CN104809940B - Geometry stereographic projection device and projecting method - Google Patents
Geometry stereographic projection device and projecting method Download PDFInfo
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- CN104809940B CN104809940B CN201510246731.9A CN201510246731A CN104809940B CN 104809940 B CN104809940 B CN 104809940B CN 201510246731 A CN201510246731 A CN 201510246731A CN 104809940 B CN104809940 B CN 104809940B
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
- G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
- G09B23/02—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics
- G09B23/04—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics for geometry, trigonometry, projection or perspective
Abstract
The present invention relates to education and instruction technical field, and the present invention provides a kind of geometry stereographic projection method and projection arrangement, projecting method comprise the following steps：Obtain 2-d plane graph；Judge whether 2-d plane graph is three-dimensional geometrical figure, is, then a point in the interface where selection 2-d plane graph is two-dimensional coordinate system origin, and the border point coordinates of 2-d plane graph is drawn according to two-dimensional coordinate system origin measurement；The three-dimensional coordinate of boundary point is obtained after the border point coordinates of 2-d plane graph is carried out into coordinate transform；Project to obtain three-dimensional graph according to the three-dimensional coordinate of boundary point, by by simple geometry solid figure, after pattern analysis, processing and conversion, it is projected out the solid figure of 3-D effect, improve interactive teaching and learning ability, it is final to help student to understand three-dimensional graph, improve the space imagining ability of student.
Description
Technical field
The present invention relates to education and instruction technical field, more particularly to a kind of geometry stereographic projection device and projection side
Method.
Background technology
It is " point, line, surface " that basic element in geometric system is increased by " point, line ", and space diagram is risen to from planar graph
Shape, it is changed into " three dimensions " from " two-dimensional space ", this is for each side such as the three dimensions visionary of student, logical thinking abilities
The ability in face is proposed higher requirement, then, this abstract for those are in the student in secondary school education stage
Imagination is but exactly their weak part.In addition, plus the imperfection of current electronic instruction equipment, pattern space sense is not easy to open up
Existing, interactive teaching and learning also is difficult to deploy.For example, in order to allow student to more fully understand the concept of common vertical line theorem, two are often borrowed
Individual instructional ruler replaces space different surface beeline, then " gesticulating " repeatedly carries out the explanation of theorem, spends a large amount of time, imitates
Fruit is not fine.In summary, exist in the prior art because user's space sense is not understood that three-dimensional graphic space knot by force
The problem of structure.
The content of the invention
It is an object of the invention to provide a kind of geometry stereographic projection device and projecting method, it is intended to solves for existing
Have in technology and exist due to existing in the prior art because user's space sense is not understood that asking for three-dimensional graphic space structure by force
Topic.
The present invention is achieved in that first aspect provides a kind of geometry stereographic projection method, the projecting method
Comprise the following steps：
A. 2-d plane graph is obtained；
B. judge whether the 2-d plane graph is three-dimensional geometrical figure, is, then perform step C, otherwise return and perform
Step A；
C. it is two-dimensional coordinate system origin to select a point in the interface where the 2-d plane graph, according to described two
The origin measurement of dimension coordinate system draws the border point coordinates of the 2-d plane graph；
D. the three-dimensional coordinate of boundary point is obtained after the border point coordinates of the 2-d plane graph being carried out into coordinate transform；
E. project to obtain three-dimensional graph according to the three-dimensional coordinate of the boundary point.
With reference in a first aspect, in the first embodiment of first aspect, the step A is specially：
Receive the 2-d plane graph of user's input or captured image is identified to obtain 2 d plane picture
Shape.
With reference in a first aspect, in second of embodiment of first aspect, the two dimensional surface is judged in the step B
The step of whether figure is three-dimensional geometrical figure be specially：
Judge with the presence or absence of the face length of dotted line, shade or adjacent surface in the 2-d plane graph, be then to sentence
The fixed 2-d plane graph is three-dimensional geometrical figure, and no, then it is not three-dimensional geometrical figure to judge the 2-d plane graph.
With reference in a first aspect, in the third embodiment of first aspect, the step D is specially：
Two-dimentional three-view diagram and two-dimensional geometry construction is obtained according to border point coordinates, two dimension is generated and calculates data；
Data are calculated according to two dimension, three-dimensional space is converted to by data input, data reparation, data processing and data output
Between model；
The coordinate data of three-dimensional space model is obtained according to three-dimensional space model.
It is described according to two in the 4th kind of embodiment of first aspect with reference to the third embodiment of first aspect
Dimension calculates data, the step of three-dimensional space model is converted to by data input, data reparation, data processing and data output it
Also include afterwards：
According to the three-dimensional space model three-dimensional coordinate transformation of chosen boundary point will be represented into relative to display screen
Two-dimensional coordinate；
By the coordinate having determined compared with the coordinate for one after the other converting to obtain until producing equal result；
Draw the three-dimensional coordinate corresponding to the two-dimensional points selected on display screen.
Second aspect of the present invention provides a kind of geometry stereographic projection device, the geometry stereographic projection device bag
Include：
Figure acquisition module, for obtaining 2-d plane graph；
Solid figure judge module, for judging whether the 2-d plane graph is three-dimensional geometrical figure, when judgement is tied
When fruit is no, the figure acquisition module is driven to work；
Coordinate obtaining module, for when the judged result of the solid figure judge module is is, selecting the two dimension
A point in interface where planar graph is two-dimensional coordinate system origin, and institute is drawn according to the two-dimensional coordinate system origin measurement
State the border point coordinates of 2-d plane graph；
Coordinate transformation module, for obtaining border after the border point coordinates of the 2-d plane graph is carried out into coordinate transform
The three-dimensional coordinate of point；
Projection module, for projecting to obtain three-dimensional graph according to the three-dimensional coordinate of the boundary point.
With reference to second aspect, in the first embodiment of second aspect, it is flat that the figure acquisition module obtains two dimension
The process of face figure is：
Receive the 2-d plane graph of user's input or captured image is set to obtain 2-d plane graph.
With reference to second aspect, in second of embodiment of second aspect, the solid figure judge module judges institute
State whether 2-d plane graph is that the process of three-dimensional geometrical figure is：
Judge with the presence or absence of the face length of dotted line, shade or adjacent surface in the 2-d plane graph, be then to sentence
The fixed 2-d plane graph is three-dimensional geometrical figure, and no, then it is not three-dimensional geometrical figure to judge the 2-d plane graph.
With reference to second aspect, in the third embodiment of second aspect, the coordinate transformation module is by the two dimension
The process for the three-dimensional coordinate that the border point coordinates of planar graph carries out obtaining boundary point after coordinate transform is：
Two-dimentional three-view diagram and two-dimensional geometry construction is obtained according to border point coordinates, two dimension is generated and calculates data；
Data are calculated according to two dimension, three-dimensional space is converted to by data input, data reparation, data processing and data output
Between model；
The coordinate data of three-dimensional space model is obtained according to three-dimensional space model.
With reference to the third embodiment of second aspect, in the 4th kind of embodiment of second aspect, the coordinate becomes
Change the mold root tuber and calculate data according to two dimension, three dimensions is converted to by data input, data reparation, data processing and data output
Also include after the process of model：
According to the three-dimensional space model three-dimensional coordinate transformation of chosen boundary point will be represented into relative to display screen
Two-dimensional coordinate；
By the coordinate having determined compared with the coordinate for one after the other converting to obtain until producing equal result；
Draw the three-dimensional coordinate corresponding to the two-dimensional points selected on display screen.
A kind of geometry stereographic projection device and projecting method provided by the invention, by by simple geometry stereogram
Shape, after pattern analysis, processing and conversion, the solid figure of 3-D effect is projected out, improves interactive teaching and learning ability, final side
Give financial aid to students physiology solution three-dimensional graph, improve the space imagining ability of student.
Brief description of the drawings
Technical scheme in order to illustrate the embodiments of the present invention more clearly, below will be to embodiment or description of the prior art
In the required accompanying drawing used be briefly described, it should be apparent that, drawings in the following description be only the present invention some
Embodiment, for those of ordinary skill in the art, without having to pay creative labor, can also be according to these
Accompanying drawing obtains other accompanying drawings.
Fig. 1 is a kind of flow chart for geometry stereographic projection method that an embodiment of the present invention provides；
Fig. 2 is a kind of structural representation for geometry stereographic projection device that another embodiment of the present invention provides；
Fig. 3 is the 3-D solid structure that a kind of geometry stereographic projection method that an embodiment of the present invention provides obtains
Schematic diagram.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
In order to illustrate technical scheme, illustrated below by specific embodiment.
An embodiment of the present invention provides a kind of geometry stereographic projection method, as shown in figure 1, projecting method include with
Lower step：
Step S101. obtains 2-d plane graph.
In this step, specifically, in one embodiment, receiving the 2-d plane graph of user's input, Ke Yigen
Draw the structure of 2-d plane graph on the touchscreen according to user, obtain 2-d plane graph；In another embodiment, may be used
To be identified captured image to obtain 2-d plane graph, the drawing paper for having image to drafting using camera is clapped
Take the photograph, camera is by catching in line weight and color de-regulation notebook computer drawing software on paper the color of paintbrush and thick
Carefully, meanwhile, by the color and ratio of Intelligent Recognition drawing paper, the color and ratio of drawing paper in drawing software are adjusted, so as to obtain
Editable image data.
Step S102. judges whether 2-d plane graph is three-dimensional geometrical figure, is, then execution step S103, no, then returns
Receipt row step S101.
In this step, specifically, judging that the step of whether 2-d plane graph is three-dimensional geometrical figure is specially：
Judge with the presence or absence of the face length of dotted line, shade or adjacent surface in 2-d plane graph, be then to judge two
Dimensional plane figure is three-dimensional geometrical figure, no, then judges that 2-d plane graph is not three-dimensional geometrical figure.
A point in interface where step S103. selection 2-d plane graphs is two-dimensional coordinate system origin, according to two
The origin measurement of dimension coordinate system draws the border point coordinates of 2-d plane graph.
In this step, specifically, selecting a point in the screen of display 2-d plane graph, using the point as two dimension
The origin of coordinate system, and border point coordinates is drawn successively.
Step S104. obtains the three-dimensional seat of boundary point after the border point coordinates of 2-d plane graph is carried out into coordinate transform
Mark.
In this step, specifically, comprising the following steps：
Step S201. obtains two-dimentional three-view diagram and two-dimensional geometry according to border point coordinates and constructed, and generates two dimension and calculates data.
Step S202. calculates data according to two dimension, is turned by data input, data reparation, data processing and data output
It is changed to three-dimensional space model.
Step S203. obtains the coordinate data of three-dimensional space model according to three-dimensional space model.
Further, in another embodiment, also include after step S202：
Step S204. according to the three-dimensional space model will represent the three-dimensional coordinate transformation of chosen boundary point into relative to
The two-dimensional coordinate of display screen.
Step S205. by the coordinate having determined compared with the coordinate for one after the other converting to obtain until produce it is equal
As a result；
Step S206. draws the three-dimensional coordinate corresponding to the two-dimensional points selected on display screen.
When the three-dimensional coordinate of one point of needs, selected point is confirmed, and determine that the two dimension of selected point is shown
Coordinate u, v, calculate corresponding displaing coordinate u ', the v ' of the coordinate of corresponding three-dimensional point wherein, and with it is selected
The coordinate of point be compared.
If u, v and u ', v ' identical, and corresponding three-dimensional coordinate returns to user or with another kind side via display
Method is automatically inputted into call function and obtains three-dimensional coordinate.
All convert and compared and none and the u if all of point, v points are identical, then call an error routine
And exit the subroutine.
According to the present invention, represent that a selected point in the two dimension display of a three-dimensional body is with following methods and its
Corresponding three-dimensional coordinate correlation：Determine the displaing coordinate of institute's reconnaissance and resulting three-dimensional point is transformed into corresponding to them
Two-dimentional displaing coordinate is identical with the displaing coordinate of selected point until the latter.
Step S105. projects to obtain three-dimensional graph according to the three-dimensional coordinate of boundary point.
In this step, specifically, according to three-dimensional coordinate, three-dimensional graph is projected out in space, shown in figure Fig. 3,
For the cuboid 3-D graphic obtained after being projected to plane cuboid.
A kind of geometry stereographic projection method provided by the invention, by by simple geometry solid figure, by figure
After conformal analysis, processing and conversion, the solid figure of 3-D effect is projected out, improves interactive teaching and learning ability, it is final to help student's reason
Three-dimensional graph is solved, improves the space imagining ability of student.
Second of embodiment of the present invention provides a kind of geometry stereographic projection device, as shown in Fig. 2 geometry solid figure
Projection arrangement includes：
Figure acquisition module 301, for obtaining 2-d plane graph；
Solid figure judge module 302, for judging whether 2-d plane graph is three-dimensional geometrical figure, work as judged result
For it is no when, drive pattern acquisition module work；
Coordinate obtaining module 303, for when the judged result of solid figure judge module is is, selecting 2 d plane picture
A point in interface where shape is two-dimensional coordinate system origin, and 2-d plane graph is drawn according to two-dimensional coordinate system origin measurement
Border point coordinates；
Coordinate transformation module 304, for obtaining border after the border point coordinates of 2-d plane graph is carried out into coordinate transform
The three-dimensional coordinate of point；
Projection module 305, for projecting to obtain three-dimensional graph according to the three-dimensional coordinate of boundary point.
Specifically, for figure acquisition module 301, in one embodiment, the 2 d plane picture of user's input is received
Shape, the structure of 2-d plane graph can be drawn on the touchscreen according to user, obtain 2-d plane graph；Implement in another kind
In mode, captured image can be identified to obtain 2-d plane graph, have image to drafting using camera
Drawing paper is shot, and camera is by catching paintbrush in line weight and color de-regulation notebook computer drawing software on paper
Color and thickness, meanwhile, by the color and ratio of Intelligent Recognition drawing paper, adjust the color and ratio of drawing paper in drawing software
Example, so as to obtain editable image data.
Specifically, for solid figure judge module 302, solid figure judge module 302 judges that 2-d plane graph is
No is that the process of three-dimensional geometrical figure is：
Judge with the presence or absence of the face length of dotted line, shade or adjacent surface in 2-d plane graph, be then to judge two
Dimensional plane figure is three-dimensional geometrical figure, no, then judges that 2-d plane graph is not three-dimensional geometrical figure.
Specifically, coordinate transformation module 304 obtains side after the border point coordinates of 2-d plane graph is carried out into coordinate transform
The process of the three-dimensional coordinate of boundary's point is：
Two-dimentional three-view diagram and two-dimensional geometry construction is obtained according to border point coordinates, two dimension is generated and calculates data.
Data are calculated according to two dimension, three-dimensional space is converted to by data input, data reparation, data processing and data output
Between model.
The coordinate data of three-dimensional space model is obtained according to three-dimensional space model.
Further, in another embodiment, coordinate transformation module 304 calculates data according to two dimension, defeated by data
Enter, the process that data reparation, data processing and data output are converted to after three-dimensional space model also includes：
According to the three-dimensional space model three-dimensional coordinate transformation of chosen boundary point will be represented into relative to display screen
Two-dimensional coordinate.
By the coordinate having determined compared with the coordinate for one after the other converting to obtain until producing equal result；
Draw the three-dimensional coordinate corresponding to the two-dimensional points selected on display screen.
When the three-dimensional coordinate of one point of needs, selected point is confirmed, and determine that the two dimension of selected point is shown
Coordinate, calculates the corresponding displaing coordinate of the coordinate of corresponding three-dimensional point wherein, and with the seat of selected point
Mark is compared.
If u, v and u ', v ' identical, and corresponding three-dimensional coordinate returns to user or with another kind side via display
Method is automatically inputted into call function and obtains three-dimensional coordinate.
All convert and compared and none and the u if all of point, v points are identical, then call an error routine
And exit the subroutine.
According to the present invention, represent that a selected point in the two dimension display of a three-dimensional body is with following methods and its
Corresponding three-dimensional coordinate correlation：Determine the displaing coordinate of institute's reconnaissance and resulting three-dimensional point is transformed into corresponding to them
Two-dimentional displaing coordinate is identical with the displaing coordinate of selected point until the latter.
Above content is to combine specific preferred embodiment further description made for the present invention, it is impossible to is assert
The specific implementation of the present invention is confined to these explanations.For general technical staff of the technical field of the invention,
Some equivalent substitutes or obvious modification are made on the premise of not departing from present inventive concept, and performance or purposes are identical, all should
It is considered as belonging to the scope of patent protection that the present invention is determined by the claims submitted.
Claims (4)
- A kind of 1. geometry stereographic projection method, it is characterised in that the projecting method comprises the following steps：A. 2-d plane graph is obtained；B. judge whether the 2-d plane graph is three-dimensional geometrical figure, is, then perform step C, no, then return performs step A；C. it is two-dimensional coordinate system origin to select a point in the interface where the 2-d plane graph, is sat according to the two dimension The origin measurement of mark system draws the border point coordinates of the 2-d plane graph；D. the three-dimensional coordinate of boundary point is obtained after the border point coordinates of the 2-d plane graph being carried out into coordinate transform；E. project to obtain three-dimensional graph according to the three-dimensional coordinate of the boundary point；The step A is specially：Captured image is identified to obtain 2-d plane graph, using camera to drawing The drawing paper for having image is shot, and camera is by catching paintbrush in line weight and color de-regulation drawing software on paper Color and thickness, meanwhile, by the color and ratio of Intelligent Recognition drawing paper, the color and ratio of drawing paper in drawing software are adjusted, So as to obtain editable image data；The step D is specially：Two-dimentional three-view diagram and two-dimensional geometry construction is obtained according to border point coordinates, two dimension is generated and calculates data；Data are calculated according to two dimension, three dimensions mould is converted to by data input, data reparation, data processing and data output Type；The coordinate data of three-dimensional space model is obtained according to three-dimensional space model；It is described that data are calculated according to two dimension, three-dimensional space is converted to by data input, data reparation, data processing and data output Between model the step of after also include：According to the three-dimensional space model three-dimensional coordinate transformation of chosen boundary point will be represented into relative to the two of display screen Dimension coordinate；By the coordinate having determined compared with the coordinate for one after the other converting to obtain until producing equal result；Draw the three-dimensional coordinate corresponding to the two-dimensional points selected on display screen.
- 2. projecting method as claimed in claim 1, it is characterised in that judge that the 2-d plane graph is in the step B No the step of being three-dimensional geometrical figure is specially：Judge with the presence or absence of the face length of dotted line, shade or adjacent surface in the 2-d plane graph, be then to judge institute It is three-dimensional geometrical figure to state 2-d plane graph, no, then it is not three-dimensional geometrical figure to judge the 2-d plane graph.
- 3. a kind of geometry stereographic projection device, it is characterised in that the geometry stereographic projection device includes：Figure acquisition module, for obtaining 2-d plane graph；Solid figure judge module, for judging whether the 2-d plane graph is three-dimensional geometrical figure, when judged result is When no, the figure acquisition module is driven to work；Coordinate obtaining module, for when the judged result of the solid figure judge module is is, selecting the two dimensional surface A point in interface where figure is two-dimensional coordinate system origin, and described two are drawn according to the two-dimensional coordinate system origin measurement The border point coordinates of dimensional plane figure；Coordinate transformation module, for obtaining boundary point after the border point coordinates of the 2-d plane graph is carried out into coordinate transform Three-dimensional coordinate；Projection module, for projecting to obtain three-dimensional graph according to the three-dimensional coordinate of the boundary point；The process that the figure acquisition module obtains 2-d plane graph is：Captured image is identified to obtain two dimension Planar graph, using camera to drafting have image drawing paper shoot, camera by catch the line weight on paper and The color and thickness of paintbrush in color de-regulation drawing software, meanwhile, by the color and ratio of Intelligent Recognition drawing paper, adjust picture The color and ratio of drawing paper in figure software, so as to obtain editable image data；The coordinate transformation module obtains boundary point after the border point coordinates of the 2-d plane graph is carried out into coordinate transform The process of three-dimensional coordinate is：Two-dimentional three-view diagram and two-dimensional geometry construction is obtained according to border point coordinates, two dimension is generated and calculates data；Data are calculated according to two dimension, three dimensions mould is converted to by data input, data reparation, data processing and data output Type；The coordinate data of three-dimensional space model is obtained according to three-dimensional space model；The coordinate transformation module calculates data according to two dimension, passes through data input, data reparation, data processing and data output Be converted to the process of three-dimensional space model also includes afterwards：According to the three-dimensional space model three-dimensional coordinate transformation of chosen boundary point will be represented into relative to the two of display screen Dimension coordinate；By the coordinate having determined compared with the coordinate for one after the other converting to obtain until producing equal result；Draw the three-dimensional coordinate corresponding to the two-dimensional points selected on display screen.
- 4. projection arrangement as claimed in claim 3, it is characterised in that the solid figure judge module judges that the two dimension is flat Whether face figure is that the process of three-dimensional geometrical figure is：Judge with the presence or absence of the face length of dotted line, shade or adjacent surface in the 2-d plane graph, be then to judge institute It is three-dimensional geometrical figure to state 2-d plane graph, no, then it is not three-dimensional geometrical figure to judge the 2-d plane graph.
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| CN105447812B (en) * | 2015-11-10 | 2018-11-27 | 南京大学 | A kind of three-dimensional moving image based on line array is shown and information concealing method |
| CN106204702A (en) * | 2016-06-23 | 2016-12-07 | 广州视睿电子科技有限公司 | The 3D effect of input word generates, inputs 3D display packing and the system of word |
| CN106910394B (en) * | 2017-02-21 | 2019-12-10 | 成都景中教育软件有限公司 | Dynamic geometric multi-coordinate system implementation method |
| CN106846435B (en) * | 2017-02-21 | 2020-05-26 | 成都景中教育软件有限公司 | Method for realizing dynamic geometric custom coordinate system based on parameters |
| CN109598992B (en) * | 2018-12-17 | 2021-06-25 | 广东小天才科技有限公司 | Question solving prompting method and learning equipment |
| CN112150049B (en) * | 2019-06-27 | 2023-01-17 | 厦门链石网络科技股份有限公司 | Stone plate boxing method based on application software |
| CN110378841A (en) * | 2019-07-24 | 2019-10-25 | 百度在线网络技术（北京）有限公司 | Display processing method and device |
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