Description of locateplace Function

Transcription

1 Description of locateplace Function This set of notes describes how the custom function locateplace works. This function expects three inputs: a longitude, a latitude, and a string. Both the longitude and latitude are in degrees. A negative longitude means that the location is west of the prime meridian. A negative latitude means that it is in the southern hemisphere. The string is, presumably, the name of a city. The locateplace function returns a three-dimensional uint8 array (with three pages), representing a color image. The following call to locateplace RGB = locateplace( ,36.75,'fresno'); produces this color image: The name Fresno appears at the bottom of the image, and a little, red square marks the location. Geographers characterize longitudes relative to the prime meridian. On a globe, the prime meridian is an imaginary curve that connects the north and south geographic poles, passing through the Royal Observatory, Greenwich, in England. On a flat world map, the prime meridian is a vertical line that passes through Greenwich. Geographers normally denote longitude with a combination of a number and a directional word: east or west. For example, we can say that Fresno has a longitude of west. This means that Fresno is west of the prime meridian. When making calculations with longitudes, it is more convenient to replace the number-plus-directional-word combination with a signed-number. Therefore, it is more convenient in a computer program to give Fresno s 1

2 longitude as , where the minus sign means west of the prime meridian. An implied positive sign (that is, no algebraic sign), on the other hand, means east of the prime meridian. The prime meridian at Greenwich west of prime meridian: east of prime meridian: + 2

3 Geographers denote latitude with a combination of a number and a directional word: north or south. For example, we can say that Fresno has a latitude of north. This means that Fresno is north of the equator. In a computer program, it is more convenient to give Fresno s latitude as 36.75, where the implied positive sign means north of the equator. A negative sign, on the other hand, means south of the equator. north of equator: + south of equator: There is a file topo.mat that comes with the MATLAB installation. When you load topo.mat, the matrix topo appears in the Workspace (along with some other variables). The matrix topo contains data for a relatively coarse topographic representation of the earth s surface. This matrix has 180 rows and 360 columns, storing a worldwide grid of elevations. Each element in topo represents, if positive, the height above sea level in meters or, if negative, the depth of the ocean in meters. The 180 rows represent the integer latitudes 89 (near the geographic south pole) through +90 (the north geographic pole). The 360 columns represent the integer longitudes 0 (the prime meridian) to 180 and 179 to 1. In other words, the first column represents the prime meridian, and each subsequent column represents a longitude that is further to the east than the previous column by 1, until a latitude of 1 is reached (having, therefore, gone around the world). We can create a three-dimensional uint8 array with three pages that represents a color image of the world using the matrix topo. At each point, defined by an integer longitude and an integer latitude, we assign a color to the corresponding pixel of the color image. If the elevation in topo for that point is negative, then the pixel is made blue, representing ocean. But if the elevation is positive, the pixel is made white, representing land. (We ignore the rare instance where the land has a negative elevation, such as occurs in Death Valley.) The result of building this color image is shown on the following page. 3

4 World map created from the matrix topo The above world map is upside-down because the rows in topo start from Antarctica and end at the geographic north pole. The function locateplace needs to fix that. Also, the left edge of the above world map is the prime meridian. Traditionally, we place the prime meridian in the center of a world map, rather than on the left. So the function locateplace should fix that as well. The polar regions are badly distorted when mapping a globe to a flat image. This makes Antarctica look like the biggest continent of all. The function locateplace removes the southernmost latitudes (and, therefore, Antarctica). The function m-file locateplace.m is shown on the next page. The file topo.mat is loaded. A new matrix, topo1, is created from the matrix topo by rearranging columns. topo1(:,180:360) = topo(:,1:181); topo1(:,1:179) = topo(:,182:360); The columns 1 (the prime meridian) through 181 (latitude 180 ) of topo are moved to columns 180 through 360 of topo1. The columns 182 (latitude 179 ) through 360 (latitude 1 ) of topo are moved to columns 1 through 179 of topo1. This rearrangement of the columns means that the prime meridian is now at the center of the world map. A new matrix, topo2, is created from the matrix topo1 by removing the first 30 rows. This removes latitudes 89 through 60 (and, therefore, Antarctica). topo2(1:150,:) = topo1(31:180,:); A new matrix, topo3, is created from the matrix topo2 by a vertical flip. That is to say, the top and bottom rows are interchanged, the second and next-to-last rows are interchanged, etc. topo3 = flipud(topo2); 4

5 function RGB = locateplace(longitude,latitude,name) % Makes an image: world map with marked location and title % Inputs: % longitude = signed longitude, deg (-177 to 178) % latitude = signed latitude, deg (-58 to 88) % name = placename (string) % Output: % RGB = 3-dimensional array representing color image % Sign convention for longitudes and latitudes: % The prime meridian, which passes through Greenwich, % England, has longitude 0 deg. A longitude between % -180 and 0 deg is west of the prime meridian. A % longitude between 0 and +180 deg is east of the prime % meridian. A latitude between -90 and 0 deg is south % south of the equator. A latitude between 0 and +90 % is north of the equator. % How this function works: % The file topo.mat, a built-in MATLAB data file, % contains a matrix with 180 rows (one for % each integer-degree latitude -89 to 90) and 360 % columns (one for each integer-degree longitude % 0 to 359). Each element in the matrix is the % elevation above sea level in meters. This function % reorganizes columns in the matrix so that the columns % correspond to geographers' designation of longitudes: % -179 deg to +180 deg. Antarctica is removed because % it distorts badly in the sphere-to-flat transformation. % Negative elevations, assumed to be ocean, are made blue, % and positive elevations, assumed to be land, are made % white. A little, red square is added at the specified % longitude and latitude. A title is added. load topo topo1(:,180:360) = topo(:,1:181); topo1(:,1:179) = topo(:,182:360); topo2(1:150,:) = topo1(31:180,:); % Antarctica removed topo3 = flipud(topo2); % top row becomes Arctic worldmap = zeros(150,360,3,'uint8'); worldmap(:,:,3) = 255; land = (topo3 > 0); worldmap(:,:,1) = 255*land; worldmap(:,:,2) = 255*land; row = round(90-latitude+1); column = round(180+longitude); worldmap(row-2:row+2,column-2:column+2,1) = 255; worldmap(row-2:row+2,column-2:column+2,2:3) = 0; RGB = inserttext(worldmap,[180,130],... name,'boxcolor','blue','textcolor','white'); end % locateplace 5

6 A three-dimensional uint8 array, worldmap, is created. The blue intensities for all pixels are set to the maximum value (255). This is the correct blue intensity for both the colors blue and white. worldmap = zeros(150,360,3,'uint8'); worldmap(:,:,3) = 255; Land is identified by asking where the elevations of the matrix topo3 are positive. The result is a logical matrix, land. An element of land is a logical 1 if the corresponding element of topo3 is positive, otherwise that element of land is a logical 0. The red and green intensities are set to the maximum value (255) for those pixels identified with a logical 1 in land. For these pixels that are identified as land, the red, green and blue intensities are therefore all 255, and the result is white. land = (topo3 > 0); worldmap(:,:,1) = 255*land; worldmap(:,:,2) = 255*land; The city s location, defined by the inputs longitude and latitude, are associated with a row and column in worldmap. The function round is used to ensure that these indices are whole, positive numbers. row = round(90-latitude+1); column = round(180+longitude); A little, red square is placed at the city s location. worldmap(row-2:row+2,column-2:column+2,1) = 255; worldmap(row-2:row+2,column-2:column+2,2:3) = 0; A new three-dimensional uint8 array, RGB, is created from worldmap by the addition of the city s name. RGB = inserttext(worldmap,[180,130],... name,'boxcolor','blue','textcolor','white'); 6