CN1164709A - Converting method for geometric figure and mathematical equation and counter using the same - Google Patents
Converting method for geometric figure and mathematical equation and counter using the same Download PDFInfo
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- CN1164709A CN1164709A CN 96106291 CN96106291A CN1164709A CN 1164709 A CN1164709 A CN 1164709A CN 96106291 CN96106291 CN 96106291 CN 96106291 A CN96106291 A CN 96106291A CN 1164709 A CN1164709 A CN 1164709A
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Abstract
The present invention provides a converting method for geometrics and mathematical equations and calculator using the same. Said invented method includes steps of sampling inputted geometrics; selecting characteristic point from sampling point; graphic recognition and graphic matching, etc.. Said invented calculator includes: input device, sampling device, characteristic point selection device, graphic recognition device, geometrical equation and characteristics storage device, matching device and output device. After said invented converting method is used in calculator, it can make student use said calculator to learn, raise learning efficiency and interest in study.
Description
The present invention relates to the conversion method between a kind of geometric figure and the mathematical equation, which kind of geometric figure the figure that can be used to differentiate user's input in computing machine or counter is, and the mathematical equation of this figure is provided.The present invention also provides a kind of counter that makes in this way.
Geometric knowledge is middle school student's a compulsory course, and its learning difficulty is bigger.And the data of lecturing and studying in the past mostly occurs in writing form with dictionary, handbook, example etc., easily makes the learner produce uninteresting sense when study, has strengthened the difficulty of study.And the student need browse a lot of data when wondering the relevant geometric knowledge of a certain geometric feature and figure, make troubles to study.
Inventor's imagination, if when study, the student imports a width of cloth geometric figure on computing machine or counter, tell title, geometric properties and relevant this geometric other knowledge of the figure that the student imports by computing machine, must improve students'interest in learning greatly, improve learning efficiency.And want computing machine or counter can realize above-mentioned functions, and must there be pair nonstandard geometric figure of user's input to discern, judge correct geometric method.
In view of this, the object of the present invention is to provide a kind of geometric figure of computing machine or counter and conversion method between the mathematical equation of can be used for, computing machine or counter are in this way, can identify the geometric shape of user's input, so that this geometric figure title, mathematical equation, geometric properties and relevant this geometric other knowledge are provided.The present invention also provides a kind of computing machine or counter that uses this method.
Conversion method between geometric figure of the present invention and the mathematical equation comprises the following steps:
(1) geometric figure of user input is sampled, obtains sampling point set, its coordinate be Xj, Yj}, j are from 1 to M, M is a sampling number;
(2) from described sampling point set, select this geometric flex point as its unique point;
(3) distance in twos before calculating in the described sampling point set between A sampled point and last A the sampled point, if a distance is arranged less than a predetermined positive number threshold value in the described distance in twos, then the geometric figure of described input is a closed figure, otherwise is non-closed figure;
(4) if in step (3), determine the figure of this input when being closed figure, described unique point selected in step (2) is carried out the figure matching operation with enclosed shape geometric figure equation respectively; If in step (3), determine the figure of this input when being non-closed figure, described unique point selected in step (2) carried out the figure matching operation with non-enclosed shape geometric figure equation respectively;
(5) the geometric figure equation consistent with described Feature Points Matching is defined as the equation of this tablet pattern.
The present invention also provides a kind of counter said method, that have figure and the mutual translation function of mathematical equation that uses, and it comprises:
Input media is used to import the input of data such as geometric figure;
Sampling apparatus links with described input media, is used for the geometric figure of user's input is sampled, and the store sample point coordinate;
The unique point selecting device links with described sampling apparatus, is used for described sample point coordinate is differentiated, and the flex point that selects is wherein imported geometric unique point as this;
The figure discriminating gear, link with described sampling apparatus, preceding A sampled point in the described sampled point and the distance in twos between last A the sampled point are scheduled to the positive number threshold ratio with one, as a distance wherein being arranged less than this threshold value, then the geometric figure of described input is a closed figure, otherwise is non-closed figure;
Geometric figure equation and characteristic storage device are used for storing in advance about various geometric equations and this geometric feature and relevant geometric knowledge;
Coalignment, link with described unique point selecting device, figure discriminating gear and described geometric figure equation and characteristic storage device, according to the result of described figure discriminating gear, be used for described unique point is carried out the figure matching operation with the various closed figure equations or the non-closed figure equation that are stored in described geometric figure equation and the characteristic storage device respectively;
Output unit links with described coalignment, and according to the result of described coalignment, the geometric figure that coupling is obtained outputs on the screen and shows.
Below in conjunction with preferred embodiment and conjunction with figs., advantage of the present invention and feature are elaborated.
Fig. 1 is the process flow diagram of the conversion method between geometric figure of the present invention and the mathematical equation;
Fig. 2 is the block scheme with counter of figure and the mutual translation function of mathematical equation of the present invention;
Fig. 3 is the synoptic diagram of the figure imported of user;
Fig. 4 is the geometric synoptic diagram of output after counter is differentiated;
Fig. 5 is the synoptic diagram that has this geometric feature of output after counter is differentiated.
As shown in Figure 1, Fig. 1 shows the conversion method between geometric figure of the present invention and the mathematical equation.At first, be to import geometric figure by the user, the user can import geometric figure by touch screen.Because the user so the figure of input as shown in Figure 3, is nonstandard with the hand input.Conversion method of the present invention is carried out the conversion of geometric figure and mathematical equation on the geometric basis of this width of cloth user input.
After user's tablet pattern, the geometric figure of user input sampled, and (step 10), { Xj, Yj} supposes to have M sampled point, this M sampled point formation sampling point set to obtain the rectangular coordinate of each sampled point.Sample frequency can be set as required.It is initial point (0,0) that screen coordinate is generally set the upper left corner, and horizontal direction (X) increases progressively from left to right, and vertical direction (Y) increases progressively from the top down.
After having obtained sampling point set, in order to reduce later operation times, can be to these sampling numbers according to filtering (step 20).Its filter type is, (coordinate is respectively { Xj, Yj} and { Xj+1 Yj+1}) carries out computing, if mXj+1-Xjm+mYj+1-Yjm＜δ, then the elimination coordinate is (Xj, sampled point Yj) to two adjacent sampled points.Should be appreciated that this step is nonessential, this step is in order to improve operation efficiency.For δ, its value should be able to reduce the operation times of subsequent step as far as possible, but can not influence precision.
Then, enter step 30, carry out unique point and choose.In the present invention, be with the geometric unique point of geometric flex point as input.For choosing of flex point, can adopt the General Principle in the geometric knowledge, describe simply at this.The opposite in sign that we know that flex point is defined as: at an X0 place, f " (X0)=0, and at the f on X0 both sides ", then putting X0 is the flex point of the represented figure of function f (x).When choosing flex point in this way, can suitably relax the criterion of flex point.
Then, enter step 40, whether the geometric figure of differentiating input seals.Its concrete method is A sampled point and last A sampled point before getting in the sampling point set, the distance in twos between the corresponding point in A sampled point of A sampled point and back before calculating.If a distance is arranged less than a predetermined positive number threshold value in the described distance in twos, then the geometric figure of described input is a closed figure, otherwise is non-closed figure.
If in step 40, the figure that determines input is a closed figure, then flow process enters step 51, the unique point of choosing in step 30 is carried out the figure matching operation with closed geometry figure equation respectively, be about to each unique point coordinate equation of closed geometry figures such as substitution such as circle, ellipse, triangle, quadrilateral, polygon respectively, if these unique points satisfy a certain geometric equation, judge that then the geometric figure that the user imports is this class geometric figure.If in step 40, the figure that determines input is non-closed figure, then flow process enters step 52, the unique point of choosing in step 30 is carried out the figure matching operation with non-closed geometry figure equation respectively, be about to each unique point coordinate respectively substitution such as straight line, para-curve, hyperbolic curve, etc. the equation of non-closed geometry figure, if these unique points satisfy a certain geometric equation, judge that then the geometric figure that the user imports is this class geometric figure.When carrying out this coupling, can with due regard to provide certain degree of error, be which kind of geometric figure in order to avoid can't determine the figure of input.
At last, enter step 60 from step 51 or 52.In step 60, the geometric figure equation that coupling is consistent in step 51 or 52 is defined as the equation of this tablet pattern.
Describe the conversion method between geometric figure of the present invention and the mathematical equation above, described the counter with figure and the mutual translation function of mathematical equation of use said method of the present invention below in detail.
Referring to Fig. 2, Fig. 2 is the block scheme with counter of figure and the mutual translation function of mathematical equation of the present invention.As shown in Figure 2, counter of the present invention comprises input media 1, sampling apparatus 2, unique point selecting device 3, figure discriminating gear 4, geometric figure equation and characteristic storage device 5, coalignment 6 and input media 7.Input media 1 is mainly used in the user and imports geometric figure and other data.In the present embodiment, input media can be a touch screen.The user with light pen by the direct tablet pattern of touch screen.Sampling apparatus 2 receives the signal that the geometric figure of user's input produces from input media 1, and this signal is sampled, and obtains and the store sample point coordinate.Unique point selecting device 3 is connected on the sampling apparatus 2, and its function is that the sample point coordinate of sampling apparatus 2 outputs is differentiated, and the flex point that selects is wherein imported geometric unique point as this, and unique point is exported to coalignment 6 thereafter.Figure discriminating gear 4 also links with described sampling apparatus 2, preceding A sampled point in the sampling point set that its calculating sampling device 2 provides and the distance in twos between last A the sampled point, and with these distances respectively with a predetermined positive number threshold ratio, as a distance wherein being arranged less than this threshold value, the geometric figure of then judging this input is a closed figure, otherwise is judged to be non-closed figure.Equally, figure discriminating gear 4 is exported to thereafter coalignment 6 to the result.The geometric figure equation is used for storing in advance relevant various geometric equation and this geometric feature and relevant geometric knowledge with characteristic storage device 5.The equation of the closed geometry figure of storage or the equation of non-closed geometry figure carry out matching operation in the unique point that coalignment 6 provides unique point selecting device 3 according to the differentiation result of figure discriminating gear 4 and geometric figure equation and the characteristic storage device 5, its operational method above is being described, no longer repeats at this.The effect of output unit 7 is the matching results according to coalignment 6, and the geometric figure that coupling is obtained outputs on the screen, and this figure is the geometric figure of standard.For the defeated non-standard figure of user's hand, after having carried out above-mentioned processing, counter has determined the circle that is of user's input as Fig. 3, and then counter is presented at (as shown in Figure 4) on the screen according to this differentiation result with the circle of a standard.Simultaneously, as required, counter can also be presented at (as shown in Figure 5) on the screen to this geometric feature and the relevant knowledge that are stored in geometric figure equation and the characteristic storage device 5.In the present embodiment, screen is above-mentioned input media 1: touch screen.
In another embodiment, counter with figure and the mutual translation function of mathematical equation of the present invention can also comprise a filtration unit (not shown), this filtration unit is connected the output terminal of sampling apparatus 2, and its output terminal is connected on unique point selecting device 3 and the figure discriminating gear 4.It filters the sampled point that sampling apparatus 2 provides, if sampled point (Xj, Yj)) satisfies | Xj+1-Xj|+|Yj+1-Yj|＜δ, then remove this sampled point, wherein δ is a predetermined positive number.
Described embodiments of the invention above, in these embodiments, can also add some characteristics and function,, allowed the user that some parameter of this figure is revised or changed as after the geometric figure that determines user's input; Allow user's modification equation etc.The realization of these functions is not difficult for prior art, therefore is not described in detail in this.
From top description as can be seen, the user utilizes the counter with figure and the mutual translation function of mathematical equation of the present invention can obtain a certain geometric relevant knowledge easily, both improved user's learning interest, can improve learning efficiency again, make the user have one comprehensively to understand geometric figure.
Claims (5)
1. the conversion method between geometric figure and the mathematical equation is characterized in that, comprises the following steps:
(1) geometric figure of user input is sampled, obtains sampling point set, its coordinate be Xj, Yj}, j are from 1 to M, M is a sampling number;
(2) from described sampling point set, select this geometric flex point as its unique point;
(3) distance in twos before calculating in the described sampling point set between A sampled point and last A the sampled point, if a distance is arranged less than a predetermined positive number threshold value in the described distance in twos, then the geometric figure of described input is a closed figure, otherwise is non-closed figure;
(4) if in step (3), determine the figure of this input when being closed figure, described unique point selected in step (2) is carried out the figure matching operation with enclosed shape geometric figure equation respectively; If in step (3), determine the figure of this input when being non-closed figure, described unique point selected in step (2) carried out the figure matching operation with non-enclosed shape geometric figure equation respectively;
(5) the geometric figure equation consistent with described Feature Points Matching is defined as the equation of this tablet pattern.
2. the method for claim 1 is characterized in that, after described step (1), described sampled point is filtered, if sampled point (Xj, Yj) satisfy | Xj+1-Xj|+|Yj+1-Yj|＜δ, then remove this sampled point, wherein δ is a predetermined positive number.
3. the counter with figure and the mutual translation function of mathematical equation is characterized in that, comprising:
Input media is used to import the input of data such as geometric figure;
Sampling apparatus links with described input media, is used for the geometric figure of user's input is sampled, and the store sample point coordinate;
The unique point selecting device links with described sampling apparatus, is used for described sample point coordinate is differentiated, and the flex point that selects is wherein imported geometric unique point as this;
The figure discriminating gear, link with described sampling apparatus, preceding A sampled point in the described sampled point and the distance in twos between last A the sampled point are scheduled to the positive number threshold ratio with one, as a distance wherein being arranged less than this threshold value, then the geometric figure of described input is a closed figure, otherwise is non-closed figure;
Geometric figure equation and characteristic storage device are used for storing in advance about various geometric equations and this geometric feature and relevant geometric knowledge;
Coalignment, link with described unique point selecting device, figure discriminating gear and described geometric figure equation and characteristic storage device, according to the result of described figure discriminating gear, be used for described unique point is carried out the figure matching operation with the various closed figure equations or the non-closed figure equation that are stored in described geometric figure equation and the characteristic storage device respectively;
Output unit links with described coalignment, and according to the result of described coalignment, the geometric figure that coupling is obtained outputs on the screen and shows.
4. counter as claimed in claim 3 is characterized in that, described input media is a touch screen.
5. counter as claimed in claim 3, it is characterized in that, also comprise a filtration unit, be connected the output terminal of described sampling apparatus, its output terminal is connected on described unique point selecting device and the described figure discriminating gear, and the sampled point that described sampling apparatus is provided filters, if sampled point (Xj, Yj)) satisfy | Xj+1-Xj|+|Yj+1-Yj|＜δ, then remove this sampled point, wherein δ is a predetermined positive number.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN96106291A CN1078954C (en) | 1996-05-03 | 1996-05-03 | Converting method for geometric figure and mathematical equation and counter using the same |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN96106291A CN1078954C (en) | 1996-05-03 | 1996-05-03 | Converting method for geometric figure and mathematical equation and counter using the same |
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| Publication Number | Publication Date |
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| CN1164709A true CN1164709A (en) | 1997-11-12 |
| CN1078954C CN1078954C (en) | 2002-02-06 |
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| Application Number | Title | Priority Date | Filing Date |
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| CN96106291A Expired - Fee Related CN1078954C (en) | 1996-05-03 | 1996-05-03 | Converting method for geometric figure and mathematical equation and counter using the same |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102750260A (en) * | 2011-03-25 | 2012-10-24 | 卡西欧计算机株式会社 | Electronic device which renders graph, and graph rendering method |
| CN104423663A (en) * | 2013-08-29 | 2015-03-18 | 联想(北京)有限公司 | Inputting identification method and electronic equipment |
| CN108074425A (en) * | 2017-12-13 | 2018-05-25 | 吉林工程技术师范学院 | A kind of higher mathematics integrated learning system |
-
1996
- 1996-05-03 CN CN96106291A patent/CN1078954C/en not_active Expired - Fee Related
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102750260A (en) * | 2011-03-25 | 2012-10-24 | 卡西欧计算机株式会社 | Electronic device which renders graph, and graph rendering method |
| CN102750260B (en) * | 2011-03-25 | 2015-09-16 | 卡西欧计算机株式会社 | Describe electronic equipment and the curve plotting method of curve |
| CN104423663A (en) * | 2013-08-29 | 2015-03-18 | 联想(北京)有限公司 | Inputting identification method and electronic equipment |
| CN104423663B (en) * | 2013-08-29 | 2017-11-28 | 联想(北京)有限公司 | A kind of input recognition method and electronic equipment |
| CN108074425A (en) * | 2017-12-13 | 2018-05-25 | 吉林工程技术师范学院 | A kind of higher mathematics integrated learning system |
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| Publication number | Publication date |
|---|---|
| CN1078954C (en) | 2002-02-06 |
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