CN105608984A - Device and method for Gauss-Kruger map projection demonstration - Google Patents
Device and method for Gauss-Kruger map projection demonstration Download PDFInfo
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- CN105608984A CN105608984A CN201610111825.XA CN201610111825A CN105608984A CN 105608984 A CN105608984 A CN 105608984A CN 201610111825 A CN201610111825 A CN 201610111825A CN 105608984 A CN105608984 A CN 105608984A
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- length
- projection
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- checking line
- length checking
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Classifications
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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
- G09B27/00—Planetaria; Globes
- G09B27/08—Globes
-
- 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
- G09B29/00—Maps; Plans; Charts; Diagrams, e.g. route diagram
- G09B29/003—Maps
- G09B29/005—Map projections or methods associated specifically therewith
Abstract
The invention relates to a device and a method for Gauss-Kruger map projection demonstration. The device comprises a foundation, a bulb and a tellurion body, wherein the bulb is arranged at the center of the tellurion body, the outer surface of the tellurion body has a deformation verification triangle, longitude lines, latitude lines, central longitude lines, an equator, a first length verification line, a second length verification line and a third length verification line, the external portion of the tellurion body is sleeved in a transparent drawing cover in the elliptical column shape, the center axis is perpendicular to an earth axis of the tellurion body, and the inner surface of the transparent drawing cover and two poles of the tellurion body are in a tangent mode. Through the device and the method, the Gauss-Kruger projection process can be represented simply and conveniently, Gauss-Kruger projection deformation properties are represented by utilizing the deformation verification triangle and the length verification lines, materials are easily obtained, design and the manufacturing technology are simple and convenient, abstract teaching is made to be vivid and visual, and the cartology teaching effect is greatly improved.
Description
Technical field
The invention belongs to college demonstration equipment technical field, be specifically related to a kind of Gauss Ke Lvge groundFigure projection demonstration device and method.
Technical background
High this ?Ke Lvge projection is to be drafted by Germany mathematics man, physicist, astronomer Gauss, by moralState geodesist Ke Lvge is supplemented projection formula, therefore be called high this ?Ke Lvge projection. Due to groundBall is an irregular spheroid, for its lip-deep Nature and Man literary composition key element is represented to go on plane,Just must use map projection, but until not have at present the very perfect map projection of one, reasonBe that earth ellipsoid face is the curved surface that can not open up, in map projection's process, have area, length, angleDistortion, and constant in order to ensure a kind of attribute, must sacrifice all the other two kinds of attributes. In a line teaching, normalUse the derivation of equation or play the mode of magic lantern and impart knowledge to students, but effect is not good enough, reason is that theory is comparatively hereinComplexity and process are comparatively abstract, and student is not easy to understand.
Summary of the invention:
In order to reform existing teaching method, promote teaching level, strengthen intuitive, life that map projection gives lessonsMoving property and interest, solve the not good problem of teaching efficiency, the invention provides a kind of map projection apparatus for demonstratingAnd method, utilize this device to demonstrate the whole process of Gaüss-Krüger projection, student can be observed intuitivelyAtural object key element is transformed into the whole process of plane from sphere, understand deformation properties and the spy of Gaüss-Krüger projectionPoint.
Meanwhile, the invention provides Gauss gram Lu that the above-mentioned Gaüss-Krüger projection apparatus for demonstrating of a kind of use is realizedLattice projection demonstration method.
The present invention realizes the technical scheme that above-mentioned technical purpose adopts:
This Gauss Ke Lvge map projection apparatus for demonstrating, comprises base and is arranged on bulb on base and thoroughlyPhotosensitiveness tellurion main body, bulb is arranged on the sphere center position of tellurion main body, and the outer surface of tellurion main body hasDistortion checking triangle and warp, parallel, central meridian, equator, the first length checking line a, the second lengthDegree checking line b and the 3rd length checking line c, the first length checking line a and the 3rd length checking line c divideCloth is at both sides and the first length checking line a, the second length checking line b, the 3rd of the second length checking line bLength checking line c is along warp direction and be distributed in different latitudes, at the outside of tellurion main body suitThere is figure paper cap, the cross section ovalize of figure paper cap thoroughly, its central shaft is vertical with the earth's axis of tellurion main bodyAnd the inner surface of figure paper cap and the two poles of the earth of tellurion main body are tangent thoroughly.
Above-mentioned the first length checking line a and the second length checking line b and the second length checking line b and the 3rdDifference of longitude between length checking line c is that 1.5 °～3 °, difference of latitude are 30 °～60 °.
Above-mentioned figure paper cap is made up of oval column sleeve and saturating drawing, and oval column sleeve is to make ellipse by thin wireColumn structure, its cross section ovalize, the major axis of cross section equate with the equatorial diameter of tellurion main body,The earth's axis of minor axis and tellurion main body is equal in length, and the equator of the height of this ellipse column sleeve and tellurion main body is straightFootpath equates, puts and is coated with drawing and forms figure paper cap at cylindroid.
Above-mentioned tellurion main body comprises tellurion skeleton and covers polyester on tellurion skeleton outer surface thinFilm, distortion checking triangle sticks on the surface of polyester film.
Utilize map projection's demenstration method of above-mentioned Gauss Ke Lvge map projection apparatus for demonstrating, by walking belowRapid realization:
(1) make bulb luminous after switching on power, the light that bulb sends see through polyester film make warp, parallel,Distortion checking triangle, the first length checking line a, the second length checking line b, the 3rd length checking line cThoroughly on figure paper cap, forming projection;
(2) in a projection zone, draw one by one on saturating figure paper cap with pencil central meridian and equator andAt the warp of central meridian both sides and the parallel of both sides, equator, then draw the leg-of-mutton projection line of distortion checking andThe projection line of the first length checking line a, the second length checking line b, the 3rd length checking line c, along saturating figureThe generatrix direction of paper cap takes off drawing, and thoroughly on drawing, institute's drawing shape is this projection after Gaüss-Krüger projectionThe plane situation of band;
(3) measure figure paper cap upslide movie queen's distortion checking triangle and warp, parallel, central meridian,The correspondence of equator, the first length checking line a, the second length checking line b and the 3rd length checking line c is longDegree, angle, and calculate the distortion checking triangle area after projection, the relatively triangle before and after projectionAngle, area change and central meridian and the first length checking line a, the second length checking line b and theThe length variations of three length checking line c, determines respectively the angle after Gaüss-Krüger projection in this projection zoneDistortion, area distortion, length deformation;
(4) put and again cover new saturating figure paper cap at cylindroid, repeat (1)～(3), under formingThe Gaüss-Krüger projection of a projection zone, until the whole projection zones of tellurion main body all complete projection, will throwThe plane that shadow is good is stitched together according to longitude scope, has formed the Gaüss-Krüger projection ground of the whole earthFigure, and demonstrate out its projection deformation.
Gauss Ke Lvge map projection's apparatus for demonstrating of the present invention and method are after switching on power, and bulb sendsLight transmission polyester film, warp, parallel, central meridian, distortion checking triangle, the first length are testedCard line, the second length checking line and the 3rd length checking line are forming projection on figure paper cap thoroughly, use pen at saturating figureOn paper cap, draw the projection line of warp, parallel, central meridian, distortion checking triangle and each length checking line,After completing, saturating drawing is taken off along oval column sleeve bus position, on drawing, institute's line drawing bar is gram Lu through Gauss thoroughlyPlane situation after lattice projection in a projection zone, the present invention can be by method simply and easily figurativelyThe process of bright Gaüss-Krüger projection utilizes distortion checking triangle and length checking line to Gauss gram Lu simultaneouslyThe deformation properties of lattice projection carries out the explanation of visual pattern, in addition the present invention draw materials conveniently, design and produce easy,Thereby abstract theory teaching visualization, livelyization can be able to be attracted to student's notice, greatlyImprove the teaching efficiency of cartography.
Brief description of the drawings
Fig. 1 is the internal structure schematic diagram of the Gauss Ke Lvge map projection apparatus for demonstrating of embodiment 1.
Fig. 2 is the right side view of Fig. 1.
Specific implementation method
Now in conjunction with the accompanying drawings and embodiments technical scheme of the present invention is further described, but the present invention is notOnly limit to following enforcement situation.
Embodiment 1
Referring to Fig. 1 and 2, the Gauss Ke Lvge map projection apparatus for demonstrating of the present embodiment is by base 1, lampBubble 3, tellurion main body 4 and saturating figure paper cap 2 form.
Wherein, base 1 is common table lamp base 1, and bulb 3 is installed on base 1, outside bulb 3Tellurion main body 4 is also installed, and bulb 3 is positioned at the sphere center position of tellurion main body 4, the ground of the present embodimentGlobe main body 4 be by thin wire according to graticule be overlapped to form spherical cancellated plain type tellurion skeleton andCover the good polyester film composition of light transmission on tellurion skeleton, this tellurion skeleton bottom is fixed on the endOn seat 1, top is fastening with pin, its specification and common tellurion measure-alike, outside polyester filmOn surface, be pasted with right angle distortion checking triangle 5, and mark warp, parallel, central meridian,Equator, the first length checking line a, the second length checking line b and the 3rd length checking line c, the first lengthChecking line a and the second length checking line b, the 3rd length checking line c are along warp direction, and the second lengthDegree checking line b is marked on central meridian, and the first length checking line a is marked at the second length checking line b'sBelow and be distributed in the left side of central meridian, and and the second length checking line b between the difference of longitude that forms be3 °, the 3rd length checking line c is marked at the top of the second length checking line b and is distributed in central meridianRight side, and and the second length checking line b between the difference of longitude that forms be 3 °, ensure the first length checkingLine a, the second length checking line b, the 3rd length are verified line c along warp direction and are distributed in different latitudesDegree, the difference of latitude between the first length checking line a and the second length checking line b is 30 °, the second length is testedDifference of latitude between card line b and the 3rd length checking line c is 30 °, guarantees to reflect in different latitudeDeformation. In the outer cover of tellurion main body 4, figure paper cap 2 is housed, the saturating figure paper cap 2 of the present embodiment isBe made up of oval column sleeve and saturating drawing, oval column sleeve is to make cylindroid tubular structure by thin wire, and it is transversalFace ovalize, the major axis of cross section equate with the equatorial diameter of tellurion main body 4, minor axis and tellurionThe earth's axis of main body 4 is equal in length, and the height of this ellipse column sleeve equates with the equatorial diameter of tellurion main body 4,Put and be coated with drawing and form figure paper cap 2 at cylindroid, figure paper cap 2 levels are installed thoroughly, i.e. drawing thoroughlyThe central shaft of cover 2 is vertical with the earth's axis of tellurion main body 4, and inner surface and the tellurion of saturating figure paper cap 2Two limits of main body 4 are tangent.
The method of carrying out map projection's demonstration with this Gauss Ke Lvge map projection apparatus for demonstrating is real by following stepsExisting:
(1) make bulb 3 luminous after switching on power, the light that bulb 3 sends makes warp, parallel, distortionChecking triangle 5, the first length checking line a, the second length checking line b, the 3rd length checking line c are thoroughlyOn figure paper cap 2, form projection.
(2), in a projection zone, thoroughly on figure paper cap 2, drawing one by one central meridian and left and right two with pencilTwo warps on limit, go out the projection line of four parallels of equator and upper and lower part with red stroke, with blueStroke go out the projection line of distortion checking triangle 5, change the position of distortion checking triangle 5, again useBlue stroke goes out another group projection line of distortion checking triangle 5, goes out the first length test with green strokeThe projection line of card line a, the second length checking line b, the 3rd length checking line c, along oval column sleeve bus sideTo taking off drawing, on saturating drawing, institute's drawing shape is the plane situation of Gaüss-Krüger projection Hou Gai projection zone.
(3) measure angle and the area of distortion checking triangle 5 on polyester film, then measure figure paper cap 2Angle and the area of upslide movie queen's distortion checking triangle 5, the distortion checking triangle before and after compared projections5 angle and area change, if projection front and rear angles equates explanation, Gaüss-Krüger projection does not have angular distortion,If area equates that explanation Gaüss-Krüger projection does not have area distortion before and after projection, otherwise, contrary.
Measure the length of central meridian on polyester film and the saturating central meridian of projection on figure paper cap 2 with tape measureLength, the length of central meridian before and after compared projections, if proof Gaüss-Krüger projection equal in length is in central authoritiesOn warp, there is no length deformation;
Again with tape measure measure respectively calculate on polyester film the first length checking line a, the second length checking line b andThe first length checking line a, second of projection on the corresponding length of the 3rd length checking line c and thoroughly figure paper cap 2The corresponding length of length checking line b and the 3rd length checking line c, is distributed in different warps before and after compared projectionsThe first length checking line a, the second length checking line b on degree and latitude and the 3rd length checking line c'sLength variations, prove in same projection zone from central meridian more away from, length deformation is larger, from equatorNearer, length deformation is larger.
(4) put and again cover new saturating figure paper cap 2 at cylindroid, repeat (1)～(3), under formingThe Gaüss-Krüger projection of a projection zone, until the whole projection zones of tellurion main body 4 all complete projection, willThe plane that projection is good is stitched together according to longitude scope, has formed the Gaüss-Krüger projection of the whole earthMap, and demonstrate out its projection deformation.
Embodiment 2
In the present embodiment, the first length checking line a and the second length checking line b, the 3rd length checking line cAlong warp direction, and the second length verifies that line b is marked on central meridian, the first length checking line aBe marked at the left side that the second length is verified the below of line b and is distributed in central meridian, and test with the second lengthThe difference of longitude forming between card line b is 1.5 °, and the 3rd length checking line c is marked at the second length checking line bTop and be distributed in the right side of central meridian, and and the second length checking line b between the difference of longitude that formsBe 1.5 °, ensure the first length checking line a, the second length checking line b, the 3rd length checking line c edgeWarp direction and be distributed in different latitudes, the first length checking line a and the second length checking line b itBetween difference of latitude be 35 °, the difference of latitude between the second length checking line b and the 3rd length checking line c is35°。
Other structure is identical with embodiment 1.
Carry out the method and embodiment 1 phase of map projection's demonstration with this Gauss Ke Lvge map projection apparatus for demonstratingWith.
Embodiment 3
In the present embodiment, the first length checking line a and the second length checking line b, the 3rd length checking line cAlong warp direction, and the second length verifies that line b is marked on central meridian, the first length checking line aBe marked at the left side that the second length is verified the below of line b and is distributed in central meridian, and test with the second lengthThe difference of longitude forming between card line b is 2 °, and the 3rd length checking line c is marked at the second length checking line bTop and be distributed in the right side of central meridian, and and the second length checking line b between the difference of longitude that formsBe 2 °, ensure the first length checking line a, the second length checking line b, the 3rd length checking line c alongWarp direction and be distributed in different latitudes, between the first length checking line a and the second length checking line bDifference of latitude be 60 °, the difference of latitude between the second length checking line b and the 3rd length checking line c is 60 °.
Other structure is identical with embodiment 1.
Carry out the method and embodiment 1 phase of map projection's demonstration with this Gauss Ke Lvge map projection apparatus for demonstratingWith.
In above-described embodiment, verify that the length of line and angle and the position etc. of distortion checking triangle 5 are all passableAdjust, if distortion checking triangle 5 can be the right angled triangle in embodiment, can be also isosceles in good timeThe triangle of triangle or equilateral triangle or other angles, it is not limited only to above-mentioned enforcement situation.
Claims (5)
1. a Gauss Ke Lvge map projection apparatus for demonstrating, is characterized in that: comprise base (1) andBe arranged on bulb (3) and light transmission tellurion main body (4) on base (1), bulb (3) is arranged onThe sphere center position of tellurion main body (4), the outer surface of described tellurion main body (4) has distortion checking triangleShape (5) and warp, parallel, central meridian, equator, the first length checking line (a), the second length checkingLine (b) and the 3rd length checking line (c), the first length checking line (a) and the 3rd length checking line (c)Be distributed in the both sides of the second length checking line (b) and the first length checking line (a), the second length checking line (b),The 3rd length checking line (c) is along warp direction and be distributed in different latitudes, in tellurion main body (4)Outer cover figure paper cap (2) is housed, the thoroughly cross section ovalize of figure paper cap (2), its central shaft and groundTwo of the inner surface of the vertical and saturating figure paper cap (2) of the earth's axis of globe main body (4) and tellurion main body (4)Extremely tangent.
2. Gauss Ke Lvge according to claim 1 map projection apparatus for demonstrating, is characterized in that: instituteState the first length checking line (a) and the second length checking line (b) and the second length checking line (b) withDifference of longitude between the 3rd length checking line (c) is that 1.5 °～3 °, difference of latitude are 30 °～60 °.
3. Gauss Ke Lvge according to claim 1 map projection apparatus for demonstrating, is characterized in that: instituteState figure paper cap (2) and be made up of oval column sleeve and saturating drawing, oval column sleeve is to make cylindroid by thin wireShape structure, its cross section ovalize, i.e. the equatorial diameter phase of the major axis of cross section and tellurion main body (4)The earth's axis Deng, minor axis and tellurion main body (4) is equal in length, the height of this ellipse column sleeve and tellurion main body(4) equatorial diameter equates, puts and is coated with drawing and forms figure paper cap (2) at cylindroid.
4. Gauss Ke Lvge according to claim 1 map projection apparatus for demonstrating, is characterized in that: instituteState tellurion main body (4) and comprise tellurion skeleton and cover the polyester film on tellurion skeleton outer surface,Distortion checking triangle (5) sticks on the surface of polyester film.
5. one kind is utilized the map projection of the Gauss Ke Lvge map projection apparatus for demonstrating described in claim 1 to drillShow method, it is characterized in that being realized by following steps:
(1) make bulb (3) luminous after switching on power, the light that bulb (3) sends sees through polyester filmMake warp, parallel, distortion checking triangle (5), the first length checking line (a), the second length checking line(b), the 3rd length checking line (c) is in the upper formation of figure paper cap (2) projection thoroughly;
(2), in a projection zone, thoroughly on figure paper cap (2), drawing one by one central meridian and red with pencilRoad and at the warp of central meridian both sides and the parallel of both sides, equator, then draw distortion checking triangle (5)Projection line and the first length checking line (a), the second length checking line (b), the 3rd length checking line (c)Projection line, take off drawing along the generatrix direction of saturating figure paper cap (2), thoroughly on drawing, institute's drawing shape isThe plane situation of Gaüss-Krüger projection Hou Gai projection zone;
(3) triangle (5) and warp, latitude are verified in the distortion that measures figure paper cap (2) upslide movie queenLine, central meridian, equator, the first length checking line (a), the second length checking line (b) and the 3rd lengthCorresponding length, the angle of degree checking line (c), and calculate the distortion checking triangle area after projection, thanTriangular angles, area change and the central meridian before and after projection and the first length checking line (a),The length variations of the second length checking line (b) and the 3rd length checking line (c), determines respectively this throwingAngular distortion in shadow bands after Gaüss-Krüger projection, area distortion, length deformation;
(4) put and again cover new saturating figure paper cap (2) at cylindroid, repeat (1)～(3), shapeBecome the Gaüss-Krüger projection of next projection zone, until the whole projection zones of tellurion main body (4) all complete throwingShadow, is stitched together plane good projection according to longitude scope, formed Gauss gram Lu of the whole earthLattice projected map, and demonstrate out its projection deformation.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610111825.XA CN105608984A (en) | 2016-02-29 | 2016-02-29 | Device and method for Gauss-Kruger map projection demonstration |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610111825.XA CN105608984A (en) | 2016-02-29 | 2016-02-29 | Device and method for Gauss-Kruger map projection demonstration |
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| CN105608984A true CN105608984A (en) | 2016-05-25 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610111825.XA Pending CN105608984A (en) | 2016-02-29 | 2016-02-29 | Device and method for Gauss-Kruger map projection demonstration |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109300391A (en) * | 2018-10-16 | 2019-02-01 | 中国人民解放军海军工程大学 | A kind of Map Design method and apparatus |
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|---|---|---|---|---|
| EP0509839A2 (en) * | 1991-04-19 | 1992-10-21 | Hitachi, Ltd. | Digital cartographic system for geographical information processing |
| CN201210364Y (en) * | 2008-01-28 | 2009-03-18 | 金忠民 | Gauss-Kruger projection instructional assistant instrument |
| CN201600828U (en) * | 2010-02-12 | 2010-10-06 | 王守峰 | Teaching demonstrator of length of day and night |
| CN205508256U (en) * | 2016-02-29 | 2016-08-24 | 西安科技大学 | Gauss ke lvge map projection presentation device |
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2016
- 2016-02-29 CN CN201610111825.XA patent/CN105608984A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0509839A2 (en) * | 1991-04-19 | 1992-10-21 | Hitachi, Ltd. | Digital cartographic system for geographical information processing |
| CN201210364Y (en) * | 2008-01-28 | 2009-03-18 | 金忠民 | Gauss-Kruger projection instructional assistant instrument |
| CN201600828U (en) * | 2010-02-12 | 2010-10-06 | 王守峰 | Teaching demonstrator of length of day and night |
| CN205508256U (en) * | 2016-02-29 | 2016-08-24 | 西安科技大学 | Gauss ke lvge map projection presentation device |
Non-Patent Citations (1)
| Title |
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| 杨国清主编: "《控制测量学》", 30 September 2005 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109300391A (en) * | 2018-10-16 | 2019-02-01 | 中国人民解放军海军工程大学 | A kind of Map Design method and apparatus |
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