CN109903357B - Curve equation drawing method and device, terminal equipment and readable storage medium - Google Patents

Abstract

The invention discloses a curved surface equation drawing method, a curved surface equation drawing device, terminal equipment and a readable storage medium. Firstly, receiving a curved surface equation drawing instruction input by a user, extracting curved surface equation data from the drawing instruction, converting the curved surface equation data into character strings, acquiring position information of preset characters, acquiring position information of target numerical values by changing the position information of the preset characters, and finally, establishing a parameter equation according to the target numerical values, and drawing a curved surface according to the parameter equation. The invention designs a curved surface equation drawing device, which can draw a corresponding curved surface graph only by providing a curved surface equation for the device, improves the perception of a user on the curved surface graph, and improves the learning efficiency of the user on higher mathematics.

Description

Surface equation drawing method, device, terminal equipment and readable storage medium

Technical Field

The present invention relates to the field of mathematical computing technology, and in particular to a surface equation drawing method, device, terminal equipment and readable storage medium.

Background Art

With the development of mathematical algorithms, mathematical algorithms play an important role in more and more fields. Surface drawing is the premise and foundation for learning multiple integral algorithms, so it is very important to be able to draw general surface graphics. Surface drawing can improve people's perceptual understanding of surface graphics.

Currently, there is no device that can automatically draw surface graphics. The surface graphics of many comprehensive equations cannot be seen intuitively. When learning multiple integral algorithms, users do not have a deep enough intuitive understanding of the surface, and the progress of learning multiple integral algorithms will be greatly reduced.

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 method, device, terminal device and readable storage medium for drawing surface equations, aiming to solve the technical problem that the prior art cannot draw surface equations and verify the drawing effect of the drawer.

To achieve the above object, the present invention provides a method for drawing a surface equation, the method comprising the following steps:

When receiving a surface equation drawing instruction input by a user, extracting surface equation data from the drawing instruction;

Convert the surface equation data into a character string, and extract a target value from the character string;

A parametric equation is established according to the target value, and a surface is drawn according to the parametric equation.

Preferably, before converting the surface equation data into a character string and extracting the target value from the character string, the surface equation drawing method further includes:

Storing a preset relationship correspondence table in a preset storage area, wherein the preset relationship correspondence table includes a correspondence between surface equation data and character strings;

The converting the surface equation data into a character string and extracting a target value from the character string specifically includes:

The surface equation data is converted into a character string according to the preset relationship correspondence table, and a target value is extracted from the character string.

Preferably, converting the surface equation data into a character string according to the preset relationship correspondence table, and extracting the target value from the character string specifically includes:

Acquire the position information of the preset character in the character string according to the character string;

Extracting the numerical string corresponding to the preset character through the position information;

Acquire new location information through the preset program, and extract the numerical string of the new location information;

The target value is extracted from the value character string corresponding to the new position information.

Preferably, before obtaining the new position information through the preset program and extracting the numerical string of the new position information, the surface equation drawing method includes:

storing a preset program in a preset storage area, wherein the preset program obtains new position information by changing the position information;

The obtaining of new location information through the preset program and extracting a numerical string of the new location information specifically includes:

The position information is changed through the preset program to obtain new position information, and a numerical string of the new position information is extracted.

Preferably, the preset relationship correspondence table further includes: a correspondence between character strings and numerical values;

The step of extracting the target value from the numerical character string corresponding to the new position information specifically includes:

According to the preset corresponding relationship table, a target character string is extracted from the numerical character string corresponding to the new position information, and the target character string is converted into the target numerical value.

Preferably, when receiving a surface equation drawing instruction input by a user, before extracting the surface equation data from the drawing instruction, the surface equation drawing method includes:

storing a preset conversion program in a preset storage area, wherein the preset conversion program can convert the surface equation into surface equation data;

When receiving the surface equation drawing instruction input by the user, extracting the surface equation data from the drawing instruction specifically includes:

Extracting the surface equation in the surface equation instruction received from the user;

The surface equation is converted into surface equation data according to the preset conversion procedure.

Preferably, establishing a parametric equation according to the target value and drawing a surface according to the parametric equation specifically includes:

Establishing a parametric equation about a coordinate system according to the target value;

The parameter equation is converted into a surface drawing instruction, and the surface is drawn according to the surface drawing instruction.

In addition, to achieve the above object, the present invention also provides a surface equation drawing device, the device comprising:

An acquisition module, configured to extract surface equation data from a drawing instruction input by a user when receiving the surface equation drawing instruction;

A calculation module, used for converting the surface equation data into a character string and extracting a target value from the character string;

A drawing module is used to establish a parametric equation according to the target value and draw a surface according to the parametric equation.

In addition, to achieve the above-mentioned purpose, the present invention also proposes a terminal device, which includes: a memory, a processor, and a surface equation drawing program stored in the memory and runnable on the processor, and the surface equation drawing program is configured to implement the steps of the surface equation drawing method described above.

In addition, to achieve the above-mentioned purpose, the present invention also proposes a readable storage medium, which is a computer-readable storage medium, and a surface equation drawing program is stored on the computer-readable storage medium. When the surface equation drawing program is executed by the processor, the steps of the surface equation drawing method are implemented.

The present invention discloses a surface equation drawing method, device, terminal device and readable storage medium. The present invention first receives a surface equation drawing instruction input by a user, extracts surface equation data from the drawing instruction, then converts the surface equation data into a character string, obtains the position information of a preset character, and obtains the position information of a target value by changing the position information of the preset character, and finally establishes a parametric equation according to the target value, and draws a surface according to the parametric equation. The present invention designs a surface equation drawing device, which can draw the corresponding surface graphics as long as a surface equation is provided to the device, thereby improving the user's perceptual understanding of the surface graphics, and also improving the user's learning efficiency of advanced mathematics.

BRIEF DESCRIPTION OF THE DRAWINGS

1 is a schematic diagram of the structure of a terminal device 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 drawing a surface equation according to the present invention;

FIG3 is a schematic flow chart of a second embodiment of a method for drawing a surface equation according to the present invention;

FIG. 4 is a schematic diagram of functional modules of the first embodiment of the surface equation drawing method of 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 terminal device in a hardware operating environment according to an embodiment of the present invention.

As shown in FIG1 , the terminal device 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. Among them, 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 terminal device, and in actual applications the terminal device 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 drawing program for a surface equation.

In the terminal device shown in FIG1 , the network interface 1004 is mainly used to establish a communication connection between the terminal device and a server storing all data required in the surface equation drawing method system; the user interface 1003 is mainly used to interact with the user for data; the terminal device calls the surface equation drawing program stored in the memory 1005 through the processor 1001, and performs the following operations:

When receiving a surface equation drawing instruction input by a user, extracting surface equation data from the drawing instruction;

Convert the surface equation data into a character string, and extract a target value from the character string;

A parametric equation is established according to the target value, and a surface is drawn according to the parametric equation.

Further, the processor 1001 may call a drawing program of a surface equation stored in the memory 1005, and perform the following operations:

Storing a preset relationship correspondence table in a preset storage area, wherein the preset relationship correspondence table includes a correspondence between surface equation data and character strings;

The converting the surface equation data into a character string and extracting a target value from the character string specifically includes:

The surface equation data is converted into a character string according to the preset relationship correspondence table, and a target value is extracted from the character string.

Further, the processor 1001 may call a drawing program of a surface equation stored in the memory 1005, and perform the following operations:

Acquire the position information of the preset character in the character string according to the character string;

Extracting the numerical string corresponding to the preset character through the position information;

Acquire new location information through the preset program, and extract the numerical string of the new location information;

The target value is extracted from the value character string corresponding to the new position information.

Further, the processor 1001 may call a drawing program of a surface equation stored in the memory 1005, and perform the following operations:

storing a preset program in a preset storage area, wherein the preset program obtains new position information by changing the position information;

The obtaining of new location information through the preset program and extracting a numerical string of the new location information specifically includes:

The position information is changed through the preset program to obtain new position information, and a numerical string of the new position information is extracted.

Further, the processor 1001 may call a drawing program of a surface equation stored in the memory 1005, and perform the following operations:

According to the preset corresponding relationship table, a target character string is extracted from the numerical character string corresponding to the new position information, and the target character string is converted into the target numerical value.

Further, the processor 1001 may call a drawing program of a surface equation stored in the memory 1005, and perform the following operations:

storing a preset conversion program in a preset storage area, wherein the preset conversion program can convert the surface equation into surface equation data;

When receiving the surface equation drawing instruction input by the user, extracting the surface equation data from the drawing instruction specifically includes:

Extracting the surface equation in the surface equation instruction received from the user;

The surface equation is converted into surface equation data according to the preset conversion procedure.

Further, the processor 1001 may call a drawing program of a surface equation stored in the memory 1005, and perform the following operations:

Establishing a parametric equation about a coordinate system according to the target value;

The parameter equation is converted into a surface drawing instruction, and the surface is drawn according to the surface drawing instruction.

Through the above scheme, this embodiment first receives the surface equation drawing instruction input by the user, extracts the surface equation data from the drawing instruction, then converts the surface equation data into a character string, obtains the position information of the preset character, and obtains the position information of the target value by changing the position information of the preset character, and finally establishes a parametric equation according to the target value, and draws the surface according to the parametric equation. This embodiment designs a surface equation drawing device, which can draw the corresponding surface graphics as long as a surface equation is provided to the device, thereby improving the user's perceptual understanding of the surface graphics, and also improving the user's learning efficiency of advanced mathematics.

The present invention is implemented based on the above hardware structure and proposes an embodiment of the method for drawing a surface equation of the present invention.

2 , which is a flow chart of a first embodiment of a method for drawing a surface equation according to the present invention.

In this embodiment, the surface equation drawing method includes the following steps:

S10: When receiving a surface equation drawing instruction input by a user, extracting surface equation data from the drawing instruction.

It is understandable that the surface equation data may be input manually by a user or data outputted from the system and waiting for further processing. In this embodiment, the surface equation data is input by a user, and the surface equation data is the surface equation to be drawn.

S20: Convert the surface equation data into a character string, and extract a target value from the character string.

Accordingly, before performing this step, the preset relationship correspondence table and the preset program need to be stored in the preset storage area. The preset relationship correspondence table includes the correspondence between the surface equation data and the character string, and the correspondence between the character string and the numerical value. The preset program obtains new position information by changing the position information of the preset characters.

In addition, in a specific embodiment, this embodiment traverses a preset storage area, and then converts the surface equation data into a character string according to the preset relationship correspondence table, and then extracts the position information of the preset characters from the character string, uses the preset program to obtain new position information from the position information, and extracts the character string of the new position information as a numerical character string, and converts the numerical character string into a numerical value.

That is, the surface equation data is converted into a character string, and the target value is extracted from the character string, specifically including:

The position information of the preset character in the character string is obtained according to the character string, the numerical string corresponding to the preset character is extracted through the position information, new position information is obtained through the preset rule, and the numerical string of the new position information is extracted, and the target numerical value is extracted from the numerical string corresponding to the new position information.

S30: Establishing a parametric equation according to the target value, and drawing a surface according to the parametric equation.

It should be understood that in step S10, the surface equation involved in drawing the surface equation has been obtained, and now it is only necessary to extract the required data from the surface equation; in step S20, the target value required for establishing the surface parametric equation is obtained through the preset correspondence table and the preset program; therefore, step S30 directly establishes the surface parametric equation according to the target value, and draws the corresponding surface according to the parametric equation.

In addition, in a specific embodiment, before drawing the surface graphics, it is also necessary to determine the value range of the parameters of the surface parameter equation, and convert the surface parameter equation into a drawing command, and finally draw through the drawing command.

In order to better understand the surface equation drawing method provided by the present invention, the following is a specific description:

1. Draw the graph corresponding to the equation of the elliptical cone.

对应的椭圆锥面，则需要输入的曲面方程为字符s＝'x^2/a^2+y^2/b^2＝z^2/c^2'。Suppose you want to draw the equation of an elliptical cone

For the corresponding elliptical cone, the surface equation that needs to be input is the characters s='x^2/a^2+y^2/b^2=z^2/c^2'.

The specific method to separate a, b, and c from the input string is as follows:

(1) Find the positions s ₁ , s ₂ and s ₃ of the three slashes '/' in the string;

(2) Extract the numerical string corresponding to position s ₁ +1 to position s ₂ -5 from the string;

(3) Convert the numerical string obtained in step (2) into the numerical value sa;

(4) Find

(5) Extract the numerical string corresponding to position s ₂ +1 to position s ₃ -5 from the string;

(6) Convert the numerical string obtained in step (5) into the numerical value sb;

(7) Find

(8) Extract the numerical string corresponding to position s ₃ +1 to position n from the string, where n is the length of the surface equation string;

(9) Convert the numerical string obtained in step (8) into the numerical value sc;

(10) Find

The parametric equations for establishing the elliptical cone are as follows:

其中u∈[-max{a,b,c},max{a,b,c}]和v∈[0,2π]；

where u∈[-max{a,b,c},max{a,b,c}] and v∈[0,2π];

The surface corresponding to the surface equation is drawn by the drawing command draw(a*u*cos(v), b*u*sin(v), c*u, [-tmp, tmp, 0, 2*pi]). Here tmp = max{a, b, c}.

和

的图形。In a similar way, we can draw an ellipse

and

Graphics.

2. Draw the graph corresponding to the equation of the ellipsoid.

对应的椭球面，则需要输入的曲面方程为字符串s＝'x^2/a^2+y^2/b^2+z^2/c^2＝d^2'。Suppose you want to draw the equation of the ellipsoid

For the corresponding ellipsoid, the surface equation that needs to be input is the string s = 'x^2/a^2+y^2/b^2+z^2/c^2=d^2'.

The specific method to separate a, b, and c from the input string is as follows:

(1) Find the positions s ₁ , s ₂ and s ₃ of the three slashes '/' in the string;

(2) Extract the numerical string corresponding to position s ₁ +1 to position s ₂ -5 from the string;

(3) Convert the numerical string obtained in step (2) into the numerical value sa;

(4) Find

(5) Extract the numerical string corresponding to position s ₂ +1 to position s ₃ -5 from the string;

(6) Convert the numerical string obtained in step (5) into the numerical value sb;

(7) Find

(8) Find the position loc of the three slashes ‘=’ in the string;

(9) Take out the numerical string corresponding to the position s ₃ +1 to the position loc-1 from the string;

(10) Convert the numerical string obtained in step (9) into the numerical value sc;

(11) Find

(12) Extract the numerical string corresponding to the position loc+1 to the position n from the string, where n is the length of the surface equation string;

(13) Convert the numerical string obtained in step (12) into a numerical value sd;

(14) Find

The parametric equations for establishing the ellipsoid are as follows:

其中u∈[0,π]和v∈[0,2π]；

where u∈[0,π] and v∈[0,2π];

The surface corresponding to the surface equation is drawn using the drawing command draw(a*d*sin(u)*sin(v), b*d*sin(u)*cos(v), c*d*cos(u), [0, pi, 0, 2*pi]).

3. Draw the graph corresponding to the equation of a single-leaf hyperboloid.

对应的单叶双曲面，则需要输入的曲面方程为字符串s＝'x^2/a^2+y^2/b^2-z^2/c^2＝d^2'。Suppose you want to plot the equation of a single leaf hyperboloid

For the corresponding single-leaf hyperboloid, the surface equation that needs to be input is the string s='x^2/a^2+y^2/b^2-z^2/c^2=d^2'.

The specific method to separate a, b, and c from the input string is as follows:

(1) Find the positions s ₁ , s ₂ and s ₃ of the three slashes '/' in the string;

(2) Extract the numerical string corresponding to position s ₁ +1 to position s ₂ -5 from the string;

(3) Convert the numerical string obtained in step (2) into the numerical value sa;

(4) Find

(5) Extract the numerical string corresponding to position s ₂ +1 to position s ₃ -5 from the string;

(6) Convert the numerical string obtained in step (5) into the numerical value sb;

(7) Find

(8) Find the position loc of the three slashes ‘=’ in the string;

(9) Take out the numerical string corresponding to the position s ₃ +1 to the position loc-1 from the string;

(10) Convert the numerical string obtained in step (9) into the numerical value sc;

(11) Find

(12) Extract the numerical string corresponding to the position loc+1 to the position n from the string, where n is the length of the surface equation string;

(13) Convert the numerical string obtained in step (12) into a numerical value sd;

(14) Find

The parametric equations for establishing a single-leaf hyperboloid are as follows:

其中

和v∈[0,2π]；

in

and v∈[0,2π];

The surface corresponding to the surface equation is drawn using the drawing command draw(a*d*sec(u)*sin(v), b*d*sec(u)*cos(v), c*d*tan(u), [-pi/3, pi/3, 0, 2*pi]).

和

的图形。A similar method can be used to draw a single leaf hyperbolic surface

and

Graphics.

4. Draw the graph corresponding to the equation of the double-leaf hyperboloid.

对应的单叶双曲面，则需要输入的曲面方程为字符串s＝'x^2/a^2-y^2/b^2-z^2/c^2＝d^2'。Suppose you want to plot the equation of a two-leaf hyperboloid

For the corresponding single-leaf hyperboloid, the surface equation that needs to be input is the string s='x^2/a^2-y^2/b^2-z^2/c^2=d^2'.

The specific method to separate a, b, and c from the input string is as follows:

(1) Find the positions s ₁ , s ₂ and s ₃ of the three slashes '/' in the string;

(2) Extract the numerical string corresponding to position s ₁ +1 to position s ₂ -5 from the string;

(3) Convert the numerical string obtained in step (2) into the numerical value sa;

(4) Find

(5) Extract the numerical string corresponding to position s ₂ +1 to position s ₃ -5 from the string;

(6) Convert the numerical string obtained in step (5) into the numerical value sb;

(7) Find

(8) Find the position loc of the three slashes ‘=’ in the string;

(9) Take out the numerical string corresponding to the position s ₃ +1 to the position loc-1 from the string;

(10) Convert the numerical string obtained in step (9) into the numerical value sc;

(11) Find

(12) Extract the numerical string corresponding to the position loc+1 to the position n from the string, where n is the length of the surface equation string;

(13) Convert the numerical string obtained in step (12) into a numerical value sd;

(14) Find

The parametric equations for establishing the double-leaf hyperboloid are as follows:

其中

和v∈[0,2π]；

in

and v∈[0,2π];

The surface corresponding to the surface equation is drawn using the drawing command draw(a*d*tan(u)*cos(v), b*d*tan(u)*sin(v), c*d*sec(u), [-pi/2, 3*pi/2, 0, 2*pi]).

和

的图形。A similar method can be used to draw a double-leaf hyperbolic surface

and

Graphics.

5. Draw the graph corresponding to the equation of the elliptic parabola.

对应的椭圆抛物面，则需要输入的曲面方程为字符串s＝'x^2/a^2+y^2/b^2＝z/c'。Suppose you want to plot the equation of an elliptical parabola

For the corresponding elliptical paraboloid, the surface equation that needs to be input is the string s='x^2/a^2+y^2/b^2=z/c'.

The specific method to separate a, b, and c from the input string is as follows:

(1) Find the positions s ₁ , s ₂ and s ₃ of the three slashes '/' in the string;

(2) Extract the numerical string corresponding to position s ₁ +1 to position s ₂ -5 from the string;

(3) Convert the numerical string obtained in step (2) into the numerical value sa;

(4) Find

(5) Extract the numerical string corresponding to position s ₂ +1 to position s ₃ -5 from the string;

(6) Convert the numerical string obtained in step (5) into the numerical value sb;

(7) Find

(8) Extract the numerical string corresponding to position s ₃ +1 to position n from the string, where n is the length of the surface equation string;

(9) Convert the numeric string obtained in step (8) into the numeric value c;

The parametric equations for the elliptical parabola are as follows:

其中u∈[0,max{a,b,c}]和v∈[0,2π]；

where u∈[0,max{a,b,c}] and v∈[0,2π];

The surface corresponding to the surface equation is drawn by the drawing command draw(a*sqrt(u)*cos(v), b*sqrt(u)*sin(v), c*u, [0, tmp, 0, 2*pi]). Here tmp = max{a, b, c}.

和

的图形。A similar method can be used to draw a double-leaf hyperbolic surface

and

Graphics.

6. Draw the graph corresponding to the equation of the hyperbolic parabola.

对应的双曲抛物面，则需要输入的曲面方程为字符串s＝'x^2/a^2-y^2/b^2＝z/c'。Suppose you want to plot the equation of a hyperbolic parabola

For the corresponding hyperbolic paraboloid, the surface equation that needs to be input is the string s='x^2/a^2-y^2/b^2=z/c'.

The specific method to separate a, b, and c from the input string is as follows:

(1) Find the positions s ₁ , s ₂ and s ₃ of the three slashes '/' in the string;

(2) Extract the numerical string corresponding to position s ₁ +1 to position s ₂ -5 from the string;

(3) Convert the numerical string obtained in step (2) into the numerical value sa;

(4) Find

(5) Extract the numerical string corresponding to position s ₂ +1 to position s ₃ -5 from the string;

(6) Convert the numerical string obtained in step (5) into the numerical value sb;

(7) Find

(8) Extract the numerical string corresponding to position s ₃ +1 to position n from the string, where n is the length of the surface equation string;

(9) Convert the numeric string obtained in step (8) into the numeric value c;

The parametric equations for the hyperbolic paraboloid are as follows:

其中u∈[-1,1]和v∈[-1,1]；

where u∈[-1,1] and v∈[-1,1];

The surface corresponding to the surface equation is drawn using the drawing command draw(a*(u+v), b*(u-v), c*4*u*v, [-1, 1, -1, 1]).

和

的图形。A similar method can be used to draw a hyperbolic parabola

and

Graphics.

7. Draw the graph corresponding to the equation of the elliptical cylinder.

对应的椭圆柱面，则需要输入的曲面方程为字符串s＝'x^2/a^2+y^2/b^2＝c^2'。Suppose you want to draw the equation of an elliptical cylinder

For the corresponding elliptical cylinder, the surface equation that needs to be input is the string s='x^2/a^2+y^2/b^2=c^2'.

The specific method to separate a, b, and c from the input string is as follows:

(1) Find the positions s ₁ , s ₂ of the three slashes '/' in the string;

(2) Extract the numerical string corresponding to position s ₁ +1 to position s ₂ -5 from the string;

(3) Convert the numerical string obtained in step (2) into the numerical value sa;

(4) Find

(5) Find the position loc of the three slashes ‘=’ in the string;

(6) Take out the numerical string corresponding to the position s ₂ +1 to the position loc-1 from the string, where n is the length of the surface equation string;

(7) Convert the numeric string obtained in step (6) into a numeric value sb;

(8) Find

(9) Extract the numerical string corresponding to the position loc+1 to the position n from the string, where n is the length of the surface equation string;

(10) Convert the numerical string obtained in step (9) into the numerical value sc;

(11) Find

The parametric equations for establishing the elliptical cylinder are as follows:

其中v∈[-max{a,b,c},max{a,b,c}]和u∈[0,2π]；

where v∈[-max{a,b,c},max{a,b,c}] and u∈[0,2π];

The surface corresponding to the surface equation is drawn by the drawing command draw(a*cos(u), b*sin(u), c+v, [0, 2*pi, -tmp, tmp]). Here tmp = max{a, b, c}.

和

的图形。In a similar way, we can draw an elliptical cylinder

and

Graphics.

8. Draw the graph corresponding to the equation of the hyperbolic cylinder.

对应的双曲柱面，则需要输入的曲面方程为字符串s＝'x^2/a^2-y^2/b^2＝c^2'。Suppose you want to plot the equation of a hyperbolic cylinder

For the corresponding hyperbolic cylinder, the surface equation that needs to be input is the string s = 'x^2/a^2-y^2/b^2=c^2'.

The specific method to separate a, b, and c from the input string is as follows:

(1) Find the positions s ₁ , s ₂ of the three slashes '/' in the string;

(2) Extract the numerical string corresponding to position s ₁ +1 to position s ₂ -5 from the string;

(3) Convert the numerical string obtained in step (2) into the numerical value sa;

(4) Find

(5) Find the position loc of the three slashes ‘=’ in the string;

(6) Take out the numerical string corresponding to the position s ₂ +1 to the position loc-1 from the string, where n is the length of the surface equation string;

(7) Convert the numerical string obtained in step (6) into the numerical value sb;

(8) Find

(9) Extract the numerical string corresponding to the position loc+1 to the position n from the string, where n is the length of the surface equation string;

(10) Convert the numerical string obtained in step (9) into the numerical value sc;

(11) Find

The parametric equations for the hyperbolic cylinder are as follows:

其中v∈[-3max{a,b,c},3max{a,b,c}]和u∈[0,2π]；

where v∈[-3max{a,b,c},3max{a,b,c}] and u∈[0,2π];

The surface corresponding to the surface equation is drawn by the drawing command draw(a*sec(u), b*tan(u), c+v, [0, 2*pi, -3*tmp, 3*tmp]). Here tmp = max{a, b, c}.

和

的图形。A similar method can be used to draw a hyperbolic cylinder

and

Graphics.

9. Draw the graph corresponding to the equation of the parabolic cylinder.

对应的抛物柱面，则需要输入的曲面方程为字符串s＝'x^2/a^2＝y/b'。Suppose you want to plot the equation of a parabolic cylinder

For the corresponding parabolic cylinder, the surface equation that needs to be input is the string s='x^2/a^2=y/b'.

The specific method to separate a, b, and c from the input string is as follows:

(1) Find the positions s ₁ , s ₂ of the three slashes '/' in the string;

(2) Extract the numerical string corresponding to position s ₁ +1 to position s ₂ -3 from the string;

(3) Convert the numerical string obtained in step (2) into the numerical value sa;

(4) Find

(5) Take out the numerical string corresponding to position s ₂ +1 to position n from the string, where n is the length of the surface equation string;

(6) Convert the numeric string obtained in step (5) into the numeric value b;

The parametric equations for the parabolic cylinder are as follows:

其中u∈[-max{a,b,c},max{a,b,c}]和v∈[-max{a,b,c},max{a,b,c}]；

where u∈[-max{a,b,c},max{a,b,c}] and v∈[-max{a,b,c},max{a,b,c}];

The surface corresponding to the surface equation is drawn by the drawing command draw(u,b/a^2*u^2,v,[-tmp,tmp,-tmp,tmp]). Here tmp＝max{a,b,c}.

和

的图形。A similar method can be used to draw a parabola

and

Graphics.

It should be noted that the above is only an example and does not constitute any limitation to the technical solution of the present application.

It is not difficult to find from the above description that the surface equation drawing method provided in this embodiment first receives the surface equation drawing instruction input by the user, extracts the surface equation data from the drawing instruction, and then converts the surface equation data into a character string, obtains the position information of the preset character, and obtains the position information of the target value by changing the position information of the preset character, and finally establishes a parametric equation according to the target value, and draws the surface according to the parametric equation. The present invention designs a surface equation drawing device, which can draw the corresponding surface graphics as long as a surface equation is provided to the device, thereby improving the user's perceptual understanding of the surface graphics, and also improving the user's learning efficiency of higher mathematics.

Furthermore, as shown in FIG3 , a second embodiment of the method for drawing a surface equation of the present invention is proposed based on the first embodiment. In this embodiment, before establishing a parametric equation according to the target value and drawing the surface according to the parametric equation, it is also necessary to convert the surface equation data into a character string, extract position information from the character string, obtain new position information based on the position information, extract the corresponding numerical character string through the new position information, and convert the numerical character string into the target value, see steps S20 and S20' in FIG3 for details.

For ease of understanding, the following is a specific description in conjunction with FIG3:

In step S20: the surface equation data is converted into a character string, and the position information is extracted from the character string.

The extracted surface equation is converted into a character string, a preset character is found in the character string according to a correspondence table between the surface equation and the character string in a storage area, and position information corresponding to the preset character is extracted according to the preset character.

It can be understood that for the character string converted from the surface equation, the fixed parameters of the surface equation such as a, b, c are generally separated from the character string, and ‘/’ is needed in the character string to represent the division operation in the surface equation. Therefore, the preset character is generally the ‘/’ character in the character string, and the position information of the ‘/’ character also needs to be obtained.

Correspondingly, in step S20': new position information is acquired according to the position information, a corresponding numerical string is extracted through the new position information, and the numerical string is converted into a target numerical value.

The preset character position information in the character string is changed by a preset program in the storage area to obtain new position information, a numerical string corresponding to the new position information is proposed based on the new position information, and the numerical string is converted into characters. The preset program can obtain new position information by changing the position information of the characters.

It can be understood that, in actual operation, what needs to be obtained is the numerical value of the fixed parameter of the surface equation. The parametric equation of the surface equation can be obtained through the numerical value of the fixed parameter, and finally the corresponding surface graphics can be drawn by the parametric equation through drawing instructions. Therefore, the new position information is obtained through the position information, that is, the position information of the fixed parameters of the surface equation is obtained by changing the position information through the preset program and serving as the new position information, and then the numerical string corresponding to the new position information is extracted according to the new position information, and the numerical string is converted into the target numerical value according to the correspondence between the string and the numerical value in the preset storage area.

In addition, the embodiment of the present invention further provides a device for drawing a surface equation. As shown in FIG4 , the device for drawing a surface equation includes: an acquisition module 10 , a calculation module 20 , and a drawing module 30 .

Among them, the acquisition module 10 is used to extract surface equation data from the drawing instruction when receiving the surface equation drawing instruction input by the user; the calculation module 20 is used to convert the surface equation data into a character string and extract the target value from the character string; the drawing module 30 is used to establish a parametric equation according to the target value and draw the surface according to the parametric equation.

It should be noted that the preset storage area mentioned in this embodiment mainly stores the correspondence between surface equation data and character strings, the correspondence between character strings and numerical values, and preset programs.

It is not difficult to find from the above description that the surface equation drawing method provided in this embodiment first receives the surface equation drawing instruction input by the user, extracts the surface equation data from the drawing instruction, and then converts the surface equation data into a character string, obtains the position information of the preset character, and obtains the position information of the target value by changing the position information of the preset character, and finally establishes a parametric equation according to the target value, and draws the surface according to the parametric equation. The present invention designs a surface equation drawing device, which can draw the corresponding surface graphics as long as a surface equation is provided to the device, thereby improving the user's perceptual understanding of the surface graphics, and also improving the user's learning efficiency of higher mathematics.

In addition, it should be noted that the device embodiments described above are merely illustrative and do not limit the scope of protection of the present invention. In practical applications, technicians in this field can select some or all of the modules according to actual needs to achieve the purpose of the present embodiment, and no restrictions are made here.

In addition, for technical details not fully described in this embodiment, reference can be made to the method for drawing the surface equation provided in any embodiment of the present invention, and will not be repeated here.

In addition, an embodiment of the present invention further provides a readable storage medium, which is a computer-readable storage medium, and on which a drawing program for a surface equation is stored. When the drawing program for the surface equation is executed by a processor, the following operations are implemented:

When receiving a surface equation drawing instruction input by a user, extracting surface equation data from the drawing instruction;

Convert the surface equation data into a character string, and extract a target value from the character string;

A parametric equation is established according to the target value, and a surface is drawn according to the parametric equation.

Furthermore, when the surface equation drawing program is executed by the processor, the following operations are also implemented:

Storing a preset relationship correspondence table in a preset storage area, wherein the preset relationship correspondence table includes a correspondence between surface equation data and character strings, and a correspondence between character strings and numerical values;

The converting the surface equation data into a character string and extracting a target value from the character string specifically includes:

The surface equation data is converted into a character string according to the preset relationship correspondence table, and a target value is extracted from the character string.

Furthermore, when the surface equation drawing program is executed by the processor, the following operations are also implemented:

Acquire the position information of the preset character in the character string according to the character string;

Extracting the numerical string corresponding to the preset character through the position information;

Acquire new location information through the preset program, and extract the numerical string of the new location information;

The target value is extracted from the value character string corresponding to the new position information.

Furthermore, when the surface equation drawing program is executed by the processor, the following operations are also implemented:

storing a preset program in a preset storage area, wherein the preset program obtains new position information by changing the position information;

The obtaining of new location information through the preset program and extracting a numerical string of the new location information specifically includes:

The position information is changed through the preset program to obtain new position information, and a numerical string of the new position information is extracted.

Furthermore, when the surface equation drawing program is executed by the processor, the following operations are also implemented:

According to the preset corresponding relationship table, a target character string is extracted from the numerical character string corresponding to the new position information, and the target character string is converted into the target numerical value.

Furthermore, when the surface equation drawing program is executed by the processor, the following operations are also implemented:

storing a preset conversion program in a preset storage area, wherein the preset conversion program can convert the surface equation into surface equation data;

Extracting the surface equation in the surface equation instruction received from the user;

The surface equation is converted into surface equation data according to the preset conversion procedure.

Furthermore, when the surface equation drawing program is executed by the processor, the following operations are also implemented:

Establishing a parametric equation about a coordinate system according to the target value;

The parameter equation is converted into a surface drawing instruction, and the surface is drawn according to the surface drawing instruction.

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 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, 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/random access memory, a magnetic disk, or an optical disk), and includes a number of instructions for enabling a terminal device (which can be a mobile phone, a computer, a server, an air conditioner, 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 drawing a surface equation, characterized in that the method for drawing a surface equation comprises the following steps: When receiving a surface equation drawing instruction input by a user, extracting surface equation data from the drawing instruction; Convert the surface equation data into a character string, and extract a target value from the character string; Establishing a parametric equation according to the target value, and drawing a surface according to the parametric equation; Wherein, before converting the surface equation data into a character string and extracting the target value from the character string, the surface equation drawing method further includes: Storing a preset relationship correspondence table in a preset storage area, wherein the preset relationship correspondence table includes a correspondence between surface equation data and character strings; The converting the surface equation data into a character string and extracting a target value from the character string specifically includes: Acquire position information of a preset character in the character string according to the character string; Extracting the numerical string corresponding to the preset character through the position information; Acquire new location information through a preset program, and extract a numerical string of the new location information; The target value is extracted from the value character string corresponding to the new position information. 2. The surface equation drawing method according to claim 1, characterized in that before obtaining the new position information through a preset program and extracting the numerical string of the new position information, the surface equation drawing method comprises: storing a preset program in a preset storage area, wherein the preset program obtains new position information by changing the position information; The obtaining of new location information through a preset program and extracting a numerical string of the new location information specifically includes: The position information is changed through the preset program to obtain new position information, and a numerical string of the new position information is extracted. 3. The surface equation drawing method according to claim 1, wherein the preset relationship correspondence table further includes: a correspondence between character strings and numerical values; The step of extracting the target value from the numerical character string corresponding to the new position information specifically includes: According to the preset relationship correspondence table, a target character string is extracted from the numerical character string corresponding to the new position information, and the target character string is converted into the target numerical value. 4. The surface equation drawing method according to claim 1, characterized in that when receiving the surface equation drawing instruction input by the user, before extracting the surface equation data from the drawing instruction, the surface equation drawing method comprises: storing a preset conversion program in the preset storage area, wherein the preset conversion program can convert the surface equation into surface equation data; When receiving the surface equation drawing instruction input by the user, extracting the surface equation data from the drawing instruction specifically includes: Extracting the surface equation in the surface equation instruction received from the user; The surface equation is converted into surface equation data according to the preset conversion procedure. 5. The method for drawing a surface equation according to any one of claims 1 to 4, wherein establishing a parametric equation according to the target value and drawing a surface according to the parametric equation specifically comprises: Establishing a parametric equation about a coordinate system according to the target value; The parameter equation is converted into a surface drawing instruction, and the surface is drawn according to the surface drawing instruction. 6. A surface equation drawing device, characterized in that the device comprises: An acquisition module, configured to extract surface equation data from a drawing instruction input by a user when receiving the surface equation drawing instruction; A calculation module, used for converting the surface equation data into a character string and extracting a target value from the character string; A drawing module, used for establishing a parametric equation according to the target value, and drawing a surface according to the parametric equation; The acquisition module is further used to store a preset relationship correspondence table into a preset storage area, wherein the preset relationship correspondence table includes a correspondence between surface equation data and character strings; The calculation module is also used to obtain the position information of the preset character in the character string according to the character string; extract the numerical string corresponding to the preset character through the position information; obtain new position information through a preset program and extract the numerical string of the new position information; extract the target value from the numerical string corresponding to the new position information. 7. A terminal device, characterized in that the terminal device comprises: a memory, a processor, and a surface equation drawing program stored in the memory and executable on the processor, wherein the surface equation drawing program is configured to implement the steps of the surface equation drawing method as described in any one of claims 1 to 5. 8. A readable storage medium, characterized in that the readable storage medium is a computer-readable storage medium, and a surface equation drawing program is stored on the computer-readable storage medium, and when the surface equation drawing program is executed by a processor, the steps of the surface equation drawing method according to any one of claims 1 to 5 are implemented.

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