โครงแผนที่และระบบพิกัด MAP PROJECTION and COORDINATE SYSTEM

 MAP PROJECTION and COORDINATE SYSTEM

Documents

อภิธานศัพท์_GIS_glossary.pdf

1_Map_Multimedia_2557.pdf

Table of Projections

Projection	Images	Type	Properties	Creator	Year	Notes
Equirectangular = equidistant cylindrical = rectangular = la carte parallélogrammatique		Cylindrical	Compromise	Marinus of Tyre	120 (c.)	Simplest geometry; distances along meridians are conserved. Plate carrée: special case having the equator as the standard parallel.
Mercator = Wright		Cylindrical	Conformal	Gerardus Mercator	1569	Lines of constant bearing (rhumb lines) are straight, aiding navigation. Areas inflate with latitude, becoming so extreme that the map cannot show the poles.
Gauss–Krüger = Gauss conformal = (Ellipsoidal) Transverse Mercator		Cylindrical	Conformal	Carl Friedrich Gauss Johann Heinrich Louis Krüger	1822	This transverse, ellipsoidal form of the Mercator is finite, unlike the equatorial Mercator. Forms the basis of the Universal Transverse Mercator system.
Gall stereographic similar to Braun		Cylindrical	Compromise	James Gall	1885	Intended to resemble the Mercator while also displaying the poles. Standard parallels at 45°N/S. Braun is horizontally stretched version with scale correct at equator.
Miller = Miller cylindrical		Cylindrical	Compromise	Osborn Maitland Miller	1942	Intended to resemble the Mercator while also displaying the poles.
Lambert cylindrical equal-area		Cylindrical	Equal-area	Johann Heinrich Lambert	1772	Standard parallel at the equator. Aspect ratio of π (3.14). Base projection of the cylindrical equal-area family.
Behrmann		Cylindrical	Equal-area	Walter Behrmann	1910	Horizontally compressed version of the Lambert equal-area. Has standard parallels at 30°N/S and an aspect ration of 2.36.
Hobo-Dyer		Cylindrical	Equal-area	Mick Dyer	2002	Horizontally compressed version of the Lambert equal-area. Very similar are Trystan Edwards and Smyth equal surface (= Craster rectangular) projections with standard parallels at around 37°N/S. Aspect ratio of ~2.0.
Gall–Peters = Gall orthographic = Peters		Cylindrical	Equal-area	James Gall (Arno Peters)	1855	Horizontally compressed version of the Lambert equal-area. Standard parallels at 45°N/S. Aspect ratio of ~1.6. Similar is Balthasart projection with standard parallels at 50°N/S.

Type of Projection

• Cylindrical: In standard presentation, these map regularly-spaced meridians to equally spaced vertical lines, and parallels to horizontal lines.
• Pseudocylindrical: In standard presentation, these map the central meridian and parallels as straight lines. Other meridians are curves (or possibly straight from pole to equator), regularly spaced along parallels.
• Pseudoazimuthal: In standard presentation, pseudoazimuthal projections map the equator and central meridian to perpendicular, intersecting straight lines. They map parallels to complex curves bowing away from the equator, and meridians to complex curves bowing in toward the central meridian. Listed here after pseudocylindrical as generally similar to them in shape and purpose.
• Conic: In standard presentation, conic (or conical) projections map meridians as straight lines, and parallels as arcs of circles.
• Pseudoconical: In standard presentation, pseudoconical projections represent the central meridian as a straight line, other meridians as complex curves, and parallels as circular arcs.
• Azimuthal: In standard presentation, azimuthal projections map meridians as straight lines and parallels as complete, concentric circles. They are radially symmetrical. In any presentation (or aspect), they preserve directions from the center point. This means great circles through the central point are represented by straight lines on the map.
• Other: Typically calculated from formula, and not based on a particular projection
• Polyhedral maps: Polyhedral maps can be folded up into a polyhedral approximation to the sphere, using particular projection to map each face with low distortion.
• Retroazimuthal: Direction to a fixed location B (by the shortest route) corresponds to the direction on the map from A to B.

Properties

• Conformal: Preserves angles locally, implying that locally shapes are not distorted.
• Equal Area: Areas are conserved.
• Compromise: Neither conformal or equal-area, but a balance intended to reduce overall distortion.
• Equidistant: All distances from one (or two) points are correct. Other equidistant properties are mentioned in the notes.
• Gnomonic: All great circles are straight lines.

1. Carlos A. Furuti. Conic Projections: Equidistant Conic Projections
2. Jarke J. van Wijk. "Unfolding the Earth: Myriahedral Projections". [1]
3. Carlos A. Furuti. "Interrupted Maps: Myriahedral Maps". [2]

Converting Between Decimal Degrees, Degrees, Minutes and Seconds, and Radians

(dd + mm/60 +ss/3600) to Decimal degrees (dd.ff)
dd = whole degrees, mm = minutes, ss = seconds
dd.ff = dd + mm/60 + ss/3600
Example 1: 30 degrees 15 minutes 22 seconds = 30 + 15/60 + 22/3600 = 30.2561
Decimal degrees (dd.ff) to (dd + mm/60 +ss/3600)
For the reverse conversion, we want to convert dd.ff to dd mm ss. Here ff = the fractional part of a decimal degree.
mm = 60*ff
ss = 60*(fractional part of mm)
Use only the whole number part of mm in the final result.
30.2561 degrees = 30 degrees
.2561*60 = 15.366 minutes
.366 minutes = 22 seconds, so the final result is 30 degrees 15 minutes 22 seconds
Decimal degrees (dd.ff) to Radians
Radians = (dd.ff)*pi/180
Radians to Decimal degrees (dd.ff)
(dd.ff) = Radians*180/pi

Degrees, Minutes and Seconds to Distance
A degree of longitude at the equator is 111.2 kilometers. A minute is 1,853 meters. A second is 30.9 meters. For other latitudes multiply by cos(lat). Distances for degrees, minutes and seconds in latitude are very similar and differ very slightly with latitude. (Before satellites, observing those differences was a principal method for determining the exact shape of the earth.)

แปลงระหว่างองศาทศนิยม, องศา, ลิปดาและพิลิปดาและเรเดียน
(dd + + mm/60 ss/3600) องศาฐานสิบ (dd.ff)
dd = องศา,  mm = ลิปดา, ss = พิลิปดา
dd.ff = dd + mm/60 + ss/3600
ตัวอย่าง: 30 องศา 15 ลิปดา 22 พิลิปดา = 30 + 15/60 + 22/3600 = 30.2561
องศาทศนิยม (dd.ff) ถึง (dd + mm/60 + ss/3600)
สำหรับการแปลงย้อนกลับที่เราต้องการแปลง dd.ff  ถึง dd mm ss. ที่นี่ ff = ส่วนที่เป็นเศษส่วนของปริญญาทศนิยม
mm = 60*ff
ss = 60 * (เศษส่วนส่วนหนึ่งของ mm )
ใช้เพียงส่วนหนึ่งจำนวนทั้งหมดของมิลลิเมตรผลสุดท้าย
30.2561 องศา = 30 องศา
0.2561 องศา * 60 = 15.366 ลิปดา
0.366 ลิปดา * 60  = 22 พิลิปดา
ดังนั้นผลสุดท้ายคือ 30 องศา 15 ลิปดา 22 พิลิปดา

องศาทศนิยม (dd.ff) ถึงเรเดียน
เรเดียน = (dd.ff) * pi/180
เรเดียนถึงองศาทศนิยม  (dd.ff)
(dd.ff) = เรเดียน *180/PI
องศาลิปดาและวินาทีถึงระยะทาง

องศา ของเส้นลองจิจูดที่เส้นศูนย์สูตรของโลกคือ 111.2 กิโลเมตร ลิปดาเป็น 1,853 เมตร พิลิปดาคือ 30.9 เมตร สำหรับละติจูดอื่น ๆ คูณด้วย cos (lat) สำหรับระยะทางองศาลิปดาและพิลิปดาในละติจูดที่คล้ายกันมากและแตกต่างกันเล็ก น้อยกับละติจูด (ก่อนที่ดาวเทียมการสังเกตความแตกต่างเหล่านั้นเป็นวิธีการหลักสำหรับการ กำหนดรูปร่างที่แท้จริงของโลก.)

There are 60 longitudinal projection zones numbered 1 to 60 starting at 180°W. Each of these zones is 6 degrees wide, apart from a few exceptions around Norway and Svalbard.
There are 20 latitudinal zones spanning the latitudes 80°S to 84°N and denoted by the letters C to X, omitting the letter O. Each of these is 8 degrees south-north, apart from zone X which is 12 degrees south-north.
Areas are referenced by quoting the longitudinal zone number, followed by the latitudinal zone letter. For example, the southern end of South America is 19F. 

Zone calculation: Z = ((x + 180)/6) + 1    where x: longitude degree.
Central Meridian Calculation: xCM  = (((Z - 1)*6) - 180) + 3

Example 1: What is UTM Zone for 104 E degree?
Here: x = 104
Z = ((x + 180)/6) + 1 = ((104 + 180)/6) + 1 = 47 + 1 = 48
Answer is UTM Zone 48

Example 2: What is Center Meridian for Zone 48?
 Here Z = 48
xC  = (((Z - 1)*6)-180) + 3 = (((48 - 1)*6) -180) + 3 = 102 + 3 = 105
Answer is Center Meridian is 105 E degree 

Within each longitudinal zone the Transverse Mercator Projection is used to give co-ordinates (eastings and northings) in metres.
For the eastings, the origin is defined as a point 500,000 metres west of the central meridian of each longitudinal zone, giving an easting of 500,000 metres at the central meridian. 

For the northings in the northern hemisphere, the origin is defined as the equator.
For the northings in the southern hemisphere, the origin is defined as a point 10,000,000 metres south of the equator. 

A degree of longitude Dx = 105300 m
A degree of latitude Dy = 110569 m
Given a Longitude x and Latitude y of a position.
Conversion Longitude and Latitude to UTM
UTM East xu = (x - xC)*Dx + 500000
UTM North yu = y*Dy 
Example 3: Longitude = 98d59'12.5472" E and Latitude = 18d48'24.7056" N
Convert to Decimal Longitude = 98.9868186 E   and Latitude = 18.8068627 N
Zone = Z = ((x + 180)/6) + 1 = ((98.9868186 + 180)/6) + 1 = (278/6) + 1 = 46 +1 = 47
UTM East xu = (98.9868186 - 99)*105300 + 500000 = -1388.00124 + 500000 = 498612 m
UTM North yu = 18.8068627*110569 = 2079456 m
Answer: UTM Zone 47 N;  UTM East = 498612; UTM North = 2079456  

Conversion UTM to Longitude and Latitude 
Longitude x = ((xu - 500000) / Dx ) + xc
Latitude y = yu / Dy
Example 4: UTM Zone 47 N;  UTM East = 498612; UTM North = 2079456
Longitude x = ((498612 - 500000) / 105300 ) + 99 = -0.0131813865 +99 = 98.9868186
Latitude y = 2079456 / 110569 = 18.8068627
Answer: Longitude = 98d59'12.5472" E and Latitude = 18d48'24.7056" N 

 The co-ordinates thus derived define a location within a UTM projection zone either north or south of the equator, but because the same co-ordinate system is repeated for each zone and hemisphere, it is necessary to additionally state the UTM longitudinal zone and either the hemisphere or latitudinal zone to define the location uniquely world-wide. 

For further details of the referencing of Grid Co-ordinates within the UTM zones, it is recommended that you visit:

• Atlas Florae Europaeae: UTM and MGRS

For conversions between latitude/longitude and UTM co-ordinates, see:

• Transverse Mercator Calculator

การบ้าน  Homework

1.คำนวณโซนและ เส้นเมริเดียนย่านกลาง (Central Meridian: CM) ของ:
1.1  ระหว่างลองจิจูดที่  97 องศา E
1.2  ระหว่างลองจิจูดที่  94 องศา E
1.3  ระหว่างลองจิจูดที่  103 องศา E
1.4  ระหว่างลองจิจูดที่  110 องศา E
1.5  ระหว่างลองจิจูดที่  88 องศา E

2.  แปลงระหว่าง พิกัดองศาลิปดพิลิปดา ถึง องศาฐานสิบ และ พิกัด UTM ของ 4 จุด:
2.1  จุดที่ 1:   98º58’42.18” E   18 º47’45.23” N
2.2  จุดที่ 2:   98º59’37.85” E   18 º47’43.34” N
2.3  จุดที่ 3:   98º59’34.70” E   18 º46’51.86” N
2.4  จุดที่ 4:   98º58’39.71”E    18 º46’53.01” N