APPLICATION OF QUADRATIC GEOMETRY IN MAPS.pptx

8/10/2019 APPLICATION OF QUADRATIC GEOMETRY IN MAPS.pptx

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PPLIC TION OFQU DR TIC

GEOMETRY IN M PSBY

ANUGRAHA THOMASARITRA BANERJEEARJUN VALlYAVEETIL

ARPIT MAURYAATHIRA NANDAKUMAR

BALAJI KUMARESAN



One of the most common coordinate systems inuse is the Geographic Coordinate System , whichuses degrees of latitude and longitude todescribe a location on the earth‘s surface.The earth is effectively a sphere, so how do wedescribe where a point is on its surface?The most common way to locate points on thesurface of the Earth is by standard, geographiccoordinates called latitude and longitude. Thesecoordinates‘ values are measured in degrees, andrepresent angular distances calculated from thecenter of the Earth.

GEOGRAPHIC COORDINATESYSTEM



Latitudes

• The ends of the axis are the North Pole at 90 ºnorthand the South Pole at 90º south. The Equator is aline around the earth, an equal distance from bothpoles. The Equator is the latitude line given thevalue of 0 degrees. This means it is the startingpoint for measuring latitude.

• Latitude values indicate the angular distancebetween the Equator and points north or south of iton the surface of the Earth.

• A line connecting all the points with the samelatitude value is called a line of latitude.



• Each degree of latitude is approximately 111 kmapart.



LONGITUDE• Lines of longitude, called meridians, run

perpendicular to lines of latitude, and all passthrough both poles. Each longitude line is part of agreat circle. The meridian line through Greenwich,England, is currently given the value of 0 degrees of

longitude;



• At the equator, and only at the equator, the

distance represented by one line of longitude isequal to the distance represented by one degree oflatitude.

• As you move towards the poles, the distance

between lines of longitude becomes progressivelyless until, at the exact location of the pole, all 360°of longitude are represented by a single point youcould put your finger on. A degree of longitude is

widest at the equator at 69.172 miles (111.321) andgradually shrinks to zero at the poles. At 40° northor south the distance between a degree oflongitude is 53 miles.





Using the geographic coordinate system, we have agrid of lines dividing the earth into squares .But notvery useful for determining the location of anythingwithin that square.A map grid must divided into small sections so that itis used to describe with an acceptable level ofaccuracy the location of a point on the map.

To accomplish this, degrees are divided into minutes(') and seconds (").There are sixty minutes in a degree, and sixty seconds

in a minute (3600 seconds in a degree).

Increments of Degrees



• The Earth is divided equally into 360 degrees of longitude.• There are 180 degrees of longitude to the east of the Prime

Meridian; when the directional designator is omitted theselongitudes are given positive values.

• There are also 180 degrees of longitude to the west of thePrime Meridian; when the directional designator is omittedthese longitudes are given negative values.

• Degrees of latitude and longitude can be further subdividedinto minutes and seconds.

•

A degree of longitude varies in size. At the equator, it isapproximately 69 miles, the same size as a degree oflatitude.

• The size gradually decreases to zero as the meridians

converge at the poles.



DECIMAL DEGREE [DD] SYSTEM :This is used to express latitude and longitude geographic coordinates as decimal

fractions and are used in many geographic information systems (GIS), web mappingand GPS devices.

• DECIMAL , MINUTES , SECONDS [DMS] SYSTEM: • Measure of an angle can be represented in subdivision of degrees into

minutes and seconds. Each degree can be divided into 60 minutes. Eachminute is further subdivided into 60 seconds.

• In a full circle there are 360 degrees.

• Each degree is split up into 60 parts. These parts are called minutes.

• Each minute is split up into 60 parts. These parts are called seconds.

• There are symbols that are used when stating angles using degrees,minutes, and seconds.

• Symbol for degree: o • Symbol for minute: ‘ • Symbol for second: “



• CONVERSION FROM DMS SYSTEM TO DD SYSTEM:To convert from the DMS system to decimal degrees (DD) theformula: (degrees)+(minutes/60)+(seconds/3600) = decimaldegrees. For example, an angle measuring 45 degrees, 45minutes and 45seconds can be converted through the above formula and the resultis (45)+(45/60)+(45/3600) = 45.7625 .

• CONVERSION FROM DD SYSTEM TO DMS SYSTEM:• First subtract the whole degree from the number. Then multiply the

remaining fraction with 60 minutes. Subtract the whole minute fromthe new number and then multiply the number with 60 seconds.Then the this number is the seconds.

• i.e. (decimal degrees) – (whole degrees) = (remaining fraction)• (remaining fraction) x 60 = (minutes)• (decimal minutes) – (whole minutes) = (remaining fraction)• (remaining fraction) x 60 = (seconds)• Answer = (whole degrees) , (whole minutes) , (seconds)• Another example is to convert 34.78 to degrees, minutes and

seconds. We can use the above method to convert it. The result is 34

degrees, 46 minutes and 48 seconds.



Properties of great Circles1. They always result when a plane passes through

the exact center of a sphere, regardless of theplane's orientation when it enters the sphere.

2. A great circle is the largest possible circle thatcan be drawn on the surface of a sphere.

3. An infinite number of great circles can bedrawn on any sphere.

4. The arc of a great circle is the shortestsurface distance between any two points on a

sphere



5. Intersecting great circles always cutone another exactly in half.

4. One and only one great circle can befound that will pass through twospecified points on thesurface of a sphere, unless those twopoints happen to be exactly opposite oneanother



1. They can be used to find the shortest route for a ship,airplane, or, less happily, a missile that must cross greatdistances.2. You can find the great circle route between two placeson a globe by stretching a string or rubber-band betweenany those two locations on the globe: It'll settle on thegreat circle.3. When you sample headings for a variety of places on thegreat circle route and then transfer the resulting linesegments onto a flat map, like a wall map, you'll produce aweird-looking path that forms an arc between the two

places (instead of a straight line).



TH NK

YOU

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APPLICATION OF QUADRATIC GEOMETRY IN MAPS.pptx