CN114973876A - Method and system for teaching drawing of solid geometric model expansion diagram - Google Patents
Method and system for teaching drawing of solid geometric model expansion diagram Download PDFInfo
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Abstract
The invention discloses a method and a system for teaching and drawing a three-dimensional geometric model development figure, wherein the method for teaching and drawing the three-dimensional geometric model development figure comprises the following steps: bending a flexible metal wire to form at least two profile contour lines; setting the geometric position relationship of at least two profile contour lines; guiding students to manually measure the length expanding information of each feature point on the at least two section contour lines, and drawing a first expansion diagram in a preset plane by using the length expanding information and the geometric position relation; creating a solid geometric model in three-dimensional drawing software according to the at least two profile contour lines and the geometric position relation; unfolding the solid geometric model in the preset plane by using the three-dimensional drawing software to form a second unfolded drawing; analyzing and comparing the first unfolded drawing and the second unfolded drawing to improve the cognition of students on a solid geometric model unfolded drawing; wherein the cross-sectional directions of any two cross-sectional contour lines are the same.
Description
Technical Field
The invention relates to the technical field of teaching and drawing of a solid geometry expansion diagram, in particular to a teaching and drawing method and system of a solid geometry model expansion diagram.
Background
With the development and progress of science and technology, drawing various drawings of solid geometry by utilizing three-dimensional modeling software or three-dimensional drawing software becomes more and more convenient, but the development trend causes drawing principles and flows of students to various drawings to become more and more strange, and the identification capability of students to developed drawings of solid geometry models with complex changes is obviously lower according to the review and investigation of drawing operations and cannot meet the labor requirement of future employment units.
The outer plate development of the solid geometry is indispensable in the production and manufacturing of various industries, and particularly for the solid geometry with multi-curvature change and local design, the development is more complicated and difficult to draw, and the precision requirement is high. In some field construction processes, corresponding software is lacked on the field to immediately generate a final drawing, so that the capability of manually drawing a multi-surface solid geometric model development drawing and quickly reading the development drawing by students is urgently needed to be cultivated so as to adapt to the working requirements.
Disclosure of Invention
The invention aims to provide a method and a system for teaching drawing of a solid geometry model expansion diagram, which are used for solving the problems of low mastering degree and poor drawing recognition capability of students on a drawing principle and a drawing process of the solid geometry expansion diagram in the prior art.
The above object of the present invention can be achieved by the following technical solutions:
the invention provides a three-dimensional geometric model expansion diagram teaching and drawing method, which comprises the following steps:
bending a flexible metal wire to form at least two profile contour lines;
setting the geometric position relationship of at least two profile contour lines;
guiding students to manually measure the length expanding information of each feature point on the at least two section contour lines, and drawing a first expansion diagram in a preset plane by using the length expanding information and the geometric position relation;
creating a solid geometric model in three-dimensional drawing software according to the at least two profile contour lines and the geometric position relation;
unfolding the solid geometric model in the preset plane by using the three-dimensional drawing software to form a second unfolded drawing;
analyzing and comparing the first unfolded drawing and the second unfolded drawing to improve the cognition of students on a solid geometric model unfolded drawing;
wherein the cross-sectional directions of any two cross-sectional contour lines are the same.
Preferably, the setting of the geometric positional relationship between at least two of the profile lines includes:
setting a three-dimensional coordinate system and determining an origin coordinate;
specifying the position information of each profile contour line in the three-dimensional coordinate system;
calculating the position coordinates of each feature point on the corresponding profile contour line according to each piece of position information;
and summarizing the position coordinates of all the characteristic points into a whole to form the geometric position relation.
Preferably, the instructing the student to manually measure the development information of each feature point on the at least two section contour lines includes instructing the student to perform the steps of:
a transparent graduated tube capable of being bent is sleeved on each flexible metal wire bent to form the profile contour line;
marking each characteristic point on the outer wall surface of the transparent graduated tube corresponding to the characteristic point;
sequentially measuring the distance between each characteristic point and the initial characteristic point by using the transparent graduated tube along the trend of the profile contour lines by taking the initial characteristic point as a reference to form the lengthening information until the measurement of each lengthening information on the at least two profile contour lines is completed;
the inner wall surface and/or the outer wall surface of the transparent graduated tube are/is provided with a graduated scale, and the characteristic points can be marked on the outer wall surface of the transparent graduated tube in the manual measuring process.
Preferably, the instructing the student to manually measure the development information of each feature point on the at least two section contour lines includes instructing the student to perform the steps of:
marking each of the feature points on the cross-sectional profile line corresponding thereto;
and sequentially measuring the distance between each characteristic point and the initial characteristic point by taking the initial characteristic point as a reference along the direction of the central axis of the flexible metal wire so as to form the lengthening information until the measurement of each lengthening information on the at least two profile contour lines is completed.
Preferably, the flexible metal wire is provided with scales to form a fixed grid, the fixed grid can be matched with the movable grid to measure the distance between any two adjacent characteristic points according to the measurement principle of the electronic vernier caliper, and the extension information is generated in the controller.
Preferably, before the measuring and acquiring each piece of length information on the at least two profile contour lines is completed, the measuring and acquiring of the length information by sequentially measuring the distance between each piece of the feature point and the starting feature point with the starting feature point as a reference along the central axis direction of the flexible metal wire further includes:
and straightening each flexible metal wire bent to form the section contour line.
Preferably, the creating a geometric model in a three-dimensional drawing software according to the at least two profile contour lines and the geometric position relationship includes:
collecting attribute information of the at least two profile contour lines, and inputting the attribute information into the three-dimensional drawing software;
establishing an original three-dimensional model according to the geometric position relation and the attribute information of two adjacent profile contour lines;
identifying each structure point in the original three-dimensional model using the three-dimensional mapping software;
based on the fact that the distance between the characteristic point and the structure point is not larger than a preset value, a corresponding mapping relation is established between the characteristic point and the structure point;
numbering each feature point according to the section contour line of the feature point and the sequence of the feature point on the section contour line based on the feature point and only one feature point corresponding to the feature point;
cutting the original solid model according to a plurality of characteristic points to form the solid geometric model;
the number information of each structure point in the solid geometric model comprises the extension information of the structure point on an X plane, a Y plane and a Z plane respectively.
Preferably, the analyzing and comparing the first and second expansions to improve student awareness of the solid geometry model expansion includes:
comparing errors between the feature points in the first expanded view and the structure points in the second expanded view corresponding thereto;
respectively acquiring the extension information of the feature point and the extension information of the structure point based on the error larger than a preset threshold;
analyzing error causes by using the extension information of the feature points, the extension information of the structure points and the geometric position relationship;
traversing each feature point in the first expanded graph and the structure point in the second expanded graph corresponding to the feature point until all error causes are analyzed and classified;
and guiding students to draw the first expanded graph again according to the classification results of all the error causes until the error between any one feature point in the first expanded graph and the structure point in the second expanded graph corresponding to the feature point is not greater than the preset threshold value.
Preferably, each of the cross-sectional profile lines includes at least three feature points, and the feature points include a start point, an end point, and at least one intermediate point located between the start point and the end point.
The invention also provides a system for teaching and drawing the expansion diagram of the solid geometric model, which comprises the following components: and (3) a module for executing the solid geometric model development drawing teaching method.
The invention has at least the following characteristics and advantages:
according to the method, the cognition of the students on the drawing principle and the flow of the development map can be deepened by analyzing the difference between the first development map drawn by the students and the second development map automatically generated by the three-dimensional drawing software, so that the cognition of the students on the three-dimensional geometric model development map is improved through continuous practice and inspection, the students can be ensured to completely master the drawing principle of the development map, and the image recognition capability of the students on the development map is improved.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a block diagram of the process of the method for teaching the development of a solid geometry model according to the present invention;
FIG. 2 is a block diagram of the process of the method for teaching the development of the solid geometry model of the present invention;
FIG. 3 is a flow chart of the method for teaching and drawing an expanded view of a solid geometry model according to the present invention;
FIG. 4 is a block diagram of the process of the method for teaching the development of the solid geometry model of the present invention;
FIG. 5 is a block diagram of the process of the method for teaching the development of the solid geometry model of the present invention;
FIG. 6 is a block diagram of the process of the method for teaching the development of the solid geometry model.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Implementation mode one
The invention provides a method for teaching and drawing a solid geometric model expansion diagram, please refer to fig. 1 to 6, comprising the following steps:
s1, bending the flexible metal wire to form at least two profile contour lines;
wherein, each section contour line comprises at least three characteristic points, and the characteristic points comprise a starting point, an end point and at least one intermediate point positioned between the starting point and the end point. In some embodiments, the feature points are located at linear changes on the cross-sectional profile, such as at the locations of bulges or depressions on the solid geometric outer profile, or at locations where curvature changes.
In some embodiments, the flexible wire is made of aluminum, aluminum alloy, or stainless steel material. Furthermore, the diameter of the flexible metal wire is not more than 2 mm, so that the subsequent collection of the wire type is more convenient and accurate. It will be understood by those skilled in the art that the cross-sectional profile can be made of other materials, and it is within the scope of the present invention to provide a cross-sectional profile that is easily bendable and maintains its linear shape in a bent state.
S2, setting the geometric position relation of at least two section contour lines;
s3, guiding students to manually measure the length extending information of each feature point on at least two section contour lines, and drawing a first expansion diagram in a preset plane by using the length extending information and the geometric position relation;
the student should determine a drawing reference line of the development when drawing the first development; then determining the relationship between the initial characteristic point in each section contour line and the datum line according to the geometric position relationship, such as the corresponding position of the initial characteristic point of each section contour line along the length direction of the datum line and the distance between the initial characteristic point of each section contour line and the datum line; and finally, unfolding the section contour line by taking the initial characteristic point as a base point, and repeating the steps until the drawing of the first unfolded drawing is finished.
S4, creating a solid geometric model in three-dimensional drawing software according to the relationship between at least two section contour lines and geometric positions;
s5, unfolding the solid geometric model in a preset plane by using three-dimensional drawing software to form a second unfolded drawing;
the three-dimensional drawing software can adopt any software in the prior art and is developed for the second time based on a corresponding development language so as to be expanded in a preset plane to form a second expanded drawing.
S6, analyzing and comparing the first unfolded drawing and the second unfolded drawing to improve the cognition of students on the unfolded drawing of the solid geometric model;
wherein, the cross-section directions of any two cross-section contour lines are the same, such as the cross-section contour lines parallel to the X plane/Y plane/Z plane.
In some embodiments, referring to fig. 2, the step S2 of setting the geometric position relationship of the at least two cross-sectional outlines includes:
s21, setting a three-dimensional coordinate system and determining an origin coordinate;
s22, specifying the position information of each section contour line in the three-dimensional coordinate system;
s23, calculating the position coordinates of each feature point on the corresponding section contour line according to each piece of position information;
and S24, collecting the position coordinates of all the characteristic points into a whole to form a geometric position relation.
In some embodiments, referring to fig. 3, instructing the student to manually measure the elongation information of each feature point on the at least two section contour lines, S3, includes instructing the student to perform the following steps:
s31, sleeving a bendable transparent graduated tube on each flexible metal wire bent to form a section contour line;
the inner wall surface and/or the outer wall surface of the transparent graduated tube are/is provided with a graduated scale, and the characteristic points can be marked on the outer wall surface of the transparent graduated tube in the manual measuring process. Furthermore, the graduated scale is clamped between the inner wall surface and the outer wall surface of the transparent graduated tube to prevent the graduations from being abraded due to use. Furthermore, the mark symbol of each feature point is marked by a symbol pen to be erased, so that the transparent graduated tube can be reused subsequently.
In some embodiments, the difference between the inner diameter of the transparent graduated tube and the outer diameter of the flexible metal wire is not greater than 1 mm, so that the accuracy of the measured data is ensured, and the workload of subsequent analysis and comparison caused by large errors is reduced.
S32, marking each characteristic point on the outer wall surface of the corresponding transparent graduated tube;
s33, sequentially measuring the distance between each characteristic point and the initial characteristic point by using a transparent graduated tube along the trend of the profile contour lines and taking the initial characteristic point as a reference to form extension information until the measurement of each extension information on at least two profile contour lines is completed;
in some embodiments, referring to fig. 4, S3, instructing the student to manually measure the elongation information of each feature point on the at least two section contour lines comprises instructing the student to perform the following steps:
s34, marking each characteristic point on the corresponding section contour line;
and S35, sequentially measuring the distance between each characteristic point and the initial characteristic point by taking the initial characteristic point as a reference along the central axis direction of the flexible metal wire to form the length information until the length information on at least two section contour lines is measured.
The flexible metal wire is provided with scales so as to form a fixed grid, the fixed grid can be matched with the movable grid to measure the distance between any two adjacent characteristic points according to the measuring principle of the electronic vernier caliper, and the extension information is generated in the controller.
In some embodiments, the moving grid starts to measure from its initial feature point along the profile line, and each time it slides to a feature point, the record key of the electronic vernier caliper is pressed until all the feature points on the profile line are measured. Further, the measurement data are processed in a controller in the electronic vernier caliper to form accumulated measurement data (i.e. the extension information of each feature point); furthermore, the electronic vernier caliper has a wireless communication function so that corresponding measurement data can be transmitted to the three-dimensional drawing software more quickly.
In some embodiments, referring to fig. 4, before measuring the distance between each feature point and the starting feature point in sequence along the central axis direction of the flexible wire with the starting feature point as a reference to form the length information until each length information on the at least two profile lines is completely measured at S35, the method further includes:
s341, straightening each flexible metal wire bent to form the section contour line.
By adopting the design, the metal wire can be straightened before the movable grid and the fixed grid are matched with the measured data, so that the situation that the measured data is inaccurate due to unstable sliding of the movable grid on the profile contour line of the section is avoided.
In some embodiments, referring to fig. 5, creating a geometric model in the three-dimensional drawing software according to the at least two profile contours and the geometric position relationship in S4 includes:
s41, collecting attribute information of at least two section contour lines, and inputting the attribute information into three-dimensional drawing software;
in some embodiments, the attribute information of the whole profile line may be obtained by taking a picture or scanning, where the attribute information includes the line length, the start feature point, the middle feature point, and the position coordinates of the end feature point of the line segment.
S42, creating an original solid model according to the geometric position relationship and the attribute information of two adjacent section contour lines;
s43, identifying each structure point in the original stereo model by using three-dimensional drawing software;
s44, based on the fact that the distance between the feature point and the structure point is not larger than a preset value, creating a corresponding mapping relation between the feature point and the structure point;
s45, numbering the feature points according to the section contour lines where the feature points are located and the sequence of the feature points on the section contour lines based on the fact that each feature point has and only has one structure point corresponding to the feature point;
the number information of each structure point in the solid geometric model comprises the extension information of the structure point on an X plane, a Y plane and a Z plane respectively.
It should be understood by those skilled in the art that the three length information in the number information is to determine whether the direction in which the section contour lines are unfolded by the students is correct in order to find the difference between the first development diagram and the second development diagram in the following steps, for example, for the teaching purpose, the students are required to unfold each section contour line in the X plane, but some students fail to understand the concept of the unfolding plane and unfold the section contour line in the Y plane/Z plane, and the teacher can determine the cognitive degrees of the students on the unfolding plane and the unfolding direction by directly comparing the length information in different planes with the length information of each feature point on the corresponding section contour line, and further correct the errors to increase the cognition of the students.
S46, cutting the original solid model according to the plurality of characteristic points to form a solid geometric model;
in some embodiments, referring to fig. 6, S6, analyzing and comparing the first unfolded view and the second unfolded view to improve the student' S knowledge of the unfolded view of the solid geometry model includes:
s61, comparing errors between the characteristic points in the first expanded graph and the structural points in the second expanded graph corresponding to the characteristic points;
s62, respectively acquiring the extension information of the feature point and the extension information of the structure point based on the error larger than a preset threshold;
s63, analyzing error cause by using the extension information of the feature point, the extension information of the structure point and the geometric position relation;
s64, traversing each feature point in the first expanded graph and the structure point in the second expanded graph corresponding to the feature point until all error causes are analyzed and classified;
and S65, guiding the student to draw the first expanded view again according to the classification result of all error causes until the error between any feature point in the first expanded view and the structure point in the second expanded view corresponding to the feature point is not greater than a preset threshold value.
The invention will be further described and illustrated by means of a specific embodiment:
step one, each student bends by using a flexible metal wire to form a section contour line of a Y plane
In some embodiments, the teacher may also group classmates, and then each group is formed into a unit with a cross-sectional outline by bending with a flexible wire.
The invention can facilitate teachers to select any mode to bend to form the profile contour line according to the number of students, thereby achieving a balance between the purpose of ensuring teaching and the inspection of teaching results.
Step two, each student unfolds each characteristic point on the profile contour line formed by bending the student in the X plane;
in teaching in groups, each student may assign a feature point to the profile line and spread the feature point in the X-plane.
Thirdly, each student numbers each feature point on the profile contour line of the student;
in some embodiments, the number format of each feature point is (section contour line name, serial number of the feature point, and length of the feature point in the X plane), and further, the section contour line name is named by student's school number for uniform management. In the teaching with the group as a unit, each classmate can only number the designated characteristic points, and the section contour line names are named by the group numbers so as to be convenient for unified management and differentiation.
Step four, the teacher sets the geometric position relation among all the profile contour lines according to the teaching scheme;
fifthly, drawing each section outline expansion line according to the geometric position relation and the serial number information of the characteristic points responsible for the geometric position relation by students, and combining and drawing to complete a first expansion diagram;
step six, demonstrating how to draw a second expansion schematic diagram in the three-dimensional drawing software to students by using all the section contour lines and the geometric position relation;
through the design, the teaching and drawing instrument can be used for operating and teaching software operation commonly used by students in later work, and can also be used for teaching and drawing the principle and the flow of field work of the students by continuously guiding the students to manually operate.
Seventhly, the teacher leads the student to compare and analyze the first development drawing and the second development drawing so as to deepen the cognition of the student on the development drawing of the solid geometric model
In some embodiments, the teacher takes the students to perform comparison analysis on each feature point on each profile contour line in turn to check whether the drawing process of each student is correct, so that the mastery degree of the knowledge points of the students can be examined and guided.
The invention has at least the following characteristics and advantages:
according to the method, the cognition of the students on the drawing principle and the flow of the development map can be deepened by analyzing the difference between the first development map drawn by the students and the second development map automatically generated by the three-dimensional drawing software, so that the cognition of the students on the three-dimensional geometric model development map is improved through continuous practice and inspection, the students can be ensured to completely master the drawing principle of the development map, and the image recognition capability of the students on the development map is improved.
Second embodiment
The embodiment of the invention also provides a solid geometry model expansion drawing teaching system which comprises a module for executing the steps of the method in any one of the embodiment modes. Those skilled in the art will appreciate that the system provided by the present invention has the same advantages as the embodiment in the first embodiment, and thus, the detailed description thereof is omitted here.
Although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A method for teaching and drawing an expansion drawing of a solid geometric model is characterized by comprising the following steps:
bending a flexible metal wire to form at least two profile contour lines;
setting the geometric position relationship of at least two profile contour lines;
guiding students to manually measure the length expanding information of each feature point on the at least two section contour lines, and drawing a first expansion diagram in a preset plane by using the length expanding information and the geometric position relation;
creating a solid geometric model in three-dimensional drawing software according to the at least two profile contour lines and the geometric position relation;
unfolding the solid geometric model in the preset plane by using the three-dimensional drawing software to form a second unfolded drawing;
analyzing and comparing the first unfolded drawing and the second unfolded drawing to improve the cognition of students on a solid geometric model unfolded drawing;
wherein the cross-sectional directions of any two cross-sectional contour lines are the same.
2. The method for teaching the unfolding view of the solid geometry model according to claim 1, wherein the setting of the geometric position relationship between at least two of the profile contour lines comprises:
setting a three-dimensional coordinate system and determining an origin coordinate;
specifying the position information of each profile contour line in the three-dimensional coordinate system;
calculating the position coordinates of each feature point on the corresponding profile contour line according to each piece of position information;
and summarizing the position coordinates of all the characteristic points into a whole to form the geometric position relation.
3. The method for teaching and drawing the unfolding view of the solid geometric model according to claim 2, wherein the step of instructing the student to manually measure the unfolding information of each feature point on the at least two section contour lines comprises the step of instructing the student to perform the following steps:
a transparent graduated tube capable of being bent is sleeved on each flexible metal wire which is bent to form the profile contour line;
marking each characteristic point on the outer wall surface of the transparent graduated tube corresponding to the characteristic point;
sequentially measuring the distance between each characteristic point and the initial characteristic point by using the transparent graduated tube based on the initial characteristic point along the trend of the profile contour lines to form the length information until the length information on the at least two profile contour lines is measured;
the inner wall surface and/or the outer wall surface of the transparent graduated tube are/is provided with a graduated scale, and the characteristic points can be marked on the outer wall surface of the transparent graduated tube in the manual measuring process.
4. The method for teaching and drawing the unfolding view of the solid geometric model according to claim 2, wherein the step of instructing the student to manually measure the unfolding information of each feature point on the at least two section contour lines comprises the step of instructing the student to perform the following steps:
marking each of the feature points on the cross-sectional profile line corresponding thereto;
and sequentially measuring the distance between each characteristic point and the initial characteristic point by taking the initial characteristic point as a reference along the central axis direction of the flexible metal wire to form the length information until the length information on the at least two profile contour lines is measured.
5. The method for teaching and drawing the expanded view of the solid geometric model according to claim 4, wherein scales are arranged on the flexible metal wire so as to form a fixed grid, the fixed grid can be matched with a movable grid to measure the distance between any two adjacent feature points according to the measurement principle of an electronic vernier caliper, and the expanded information is generated in a controller.
6. The method for teaching development of geometric solid model according to claim 5, wherein before the sequentially measuring the distance between each feature point and the starting feature point with the starting feature point as a reference along the central axis direction of the flexible wire to form the elongation information until the measurement and acquisition of each elongation information on the at least two profile contour lines are completed, the method further comprises:
and straightening each flexible metal wire bent to form the section contour line.
7. The method for teaching the unfolding drawing of the solid geometry model according to claim 2, wherein the creating the solid geometry model in the three-dimensional drawing software according to the at least two profile contour lines and the geometric position relationship comprises:
collecting attribute information of the at least two profile contour lines, and inputting the attribute information into the three-dimensional drawing software;
establishing an original three-dimensional model according to the geometric position relation and the attribute information of two adjacent profile contour lines;
identifying each structure point in the original three-dimensional model using the three-dimensional mapping software;
based on the fact that the distance between the characteristic point and the structure point is not larger than a preset value, a corresponding mapping relation is established between the characteristic point and the structure point;
based on that each feature point has only one structure point corresponding to the feature point, numbering the feature points according to the section contour line of the feature points and the sequence of the feature points on the section contour line;
cutting the original solid model according to a plurality of characteristic points to form the solid geometric model;
the number information of each structure point in the solid geometric model comprises the extension information of the structure point on an X plane, a Y plane and a Z plane respectively.
8. The method for teaching expansion of geometric solid model according to claim 7, wherein the analyzing and comparing the first and second expansions to improve student's perception of the expansion of geometric solid model comprises:
comparing errors between the feature points in the first expanded view and the structure points in the second expanded view corresponding thereto;
respectively acquiring the extension information of the feature point and the extension information of the structure point based on the error larger than a preset threshold;
analyzing error causes by using the extension information of the feature points, the extension information of the structure points and the geometric position relation;
traversing each feature point in the first expanded graph and the structure point in the second expanded graph corresponding to the feature point until all error causes are analyzed and classified;
and guiding students to draw the first expansion diagram again according to the classification results of all the error causes until the error between any feature point in the first expansion diagram and the structure point in the second expansion diagram corresponding to the feature point is not greater than the preset threshold value.
9. The method for teaching and drawing a solid geometry model development drawing according to any one of claims 1 to 8, wherein each of the section contour lines includes at least three feature points including a start point, an end point and at least one intermediate point between the start point and the end point.
10. A solid geometry model expansion drawing teaching system is characterized by comprising:
a module for executing the method for teaching the solid geometry model development drawing of any one of claims 1 to 9.
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