CN101625807A - Four-color map teaching instrument and manufacturing method thereof - Google Patents
Four-color map teaching instrument and manufacturing method thereof Download PDFInfo
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- CN101625807A CN101625807A CN200910060374A CN200910060374A CN101625807A CN 101625807 A CN101625807 A CN 101625807A CN 200910060374 A CN200910060374 A CN 200910060374A CN 200910060374 A CN200910060374 A CN 200910060374A CN 101625807 A CN101625807 A CN 101625807A
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Abstract
The invention discloses a four-color map teaching instrument and a manufacturing method thereof, relating to the education and teaching field of mathematics and geography and aiming at solving the technical problem that each country can only publish and issue five-color maps, six-color maps and other maps, the number of the colors of which is more than 4 at present. The four-color map of the invention has administrative divisions drawn by four independent colors, the administrative divisions at the same level, which share boundaries, have different colors, and the four-color map is drawn on the carriers such as globes, wall maps, slides, jigsaws and the like. The invention is suitable for drawing the map with four colors.
Description
Technical field
The present invention relates to mathematics and geographical field of Education and teaching, particularly a kind ofly be used for instruments used for education and the using method thereof that four-color map is tinted.
Background technology
1852, the four-color map guess is proposed in the British Gus, be four-colour problem again or be " four colour theorem ": " draw any width of cloth administrative division map, 4 kinds of colors at the most just can make the national colours difference of conterminousness." over 160 years, mathematician, map expert and computer elite study four-colour problem, prove four colour theorem, the theory and the method for drawing four-color map, can be referred to as " the painted theory of doubling-up ", do not have thoroughly to solve the proof of four colour theorem.U.S.'s mathematics can be announced in 1976: " mathematician Ha Ken and computer elite A Peier calculate 10000 special figure with computing machine, and four colour theorem is set up." obviously; it is impossible removing to calculate infinite many special figure with computing machine; people can't finish the work that U.S.'s mathematics home computer proof four colour theorem carries out computing, so U.S. mathematician does not have last proof four colour theorem in the scope of infinite multirow administrative division.Under such technical background, countries in the world can only publish and distribute multicolored map more than four looks, six look maps etc.
Summary of the invention
The present invention is intended to solve the technical matters that present countries in the world can only publish and distribute multicolored map more than four looks, six look maps etc., so that a kind of four-color map teaching instrument that four kinds of colors can finish exactly and preparation method thereof that only uses to be provided.
The objective of the invention is to be achieved through the following technical solutions.
Four-color map teaching instrument of the present invention, wherein each administrative division of four-color map is drawn by four kinds of colors independently, and the administrative area at the same level color difference of conterminousness, and aforementioned four-color map is drawn on the carriers such as terrestrial globe, wall chart, lantern slide, picture mosaic.
Aforesaid four-color map teaching instrument method for making wherein comprises following steps:
A) all administrative areas on the map are marked with 1～N;
B) make trial balance, the first from left of trial balance is classified the primary area as, and second classifies attribute area as, and the 3rd row beginning be to the right the adjacent area, is arranged in order digital 1～N in the primary area from top to bottom; Each administrative division of corresponding 1～N representative, as corresponding certain digital boundary line, administrative area is end to end closed sides boundary line, then in its colleague's secondary series attribute area, mark it for closing the circle attribute, as the open boundary line of corresponding certain digital boundary line, administrative area for not joining from beginning to end, then the secondary series attribute area its colleague marks it for opening the circle attribute, by the administrative division of aforementioned rule correspondence 1～N, close the circle attribute or open the circle attribute at its corresponding secondary series attribute area mark; The administrative division of corresponding 1～N representative lists respectively in its corresponding colleague adjacent area that to fill in the administrative division adjacent in turn with its border corresponding digital;
C) as the attribute area of certain administrative division correspondence for closing the circle attribute, according to the corresponding administrative division color of colleague primary area institute with go together the different chromogens of all adjacent areas corresponding administrative division colors of institute then, the different chromogens of the adjacent adjacent area corresponding administrative division color of institute then, the corresponding administrative division color of the first from left row adjacent area institute of going together and the rightest row adjacent area different chromogen of corresponding administrative division color then, can lack look few chromogen then, use ABCD to represent four kinds of colors respectively, the administrative division color that primary area and adjacent area are respectively listed marks; As the attribute area of certain administrative division correspondence for opening the circle attribute, according to the corresponding administrative division color of colleague primary area institute with go together the different chromogens of all adjacent areas corresponding administrative division colors of institute then, the different chromogens of the adjacent adjacent area corresponding administrative division color of institute then, the corresponding administrative division color of the first from left row adjacent area institute of going together and the rightest row adjacent area corresponding administrative division color can homochromy principles, can lack look few chromogen then, use ABCD to represent four kinds of colors respectively, the administrative division color that primary area and adjacent area are respectively listed marks;
D) according to above-mentioned steps c) color in principle and method, respectively the color mark is carried out in each primary area of going of numbering 1～N, the administrative division of adjacent area representative, the same color mark is used in the administrative division of identical numbering, finishes until the whole marks of the administrative division color of 1～N;
E) the corresponding alphabetical ABCD of four kinds of colors is used in corresponding 1～N the administrative division that finishes with the ABCD mark respectively, carries out painted to each administrative division;
F) above-mentioned completed four-color map is drawn on the carriers such as terrestrial globe, wall chart, lantern slide, picture mosaic.
The beneficial effect of four-color map teaching instrument of the present invention and preparation method thereof:
1. only use four kinds of colors can finish painted to all kinds of maps, result of calculation is accurate;
2. method is simple;
3. instruments used for education such as the terrestrial globe of use four-color map drafting, wall chart, lantern slide, picture mosaic can increase the ability that child and student learn, know number, knowledge figure, space imagination and thinking;
Description of drawings
Fig. 1 is an example map of the present invention
Embodiment
Accompanying drawing 1 is consulted in application principle of the present invention, effect etc., is illustrated by following embodiment.
A fundamental property of four-color map is " the adjacent lines administrative division is not homochromy ", therefore, if Guangdong, Hainan, Taiwan, or Bulgaria, Georgia into homochromy four-color map be false four-color map.
On terrestrial globe, or on map, references object is used as in certain administrative area, is called the primary area, the primary area constitutes circle with all adjacent areas that are connected this primary area in turn.The circle branch closes circle and opens circle two classes.Primary area 1 and one of his all adjacent areas formation are closed circle in the accompanying drawing 1, be designated as 1 ⊙, but the row formula are 1 ⊙ 24567.Primary area 4 and one of his all adjacent areas formation are opened circle among Fig. 1, be designated as 4 ∈, but the row formula are 4 ∈ 5123.
String circle: two or arrange in turn, constitute the string circle more than two and even infinite a plurality of circle.
The painted theory of string circle: general principle is adjacent not homochromy, is subdivided into following two classes.
1. close the painted theory of circle: main neighbour is not homochromy, and is adjacent not homochromy, and head and the tail are not homochromy, can lack not polychrome.
2. open the painted theory of circle: main neighbour is not homochromy, and is adjacent not homochromy, and head and the tail can be homochromy, can lack not polychrome.
Annotate: " head and the tail are not homochromy " by closing the adjacent decision of head and the tail in the circle, " head and the tail can be homochromy " is by opening the non-conterminous decision of head and the tail in the circle.The principle that " can lack not polychrome " is in the circle that has, can dichromatism, just not three looks; Can three looks, just not four looks.
The flow process of string circle colouring comprises: 1. serialization; 2. calculate; 3. painted.
The calculating here is meant and leaves map, and the painted theory of application strings circle is tabulated or is listed as careless formula, uses written calculation, or calculates with counter, draws each all types administrative area, various countries, the continent zoning four-color map with character express.
Choose arbitrary administrative area on accompanying drawing 1, it is masked as 1, other administrative areas are masked as 2,3,4 to 7 with random fashion;
The the first from left of trial balance is classified the primary area as, and second classifies attribute area as, and the 3rd row beginning be to the right the adjacent area, is arranged in order digital 1～7 in the primary area from top to bottom; Each administrative division of corresponding 1～7 representative, as corresponding certain digital boundary line, administrative area is end to end closed sides boundary line, then in its colleague's secondary series attribute area, mark it for closing the circle attribute, as the open boundary line of corresponding certain digital boundary line, administrative area for not joining from beginning to end, then the secondary series attribute area its colleague marks it for opening the circle attribute, by the administrative division of aforementioned rule correspondence 1 to 7, close the circle attribute or open the circle attribute at its corresponding secondary series attribute area mark; The administrative division of corresponding 1～7 representative respectively lists in its corresponding colleague adjacent area and to fill in the corresponding numeral of the administrative division adjacent with its border, and (wherein ∈ represents and opens circle to be produced as follows trial balance; Circle is closed in the ⊙ representative):
According to closing the painted theory of circle: main neighbour is not homochromy, and is adjacent not homochromy, and head and the tail are not homochromy, can lack not polychrome.
As the attribute area of administrative division correspondence for closing the circle attribute, according to the corresponding administrative division color of colleague primary area institute with go together the different chromogens of all adjacent areas corresponding administrative division colors of institute then, the different chromogens of the adjacent adjacent area corresponding administrative division color of institute then, the corresponding administrative division color of the first from left row adjacent area institute of going together and the rightest row adjacent area different chromogen of corresponding administrative division color then, can lack look few chromogen then, use ABCD to represent four kinds of colors respectively, the administrative division color that primary area and adjacent area are respectively listed marks.
According to opening the painted theory of circle: main neighbour is not homochromy, and is adjacent not homochromy, and head and the tail can be homochromy, can lack not polychrome.
As the attribute area of administrative division correspondence for opening the circle attribute, according to the corresponding administrative division color of colleague primary area institute with go together the different chromogens of all adjacent areas corresponding administrative division colors of institute then, the different chromogens of the adjacent adjacent area corresponding administrative division color of institute then, the corresponding administrative division color of the first from left row adjacent area institute of going together and the rightest row adjacent area corresponding administrative division color can homochromy principles, can lack look few chromogen then, use ABCD to represent four kinds of colors respectively, the administrative division color that primary area and adjacent area are respectively listed marks; According to aforementioned principle, be expressed as trial balance is painted:
Does 1 painted A by main adjacent different chromogens then, get 2B 4C 5B 6C 7 on the row in primary area 1?, and 7 not A; By adjacent not homochromy, 7 not C; By head and the tail different chromogens then, 7 not B, so 7D must be arranged.At this moment, is painted result 2B 3 on the row in primary area 2? 4C 1A 7D.By main adjacent different chromogens then, 3 not B; By adjacent not homochromy, 3 not C, by head and the tail not homochromy, 3 not D, so 3A must be arranged.
7 administrative areas are all painted.Need not calculate each row in primary area 3～7, but the painted result in primary area 1～2 can be write on each row in primary area 3～7, test, avoid adjacent homochromy wrong configuration, the four-color map with textual representation in obtaining showing is: 1A 2B 3A 4C 5B 6C 7D.
Also can be 2 from the primary area, according to lacking not polychrome, primary area 2 respectively be listed as three looks, result of calculation is: 2A 3B 4C 1B 7C.Remake primary area 1 or primary area 3 can, or the like.
The corresponding alphabetical ABCD of four kinds of colors is used in corresponding 7 administrative divisions that finish with the ABCD mark respectively, carries out painted to each administrative division.
Above-mentioned completed four-color map is drawn on the carriers such as terrestrial globe, wall chart, lantern slide, picture mosaic.
Below be " administrative division, the world four-color map " example that adopts colorize method of the present invention to finish, wherein ABCD represents four kinds of independent color respectively:
1 Chilean ∈ A, 2 Argentinian ∈ B, 3 Uruguay ∈ C, 4 Brazilian ∈ D, 5 crust rubbish Gui ⊙ A, 6 Bolivia ⊙ C, 7 Peru ∈ B, 8 Ecuador ∈ C, 9 Colombia ∈ A, 10 Venezuela ∈ B, 11 Guyana ∈ A, 12 Surinam ∈ B, 13 French Guiana ∈ A, 14 Trinidad and Tobago ∈ D, 15 Grenada ∈ C, 16 Barbados ∈ B, 17 Saint Vincent and the Grenadines ∈ D, 18 St. Lucia ∈ A, 19 Dominica ∈ C, 20 Antigua and Barbuda ∈ B, 21 St. Kitts and Nevis ∈ D, 22 Peurto Rican ∈ A, 23 Dominica ∈ B, 24 Haiti ∈ C, 25 Bahamas ∈ A, 26 Cuba ∈ D, 27 Jamaica ∈ A, 28 Panamanian ∈ B, 29 Costa Rica ∈ C, 30 Nicaragua ∈ D, 31 Salvador ∈ A, 32 Honduras ∈ B, 33 Guatemala ∈ D, 34 Belize ∈ A, 35 Mexico ∈ C, 36 U.S. ∈ B, 37 Canadian ∈ D, 38 Greenland (pellet) ∈ C, 39 Iceland ∈ B, 40 Russian ∈ D, 41 Ukraine ∈ A, ⊙ B more than 42 moles watts, 43 Romanian C, 44 Bulgarian ∈ A, 45 Greece ∈ B, 46 Macedonia ⊙ C, 47 Albanian ∈ D, 48 Studenica Monastery ∈ B, the 49 ∈ D of Bosnia-Herzegovena, 50 Croatia ∈ A, 51 Slovenia ⊙ D, 52 Italian ∈ C, 53 the Vatican ⊙ D, 54 holy horse Nino ⊙ A, 55 Switzerland ⊙ D, 56 Liechtenstein ⊙ A, 57 Austrian ⊙ B, 58 Hungary ⊙ D, 59 Slovakia ⊙ C, 60 Czech ⊙ A, 61 Polish ∈ B, 62 Russian @ ∈ D, 63 Lithuania ∈ A, 64 Latvia ∈ B, 65 Byelorussia ∈ C, 66 Estonia ∈ A, 67 Finland ∈ B, 68 Sweden ∈ D, 69 Norway ∈ A, 70 Denmark ∈ B, 71 Irish ∈ A, 72 Britain ∈ D, 73 German ∈ C, 74 Dutch ∈ A, 75 Belgian ∈ B, 76 Luxembourg ⊙ D, 77 Monaco ∈ B, 78 French ∈ A, 79 Andorra ⊙ B, 80 Spain ∈ C, 81 Portugal ∈ D, 82 Maltese ∈ A, 83 Tunisia ∈ B, 84 Algerian ∈ D, 85 Morocco ∈ B, 86 Western Sahara ∈ C, 87 Mao Litaliya ∈ B, 88 Malian ⊙ C, 89 Senegal ∈ D, 90 Gambia ∈ B, 91 Cape Verde ∈ A, 92 Guinea-Bissau ∈ C, 93 Guinea ∈ B, 94 Sierra Leone ∈ D, 95 Liberia ∈ C, 96 Cote d'lvoire ∈ D, 97 Ghana ∈ C, 98 Togo ∈ D, 99 Benin ∈ C, 100 Burkina Faso ⊙ A, 101 Niger ⊙ B, 102 Chad ⊙ D, non-⊙ C in 103, the 104 ∈ B of Cameroon, 105 Nigeria ∈ A, 106 Sao Tome and Principe ∈ A, 107 Equatorial Guinea ∈ D, 108 Gabon ∈ C, 109 the Congo (cloth) ∈ D, 110 B of Congo (Congo-Kinshasa), 111 Angola ∈ C, 112 Zambia ⊙ D, 113 Namibia ∈ B, 114 Botswana ⊙ C, 115 South Africa ∈ D, 116 Lesotho ⊙ C, 117 Swaziland ∈ A, 118 Mozambique ∈ B, 119 Zimbabwe ⊙ A, 120 Madagascar ⊙ C, 121 Mauritanian ∈ B, 122 Seychelles ∈ A, 123 the Comoros ∈ D, 124 Malawi ⊙ A, 125 Tanzania ∈ C, 126 Burundi ⊙ D, 127 Rwanda ⊙ A, 128 Uganda ⊙ D, 129 Kenya ∈ B, 130 Somalia ∈ A, 131 Ethiopia ⊙ C, 132 lucky skins are carried ∈ D, 133 Eritrea ∈ B, 134 the Sudan ∈ A, 135 Libya ∈ C, 136 Egyptian ∈ B, 137 Arabic regional ⊙ C, 138 Israel ∈ D, 139 Palestinian areas ∈ C, 140 Jordan ⊙ A, 141 Saudi Arabia ∈ D, 142 Yemen ∈ C, 143 Oman ∈ A, 144 United Arab Emirates ∈ B, 145 Qatar ∈ A, 146 Bahrain ∈ B, 147 Kuwait ∈ A, 148 Iraq ∈ B, 149 Syria ∈ C, 150 Lebanon ∈ B, 151 Cyprus ∈ A, its ∈ D of 152 scholar's ears, 153 Georgia ∈ C, 154 Azerbaijan ∈ B, 155 Armenia ∈ A, 156 Azerbaijan @ ⊙ B, 157 Iranian ∈ C, 158 Turkmenistan ∈ A, 159 Kazakhstan ∈ C, 160 Mongolian ⊙ B, 161 Korea ∈ C, 162 Korea S ∈ D, 163 Japanese ∈ B, 164 Philippine ∈ C, 165 Chinese ∈ A, 166 Kirghizstan ⊙ B, 167 Uzbekistan ⊙ D, 168 Tajikistan ⊙ C, 169 Afghan ⊙ B, 170 Kashmir ⊙ C, 171 Pakistani ∈ D, 172 India ∈ B, 173 Maldivian ∈ D, 174 Sri Lanka ∈ A, 175 Nepal ⊙ C, 176 Sillim ⊙ D, 177 Bhutanese ⊙ C, 178 Bangladesh ∈ D, 179 Burma ∈ C, 180 Laos ⊙ B, 181 Vietnam ∈ B, 182 Cambodia ∈ C, 183 Thailand ∈ A, 184 Malaysian ∈ B, 185 Singapore ∈ C, 186 Brunei ∈ D, 187 East Timor ∈ B, 188 Indonesia ∈ D, 189 Australian ∈ A, 190 Papua New Guinea ∈ C, 191 Palau ∈ A, 192 Saipan ∈ D, 193 Guam ∈ C, the 194 ∈ B of Micronesia Federated States, 195 Marshall Islands ∈ C, 196 Nauru ∈ A, 197 Kiribati ∈ D, 198 the Cook Islands ∈ B, 199 Tuvalu ∈ C, 200 Solomon Islands ∈ B, 201 Samoa ∈ D, 202 Tonga ∈ C, the 203 ∈ A of Fiji Islands, 204 Vanuatu ∈ D, 205 New Zealand ∈ C.
Illustrate: application strings circle colouring, can be for everyone draws a width of cloth different " administrative division, world four-color map " in the world, and by 1-13, " South America administrative division four-color map "; By 14-37, get " administrative division, North America four-color map "; By 38-82, get " African administrative division four-color map "; By 83-136, get " European administrative division four-color map "; By 137-188, get " administrative division, Asia four-color map "; By 189-205, get " administrative division, Oceania four-color map ".
Below be " the Chinese administrative division four-color map " example that adopts colorize method of the present invention to finish, wherein ABCD represents four kinds of independent color respectively:
1 Ningxia ⊙ A, 2 Shaanxi ⊙ C, 3 Sichuan ⊙ A, 4 Qinghai ⊙ B, 5 Chongqing ⊙ D, 6 Guizhou ⊙ C, 7 Hunan ⊙ A, 8 Jiangxi ⊙ C, 9 Hubei ⊙ B, 10 Anhui ⊙ D, 11 Henan ⊙ A, 12 Shanxi ⊙ D, 13 Beijing ⊙ A, 14 Tianjin ∈ D, 15 Hebei ∈ C, 16 Shandong ∈ B, 17 Jiangsu ∈ C, 18 Shanghai ∈ D, 19 Zhejiang ∈ A, 20 Fujian ∈ B, 21 Taiwan ∈ C, 22 Guangdong ∈ D, 23 Hong Kong ∈ A, the 24 ∈ B of Macao, 25 Hainan ∈ A, 26 Guangxi ∈ B, 27 Yunnan ∈ D, 28 Tibet ∈ C, 29 Xinjiang ∈ A, 30 Gansu ∈ D, 31 Inner Mongol ∈ B, 32 Heilungkiang ∈ C, 33 Jilin ∈ A, 34 Liaoning ∈ D.
Use above-mentioned provincial administrative area sequence number, another that can get " Chinese administrative division four-color map " separated and is:
Red (representing with A) has: 2,4,6,8,13,16,21,24,32;
Green (representing with B) has: 7,11,14,19,25,28,31,34;
Yellow (representing with C) has: 1,3,9,12,17,20,23,26,29;
Purple (representing with D) has: 5,10,15,18,22,27,30,33.
With string circle colouring, can calculate 〉=9 * 2
26" the Chinese administrative division four-color map " that the width of cloth is different is for each Chinese draws a diverse four-color map.In like manner, can get " U.S.'s administrative division four-color map ", " Britain's administrative division four-color map " or the like.
From the above, four-color map teaching instrument of the present invention and preparation method thereof, it is right only to use four kinds of colors to finish All kinds of maps painted, result of calculation is accurate, method is simple, can increase child and Students ' Learning, knowledge number, knowledge figure, sky Between the imagination and ability, production and the use cost of thinking low, simple in structure, be easy to plurality of advantages and the characteristics such as manufacturing.
Claims (2)
1. four-color map teaching instrument, it is characterized in that: each administrative division of four-color map is by independently four kinds of colors draftings, and the administrative area at the same level color difference of conterminousness, aforementioned four-color map is drawn on the carriers such as terrestrial globe, wall chart, lantern slide, picture mosaic.
2. the method for making of four-color map teaching instrument as claimed in claim 1 is characterized in that comprising following steps:
A) all administrative areas on the map are marked with 1～N;
B) make trial balance, the first from left of trial balance is classified the primary area as, and second classifies attribute area as, and the 3rd row beginning be to the right the adjacent area, is arranged in order digital 1～N in the primary area from top to bottom; Each administrative division of corresponding 1～N representative, as corresponding certain digital boundary line, administrative area is end to end closed sides boundary line, then in its colleague's secondary series attribute area, mark it for closing the circle attribute, as the open boundary line of corresponding certain digital boundary line, administrative area for not joining from beginning to end, then the secondary series attribute area its colleague marks it for opening the circle attribute, by the administrative division of aforementioned rule correspondence 1～N, close the circle attribute or open the circle attribute at its corresponding secondary series attribute area mark; The administrative division of corresponding 1～N representative lists respectively in its corresponding colleague adjacent area that to fill in the administrative division adjacent in turn with its border corresponding digital;
C) as the attribute area of certain administrative division correspondence for closing the circle attribute, according to the corresponding administrative division color of colleague primary area institute with go together the different chromogens of all adjacent areas corresponding administrative division colors of institute then, the different chromogens of the adjacent adjacent area corresponding administrative division color of institute then, the corresponding administrative division color of the first from left row adjacent area institute of going together and the rightest row adjacent area different chromogen of corresponding administrative division color then, can lack look few chromogen then, use ABCD to represent four kinds of colors respectively, the administrative division color that primary area and adjacent area are respectively listed marks; As the attribute area of certain administrative division correspondence for opening the circle attribute, according to the corresponding administrative division color of colleague primary area institute with go together the different chromogens of all adjacent areas corresponding administrative division colors of institute then, the different chromogens of the adjacent adjacent area corresponding administrative division color of institute then, the corresponding administrative division color of the first from left row adjacent area institute of going together and the rightest row adjacent area corresponding administrative division color can homochromy principles, can lack look few chromogen then, use ABCD to represent four kinds of colors respectively, the administrative division color that primary area and adjacent area are respectively listed marks;
D) according to above-mentioned steps c) color in principle and method, respectively the color mark is carried out in each primary area of going of numbering 1～N, the administrative division of adjacent area representative, the same color mark is used in the administrative division of identical numbering, finishes until the whole marks of the administrative division color of 1～N;
E) the corresponding alphabetical ABCD of four kinds of colors is used in corresponding 1～N the administrative division that finishes with the ABCD mark respectively, carries out painted to each administrative division;
F) above-mentioned completed four-color map is drawn on the carriers such as terrestrial globe, wall chart, lantern slide, picture mosaic.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2012072116A1 (en) * | 2010-11-30 | 2012-06-07 | Tomtom International B.V. | Methods and systems for formatting maps |
| CN105227646A (en) * | 2015-09-16 | 2016-01-06 | 中国测绘科学研究院 | A kind of HTML5 rich client administrative division map making method |
-
2009
- 2009-08-18 CN CN200910060374A patent/CN101625807A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2012072116A1 (en) * | 2010-11-30 | 2012-06-07 | Tomtom International B.V. | Methods and systems for formatting maps |
| CN105227646A (en) * | 2015-09-16 | 2016-01-06 | 中国测绘科学研究院 | A kind of HTML5 rich client administrative division map making method |
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Open date: 20100113 |