

Furthermore, if in the curve integral model, f2>0, f3>0, f4>0, f9>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the integral result of the plane curve integral of the arc length. In this case, the integral calculation formula to be selected is:

Integral calculation formula 3:

表示积分弧段，f(x(t)，y(t))表示被积函数，

表示弧微分。It should be understood that in the above integral calculation formula, I represents the plane curve integral of the arc length,

represents the integral arc, f(x(t), y(t)) represents the integrand,

represents the arc differential.

Furthermore, if in the curve integral model, f1>0, f3>0, f4>0, f8>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the integral result of the spatial curve integral of the arc length. In this case, the integral calculation formula to be selected is:

Integral calculation formula 4:

表示积分弧段，f(x(z)，y(z)，z)表示被积函数，

表示弧微分。It should be understood that in the above integral calculation formula, S represents the spatial curve integral of the arc length.

represents the integral arc, f(x(z), y(z), z) represents the integrand,

represents the arc differential.

Furthermore, if in the curve integral model, f1>0, f3>0, f5>0, f7>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the integral result of the spatial curve integral of the arc length. In this case, the integral calculation formula to be selected is:

Integral calculation formula 5:

表示积分弧段，f(x(y)，y，z(y))表示被积函数，

表示弧微分。It should be understood that in the above integral calculation formula, S represents the spatial curve integral of the arc length.

represents the integral arc, f(x(y), y, z(y)) represents the integrand,

represents the arc differential.

Furthermore, if in the curve integral model, f1>0, f4>0, f5>0, f6>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the integral result of the spatial curve integral of the arc length. In this case, the integral calculation formula to be selected is:

Integral calculation formula 6:

表示积分弧段，f(x，y(x)，z(x))表示被积函数，

表示弧微分。It should be understood that in the above integral calculation formula, S represents the spatial curve integral of the arc length.

represents the integral arc, f(x, y(x), z(x)) represents the integrand,

represents the arc differential.

Furthermore, if in the curve integral model, f1>0, f3>0, f4>0, f5>0, f9>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the integral result of the spatial curve integral of the arc length. In this case, the integral calculation formula to be selected is:

Integral calculation formula 7:

表示积分弧段，f(x(t)，y(t)，z(t))表示被积函数，

表示弧微分。It should be understood that in the above integral calculation formula, S represents the spatial curve integral of the arc length.

represents the integral arc, f(x(t), y(t), z(t)) represents the integrand,

represents the arc differential.

Furthermore, if in the curve integral model, f3>0, f7>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the arc length of the plane curve. In this case, the integral calculation formula to be selected is:

Integral calculation formula 8:

表示积分弧段，

表示弧微分。It should be understood that in the above integral calculation formula, L _I represents the arc length of the plane curve.

represents the integral arc segment,

represents the arc differential.

Furthermore, if in the curve integral model, f1=0, f2>0, f3>0, f4=0, f7>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the arc length of the plane curve. In this case, the integral calculation formula to be selected is:

Integral calculation formula 9:

表示积分弧段，

表示弧微分。It should be understood that in the above integral calculation formula, L _I represents the arc length of the plane curve.

represents the integral arc segment,

represents the arc differential.

Furthermore, if in the curve integral model, f3>0, f4>0, f9>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the arc length of the plane curve. In this case, the integral calculation formula to be selected is:

Integral calculation formula 10:

表示积分弧段，

表示弧微分。It should be understood that in the above integral calculation formula, L _I represents the arc length of the plane curve.

represents the integral arc segment,

represents the arc differential.

Furthermore, if in the curve integral model, f3>0, f4>0, f8>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the arc length of the space curve. In this case, the integral calculation formula to be selected is:

Integral calculation formula 11:

表示积分弧段，

表示弧微分。It should be understood that in the above integral calculation formula, _Ls represents the arc length of the space curve.

represents the integral arc segment,

represents the arc differential.

Furthermore, if in the curve integral model, f3>0, f5>0, f7>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the arc length of the space curve. In this case, the integral calculation formula to be selected is:

Integral calculation formula 12:

表示积分弧段，

表示弧微分。It should be understood that in the above integral calculation formula, _Ls represents the arc length of the space curve.

represents the integral arc segment,

represents the arc differential.

Furthermore, if in the curve integral model, f1=0, f2>0, f3>0, f4=0, f7>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the arc length of the space curve. In this case, the integral calculation formula to be selected is:

Integral calculation formula 13:

表示积分弧段，

表示弧微分。It should be understood that in the above integral calculation formula, _Ls represents the arc length of the space curve.

represents the integral arc segment,

represents the arc differential.

Furthermore, if in the curve integral model, f1=0, f2>0, f3>0, f4=0, f7>0, and the rest are equal to 0, it is determined that the curve integral of the arc length that the user needs to calculate is actually the arc length of the space curve. In this case, the integral calculation formula to be selected is:

Integral calculation formula 14:

表示积分弧段，

表示弧微分。It should be understood that in the above integral calculation formula, _Ls represents the arc length of the space curve.

represents the integral arc segment,

represents the arc differential.

It should be understood that what is given above is only a specific implementation method of determining the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model, and does not constitute any limitation on the technical solution of the present invention. In specific applications, technicians in this field can make settings as needed, and the present invention does not impose any restrictions on this.

Step S40: Calculate the integral result corresponding to the curve integral of the arc length according to the value range corresponding to the first integral element and the integral calculation formula.

For ease of understanding, the operation of calculating the integral result corresponding to the curve integral of the arc length according to the value range corresponding to the first integral element and the integral calculation formula in step S40 is described by taking the first integral elements being the integral arc segment element and the coordinate element as an example:

First, the upper and lower limits of the integral are determined according to the value range corresponding to the integral arc segment element;

Then, the arc differential is determined according to the value range corresponding to the coordinate element;

Next, the upper and lower limits of the integral and the arc differential are substituted into the integral calculation formula to obtain the target integral calculation formula;

Finally, according to the target integral calculation formula, the integral result corresponding to the curve integral of the arc length is calculated.

It should be understood that what is given above is only a specific implementation method for calculating the integral result corresponding to the curve integral of the arc length, and does not constitute any limitation to the technical solution of the present invention. In specific applications, technicians in this field can make settings as needed, and the present invention does not impose any restrictions on this.

It is not difficult to find from the above description that the curve integral calculation method for arc length provided in this embodiment, when calculating the integral result of the curve integral for arc length, obtains the integral data corresponding to the curve integral for arc length, extracts the first integral element related to the curve integral for arc length currently to be calculated and the value range corresponding to each first integral element from the integral data, and then determines the curve integral model corresponding to the curve integral for arc length currently to be calculated according to the extracted first integral element, and then determines the integral calculation formula corresponding to the curve integral for the arc length according to the determined curve integral model, and finally automatically calculates the integral result of the curve integral for the arc length according to the value range corresponding to each first integral element and the determined integral calculation formula. Since the process of determining the curve integral model corresponding to the curve integral for the arc length is based on the extracted first integral element, rather than directly based on the integral data provided by the user, the format of the integral data provided by the user is not limited to conform to the 14 existing native curve integral models, so that the user can provide integral data according to his own input habits, thereby greatly facilitating the use of the user, and effectively solving the technical problem that the curve integral calculation method for arc length in the prior art is too single and cannot meet the actual needs of the user.

Refer to FIG. 3 , which is a flow chart of a second embodiment of a curve integral calculation method for arc length according to the present invention.

Based on the first embodiment, the curve integral calculation method for arc length in this embodiment further includes, before step S10:

Step S00, determining whether the curve integral model is available.

Accordingly, if it is determined that the curve integral model is available, step S30 is executed; if it is determined that the curve integral model is not available, step S50 is executed to give an error prompt to the user so that the user can modify the integral data according to the error prompt.

In order to facilitate understanding of the operation of determining whether the curve integral model is available in the above step S00, this embodiment provides a specific determination method, which is roughly as follows:

Comparing the curve integral model with a preset curve integral model in a pre-built curve integral model library, and determining that the curve integral model is available if there is a preset curve integral model in the curve integral model library that is identical to the curve integral model;

Otherwise, it is determined that the curve integration model is not applicable.

It should be understood that the above is only a specific implementation method for determining whether the curve integral model is applicable, and does not constitute any limitation on the technical solution of the present invention. In specific applications, technicians in this field can make settings as needed, and the present invention does not impose any limitation on this.

In addition, it is worth mentioning that in order to ensure the smooth progress of the above operations, before comparing the curve integral model with the preset curve integral model in the pre-constructed curve integral model library, it is necessary to first construct the curve integral model library, that is, it is necessary to first generate the preset curve integral model and add the preset curve integral model to the curve integral model library.

For ease of understanding, a specific method for generating the preset curve integral model is given below, which is roughly as follows:

First, a predetermined primary curve integral model is obtained, and a second integral element included in the primary curve integral model is extracted;

Then, adjusting the position of the second integral element in the primary curve integral model to obtain a secondary curve integral model equivalent to the primary curve integral model, wherein the secondary curve integral model includes the primary curve integral model;

Finally, the secondary curve integral model is used as the preset curve integral model.

The operation of adjusting the position of the second integral element in the primary curve integral model to obtain a secondary curve integral model equivalent to the primary curve integral model may specifically be:

First, the number N of second integral elements included in the primary curve integral model is counted, where N is an integer greater than or equal to 2;

Then, according to the number N, the number M of secondary curve integral models equivalent to the primary curve integral model is determined, where M is an integer greater than or equal to N;

Next, determining an adjustment rule of the primary curve integral model according to the number M and the second integral element;

Finally, according to the adjustment rule, the position of the second integral element in the primary curve integral model is adjusted to obtain M secondary curve integral models equivalent to the primary curve integral model.

It should be understood that the above is only a specific implementation method for generating the preset curve integral model, which does not constitute any limitation on the technical solution of the present invention. In specific applications, technicians in this field can make settings as needed, and the present invention does not impose any limitations on this.

In addition, the "second" in the above-mentioned "second integral element" is only used to indicate that the integral element is extracted from the first-level curve integral model, and does not limit the first-level curve integral model itself, and the second integral element can be any integral element in the first-level curve integral model.

In addition, it is worth mentioning that since the 14 first-order curve integral models correspond to four different curve integrals of arc length, the generated curve integral model is an equivalent model corresponding to each first-order curve integral model.

Therefore, for ease of understanding, the following curve integral models corresponding to the four curve integrals of arc length are given in turn for the four angles of finding the arc length of a plane curve, finding the plane curve integral with respect to the arc length, finding the arc length of a space curve, and finding the space curve integral with respect to the arc length.

Specifically, there are three first-order curve integral models corresponding to the arc length of the plane curve, namely: (1) y = y(x), a≤x≤b; (2) x = x(y), c≤y≤d; (3) x = x(t), y = y(t), α≤t≤β.

Correspondingly, for the first-order curve integral model "y=y(x), a≤x≤b", the number of equivalent second-order curve integral models determined is M=2! =2. After adjusting the position of the second integral element, the two preset curve integral models obtained are:

①y＝y(x), a≤x≤b; ②a≤x≤b, y＝y(x).

Accordingly, for the first-order curve integral model "=x(y), c≤y≤d", the number of equivalent second-order curve integral models determined is M=2! =2. After adjusting the position of the second integral element, the two preset curve integral models obtained are:

①x＝x(y), c≤y≤d; ②c≤y≤d, x＝x(y).

Correspondingly, for the first-order curve integral model "x = x(t), y = y(t), α≤t≤β", the number of equivalent second-order curve integral models determined is M = 3! = 6. After adjusting the position of the second integral element, the 6 preset curve integral models obtained are:

①x＝x(t), y＝y(t), α≤t≤β; ②y＝y(t), x＝x(t), α≤t≤β;

③x＝x(t),α≤t≤β,y＝y(t); ④α≤t≤β,x＝x(t),y＝y(t);

⑤y＝y(t), α≤t≤β, x＝x(t); ⑥α≤t≤β, y＝y(t), x＝x(t).

In addition, there are also three first-order curve integral models corresponding to the plane curve integral of arc length, namely: (1) f = f(x, y), y = y(x), a≤x≤b; (2) f = f(x, y), x = x(y), c≤y≤d; (3) f = f(x, y), x = x(t), y = y(t), α≤t≤β.

Correspondingly, for the first-order curve integral model "f = f (x, y), y = y (x), a ≤ x ≤ b", the number of equivalent second-order curve integral models determined is M = 3! = 6. After adjusting the position of the second integral element, the 6 preset curve integral models obtained are:

①f＝f(x,y),y＝y(x),a≤x≤b; ②y＝y(x),f＝f(x,y),a≤x≤b;

③f＝f(x,y),a≤x≤b,y＝y(x); ④a≤x≤b,f＝f(x,y),y＝y(x);

⑤y＝y(x), a≤x≤b, f＝f(x,y); ⑥a≤x≤b, y＝y(x), f＝f(x,y).

Correspondingly, for the first-order curve integral model "f = f (x, y), x = x (y), c ≤ y ≤ d", the number of equivalent second-order curve integral models determined is M = 3! = 6. After adjusting the position of the second integral element, the 6 preset curve integral models obtained are:

①f＝f(x,y),x＝x(y),c≤y≤d; ②x＝x(y),f＝f(x,y),c≤y≤d;

③f＝f(x,y),c≤y≤d,x＝x(y); ④c≤y≤d,f＝f(x,y),x＝x(y);

⑤x＝x(y), c≤y≤d, f＝f(x,y); ⑥c≤y≤d, x＝x(y), f＝f(x,y).

Accordingly, for the first-order curve integral model "f = f(x, y), x = x(t), y = y(t), α≤t≤β", the number of equivalent second-order curve integral models determined is M = 4! = 24. After adjusting the position of the second integral element, the 24 preset curve integral models are obtained, as shown in Table 1.

Table 1 Preset curve integral model corresponding to the first-order curve integral model "f = f (x, y), x = x (t), y = y (t), α ≤ t ≤ β"

serial number Preset Curve Integration Model serial number Preset Curve Integration Model 1 f＝f(x,y),x＝x(t),y＝y(t),α≤t≤β 13 x＝x(t),y＝y(t),f＝f(x,y),α≤t≤β 2 f＝f(x,y),y＝y(t),x＝x(t),α≤t≤β 14 y＝y(t),x＝x(t),f＝f(x,y),α≤t≤β 3 f＝f(x,y),x＝x(t),α≤t≤β,y＝y(t) 15 x＝x(t),α≤t≤β,f＝f(x,y),y＝y(t) 4 f＝f(x,y),α≤t≤β,x＝x(t),y＝y(t) 16 α≤t≤β,x=x(t),f=f(x,y),y=y(t) 5 f＝f(x,y),y＝y(t),α≤t≤β,x＝x(t) 17 y＝y(t),α≤t≤β,f＝f(x,y),x＝x(t) 6 f＝f(x,y),α≤t≤β,y＝y(t),x＝x(t) 18 α≤t≤β,y=y(t),f=f(x,y),x=x(t) 7 x＝x(t),f＝f(x,y),y＝y(t),α≤t≤β 19 x＝x(t),y＝y(t),α≤t≤β,f＝f(x,y) 8 y＝y(t),f＝f(x,y),x＝x(t),α≤t≤β 20 y＝y(t),x＝x(t),α≤t≤β,f＝f(x,y) 9 x＝x(t),f＝f(x,y),α≤t≤β,y＝y(t) twenty one x＝x(t),α≤t≤β,y＝y(t),f＝f(x,y) 10 α≤t≤β,f＝f(x,y),x＝x(t),y＝y(t) twenty two α≤t≤β,x=x(t),y=y(t),f=f(x,y) 11 y＝y(t),f＝f(x,y),α≤t≤β,x＝x(t) twenty three y＝y(t),α≤t≤β,x＝x(t),f＝f(x,y) 12 α≤t≤β,f＝f(x,y),y＝y(t),x＝x(t) twenty four α≤t≤β,y=y(t),x=x(t),f=f(x,y)

In addition, there are four first-order curve integral models corresponding to the arc length of the space curve, namely: (1) y = y(x), z = z(x), a≤x≤b; (2) x = x(y), z = z(y), c≤y≤d; (3) x = x(z), y = y(z), p≤z≤q; (4) x = x(t), y = y(t), z = z(t), α≤t≤β.

Correspondingly, for the first-order curve integral model "y = y (x), z = z (x), a ≤ x ≤ b", the number of equivalent second-order curve integral models determined is M = 3! = 6. After adjusting the position of the second integral element, the 6 preset curve integral models obtained are:

①z＝z(x), y＝y(x), a≤x≤b; ②y＝y(x), z＝z(x), a≤x≤b;

③z＝z(x), a≤x≤b, y＝y(x); ④a≤x≤b, z＝z(x), y＝y(x);

⑤y＝y(x), a≤x≤b, z＝z(x); ⑥a≤x≤b, y＝y(x), z＝z(x).

Correspondingly, for the first-order curve integral model "x = x (y), z = z (y), c ≤ y ≤ d", the number of equivalent second-order curve integral models determined is M = 3! = 6. After adjusting the position of the second integral element, the 6 preset curve integral models obtained are:

①x＝x(y), z＝z(y), c≤y≤d; ②z＝z(y), x＝x(y), c≤y≤d;

③x＝x(y), c≤y≤d, z＝z(y); ④c≤y≤d, x＝x(y), z＝z(y);

⑤z＝z(y), c≤y≤d, x＝x(y); ⑥c≤y≤d, z＝z(y), x＝x(y).

Accordingly, for the first-order curve integral model "x = x(z), y = y(z), p≤z≤q", the number of equivalent second-order curve integral models determined is M = 3! = 6. After adjusting the position of the second integral element, the 6 preset curve integral models obtained are:

①x＝x(z), y＝y(z), p≤z≤q; ②y＝y(z), x＝x(z), p≤z≤q;

③x＝x(z), p≤z≤q, y＝y(z); ④p≤z≤q, x＝x(z), y＝y(z);

⑤y＝y(z), p≤z≤q, x＝x(z); ⑥p≤z≤q, y＝y(z), x＝x(z).

Accordingly, for the first-order curve integral model "x = x(t), y = y(t), z = z(t), α≤t≤β", the number of equivalent second-order curve integral models determined is M = 4! = 24. After adjusting the position of the second integral element, the 24 preset curve integral models are obtained, as shown in Table 2.

Table 2 Preset curve integral model corresponding to the first-level curve integral model “x＝x(t), y＝y(t), z＝z(t), α≤t≤β”

In addition, there are also four first-order curve integral models corresponding to the spatial curve integral of arc length, namely: (1) f = f(x, y, z), y = y(x), z = z(x), a≤x≤b; (2) f = f(x, y, z), x = x(y), z = z(y), c≤y≤d; (3) f = f(x, y, z), x = x(z), y = y(z), p≤z≤q; (4) f = f(x, y, z), x = x(t), y = y(t), z = z(t), α≤t≤β.

Accordingly, for the first-order curve integral model "f = f (x, y, z), y = y (x), z = z (x), a ≤ x ≤ b", the number of equivalent second-order curve integral models determined is M = 4! = 24. After adjusting the position of the second integral element, the 24 preset curve integral models are obtained, as shown in Table 3.

Table 3 Preset curve integral model corresponding to the first-level curve integral model "f＝f(x，y，z), y＝y(x), z＝z(x), a≤x≤b"

serial number Preset Curve Integration Model serial number Preset Curve Integration Model 1 f＝f(x,y,z),y＝y(x),z＝z(x),a≤x≤b 13 f＝f(x,y,z),y＝y(x),a≤x≤b,z＝z(x) 2 f＝f(x,y,z),z＝z(x),y＝y(x),a≤x≤b 14 f＝f(x,y,z),z＝z(x),a≤x≤b,y＝y(x) 3 f＝f(x,y,z),a≤x≤b,y＝y(x),z＝z(x) 15 f＝f(x,y,z),a≤x≤b,z＝z(x),y＝y(x) 4 y＝y(x),f＝f(x,y,z),z＝z(x),a≤x≤b 16 y＝y(x),f＝f(x,y,z),a≤x≤b,z＝z(x) 5 y＝y(x),z＝z(x),f＝f(x,y,z),a≤x≤b 17 y＝y(x),z＝z(x),a≤x≤b,f＝f(x,y,z) 6 y＝y(x),a≤x≤b,f＝f(x,y,z),z＝z(x) 18 y＝y(x),a≤x≤b,z＝z(x),f＝f(x,y,z) 7 z＝z(x),y＝y(x),f＝f(x,y,z),a≤x≤b 19 z＝z(x),y＝y(x),a≤x≤b,f＝f(x,y,z) 8 z＝z(x),f＝f(x,y,z),y＝y(x),a≤x≤b 20 z＝z(x),f＝f(x,y,z),a≤x≤b,y＝y(x) 9 z＝z(x),a≤x≤b,y＝y(x),f＝f(x,y,z) twenty one z＝z(x),a≤x≤b,f＝f(x,y,z),y＝y(x) 10 a≤x≤b,y＝y(x),z＝z(x),f＝f(x,y,z) twenty two a≤x≤b,y＝y(x),f＝f(x,y,z),z＝z(x) 11 a≤x≤b,z＝z(x),y＝y(x),f＝f(x,y,z) twenty three a≤x≤b,z＝z(x),f＝f(x,y,z),y＝y(x) 12 a≤x≤b,f＝f(x,y,z),y＝y(x),z＝z(x) twenty four a≤x≤b,f＝f(x,y,z),z＝z(x),y＝y(x)

Accordingly, for the first-order curve integral model "f = f (x, y, z), x = x (y), z = z (y), c ≤ y ≤ d", the number of equivalent second-order curve integral models determined is M = 4! = 24. After adjusting the position of the second integral element, the 24 preset curve integral models are obtained, as shown in Table 4.

Table 4 Preset curve integral model corresponding to the first-level curve integral model “f＝f(x，y，z), x＝x(y), z＝z(y), c≤y≤d”

Accordingly, for the first-order curve integral model "f = f (x, y, z), x = x (z), y = y (z), p ≤ z ≤ q", the number of equivalent second-order curve integral models determined is M = 4! = 24. After adjusting the position of the second integral element, the 24 preset curve integral models are obtained, as shown in Table 5.

Table 5 Preset curve integral model corresponding to the first-level curve integral model “f＝f(x，y，z), x＝x(z), y＝y(z), p≤z≤q”

serial number Preset Curve Integration Model serial number Preset Curve Integration Model 1 f＝f(x,y,z),x＝x(z),y＝y(z),p≤z≤q 13 f＝f(x,y,z),x＝x(z),p≤z≤q,y＝y(z) 2 f＝f(x,y,z),y＝y(z),x＝x(z),p≤z≤q 14 f＝f(x,y,z),y＝y(z),p≤z≤q,x＝x(z) 3 f＝f(x,y,z),p≤z≤q,x＝x(z),y＝y(z) 15 f＝f(x,y,z),p≤z≤q,y＝y(z),x＝x(z) 4 x＝x(z),f＝f(x,y,z),y＝y(z),p≤z≤q 16 x＝x(z),f＝f(x,y,z),p≤z≤q,y＝y(z) 5 x＝x(z),y＝y(z),f＝f(x,y,z),p≤z≤q 17 x＝x(z),y＝y(z),p≤z≤q,f＝f(x,y,z) 6 x＝x(z),p≤z≤q,f＝f(x,y,z),y＝y(z) 18 x＝x(z),p≤z≤q,y＝y(z),f＝f(x,y,z) 7 y＝y(z),x＝x(z),f＝f(x,y,z),p≤z≤q 19 y＝y(z),x＝x(z),p≤z≤q,f＝f(x,y,z) 8 y＝y(z),f＝f(x,y,z),x＝x(z),p≤z≤q 20 y＝y(z),f＝f(x,y,z),p≤z≤q,x＝x(z) 9 y＝y(z),p≤z≤q,x＝x(z),f＝f(x,y,z) twenty one y＝y(z),p≤z≤q,f＝f(x,y,z),x＝x(z) 10 p≤z≤q,x＝x(z),y＝y(z),f＝f(x,y,z) twenty two p≤z≤q,x＝x(z),f＝f(x,y,z),y＝y(z) 11 p≤z≤q,y＝y(z),x＝x(z),f＝f(x,y,z) twenty three p≤z≤q,y＝y(z),f＝f(x,y,z),x＝x(z) 12 p≤z≤q,f＝f(x,y,z),x＝x(z),y＝y(z) twenty four p≤z≤q,f＝f(x,y,z),y＝y(z),x＝x(z)

Accordingly, for the first-order curve integral model "f = f (x, y, z), x = x (t), y = y (t), z = z (t), α ≤ t ≤ β", the number of equivalent second-order curve integral models determined is M = 5! = 120. After adjusting the position of the second integral element, the 120 preset curve integral models are obtained, as shown in Table 6.

Table 6 Preset curve integral model corresponding to the first-level curve integral model “f＝f(x，y，z), x＝x(t), y＝y(t), z＝z(t), α≤t≤β”

It should be understood that only 280 specific preset curve integral models are given in Tables 1 to 6, which do not constitute any limitation on the technical solution of the present invention. In practical applications, technicians in this field can modify the preset curve integral models in Tables 1 to 6 according to actual needs, and no limitation is made here.

It is not difficult to find from the above description that the curve integral calculation method for arc length provided in this embodiment, before executing the step of determining the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model, compares the curve integral model determined according to the integral data input by the user with any preset curve integral model in the pre-built curve integral model library storing 280 preset curve integral models. When it is determined that there is a preset curve integral model in the curve integral model library that is the same as the currently determined curve integral model, the operation of determining the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model is executed. Otherwise, an error prompt is directly given to the user, so that the user can modify the provided integral data according to the error prompt. In this way, not only the calculation of the integral result of the curve integral of the arc length is realized, but also the calculation scheme of the curve integral of the arc length is complete and fault-tolerant, which greatly improves the user experience.

In addition, an embodiment of the present invention further proposes a computer-readable storage medium, on which a curve integral calculation program for arc length is stored. When the curve integral calculation program for arc length is executed by a processor, the steps of the curve integral calculation method for arc length as described above are implemented.

4, which is a structural block diagram of a first embodiment of a curve integral calculation device for arc length according to the present invention.

As shown in FIG. 4 , the curve integral calculation device for arc length proposed in the embodiment of the present invention includes: an extraction module 4001 , a first determination module 4002 , a second determination module 4003 and a calculation module 4004 .

Among them, the extraction module 4001 is used to obtain the integral data corresponding to the curve integral of the arc length to be calculated, and extract at least two first integral elements and the value range corresponding to the first integral elements from the integral data; the first determination module 4002 is used to determine the curve integral model corresponding to the curve integral of the arc length according to the first integral elements; the second determination module 4003 is used to determine the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model; the calculation module 4004 is used to calculate the integral result corresponding to the curve integral of the arc length according to the value range corresponding to the first integral element and the integral calculation formula.

It is not difficult to find from the above description that the curve integral calculation device for arc length provided in this embodiment, when calculating the integral result of the curve integral for arc length, obtains the integral data corresponding to the curve integral for arc length, extracts the first integral element related to the curve integral for arc length currently to be calculated and the value range corresponding to each first integral element from the integral data, and then determines the curve integral model corresponding to the curve integral for arc length currently to be calculated according to the extracted first integral element, and then determines the integral calculation formula corresponding to the curve integral for the arc length according to the determined curve integral model, and finally automatically calculates the integral result of the curve integral for the arc length according to the value range corresponding to each first integral element and the determined integral calculation formula. Since the process of determining the curve integral model corresponding to the curve integral for the arc length is based on the extracted first integral element, rather than directly based on the integral data provided by the user, the format of the integral data provided by the user is not limited to conform to the 14 existing native curve integral models, so that the user can provide integral data according to his own input habits, thereby greatly facilitating the use of the user, and effectively solving the technical problem that the curve integral calculation method for arc length in the prior art is too single and cannot meet the actual needs of the user.

It should be noted that the workflow described above is merely illustrative and does not limit the scope of protection of the present invention. In practical applications, technicians in this field can select part or all of them according to actual needs to achieve the purpose of the present embodiment, and no limitation is made here.

In addition, for technical details not fully described in this embodiment, reference may be made to the curve integral calculation method for arc length provided in any embodiment of the present invention, and will not be repeated here.

In addition, it should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or system. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or system including the element.

The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which is stored in a storage medium (such as a read-only memory (ROM)/RAM, a magnetic disk, or an optical disk), and includes a number of instructions for a terminal device (which can be a mobile phone, a computer, a server, or a network device, etc.) to execute the methods described in each embodiment of the present invention.

The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims (8)

1. A method for calculating the curve integral of arc length, characterized in that the method comprises: Obtaining integral data corresponding to the curve integral of the arc length to be calculated, and extracting at least two first integral elements and value ranges corresponding to the first integral elements from the integral data; Determining a curve integral model corresponding to the curve integral of the arc length according to the first integral element; Determine, according to the curve integral model, an integral calculation formula corresponding to the curve integral of the arc length; Calculate the integral result corresponding to the curve integral of the arc length according to the value range corresponding to the first integral element and the integral calculation formula; The step of extracting at least two first integral elements and the value ranges corresponding to the first integral elements from the integral data comprises: According to a preset correspondence table, the integral data is converted into a character string to obtain a character string to be processed; According to a preset illegal character table, illegal characters in the character string to be processed are filtered to obtain a target character string; Extracting at least two first integral elements and value ranges corresponding to the first integral elements from the target character string; The first integral element includes an integral arc element and a coordinate element; The step of calculating the integral result corresponding to the curve integral of the arc length according to the value range corresponding to the first integral element and the integral calculation formula includes: Determine the upper and lower limits of the integral according to the value range corresponding to the integral arc segment element; Determining the arc differential according to the value range corresponding to the coordinate element; Substitute the integral upper and lower limits and the arc differential into the integral calculation formula to obtain a target integral calculation formula; According to the target integral calculation formula, the integral result corresponding to the curve integral of the arc length is calculated. 2. The method according to claim 1, characterized in that the step of determining the curve integral model corresponding to the curve integral of the arc length according to the first integral element comprises: Determining the position of each first integral element in the integral data; According to the order of the positions of the first integral elements in the integral data, the first integral elements are arranged in order, and a preset interval is set between two adjacent first integral elements to obtain the curve integral model corresponding to the curve integral of the arc length. 3. The method according to any one of claims 1 to 2, characterized in that before the step of determining the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model, the method further comprises: Determining whether the curve integration model is available; If the curve integral model is available, then performing the step of determining the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model; If the curve integral model is not available, an error prompt is given to the user, so that the user can modify the integral data according to the error prompt; Wherein, the step of determining whether the curve integral model is available comprises: Comparing the curve integral model with a preset curve integral model in a pre-built curve integral model library, and determining that the curve integral model is available if there is a preset curve integral model in the curve integral model library that is identical to the curve integral model; Otherwise, it is determined that the curve integration model is not applicable. 4. The method according to claim 3, characterized in that before the step of comparing the curve integral model with a preset curve integral model in a pre-built curve integral model library, the method further comprises: Acquire a predetermined primary curve integral model, and extract a second integral element included in the primary curve integral model; Adjusting the position of the second integral element in the primary curve integral model to obtain a secondary curve integral model equivalent to the primary curve integral model, wherein the secondary curve integral model includes the primary curve integral model; The secondary curve integral model is used as the preset curve integral model. 5. The method according to claim 4, characterized in that before the step of adjusting the position of the second integral element in the primary curve integral model to obtain a secondary curve integral model equivalent to the primary curve integral model, the method further comprises: Counting the number N of second integral elements included in the primary curve integral model, where N is an integer greater than or equal to 2; According to the number N, determining the number M of secondary curve integral models equivalent to the primary curve integral model, where M is an integer greater than or equal to N; Determining an adjustment rule of the primary curve integral model according to the number M and the second integral element; The step of adjusting the position of the second integral element in the primary curve integral model to obtain a secondary curve integral model equivalent to the primary curve integral model includes: According to the adjustment rule, the position of the second integral element in the primary curve integral model is adjusted to obtain M secondary curve integral models equivalent to the primary curve integral model. 6. A device for calculating the curve integral of arc length, characterized in that the device comprises: An extraction module, used to obtain integral data corresponding to the curve integral of the arc length to be calculated, and extract at least two first integral elements and a value range corresponding to the first integral elements from the integral data; A first determining module, configured to determine a curve integral model corresponding to the curve integral of the arc length according to the first integral element; A second determination module is used to determine the integral calculation formula corresponding to the curve integral of the arc length according to the curve integral model; A calculation module, used for calculating the integral result corresponding to the curve integral of the arc length according to the value range corresponding to the first integral element and the integral calculation formula; The extraction module is further used to convert the integral data into a character string according to a preset corresponding relationship table to obtain a character string to be processed; filter illegal characters in the character string to be processed according to a preset illegal character table to obtain a target character string; extract at least two first integral elements and a value range corresponding to the first integral elements from the target character string; The first integral element includes an integral arc element and a coordinate element; The calculation module is also used to determine the upper and lower limits of the integral according to the value range corresponding to the integral arc segment element; determine the arc differential according to the value range corresponding to the coordinate element; substitute the upper and lower limits of the integral and the arc differential into the integral calculation formula to obtain the target integral calculation formula; calculate the integral result corresponding to the curve integral of the arc length according to the target integral calculation formula. 7. A device for calculating the curve integral of arc length, characterized in that the device comprises: a memory, a processor, and a curve integral calculation program for arc length stored in the memory and executable on the processor, wherein the curve integral calculation program for arc length is configured to implement the steps of the curve integral calculation method for arc length as described in any one of claims 1 to 5. 8. A computer-readable storage medium, characterized in that a curve integral calculation program for arc length is stored on the computer-readable storage medium, and when the curve integral calculation program for arc length is executed by a processor, the steps of the curve integral calculation method for arc length as described in any one of claims 1 to 5 are implemented.

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