8.1. Basic level (PIC 10A only, or C-style)

Do use an array such as p[0],p[1],p[2] for a point, but to keep things straight, follow the suggestion above by defining x,y,z to be coordinates indices 0,1,2, rather than the actual coordinate values, so that you can say p[x],p[y],p[z] when you wish but also do loops with p[i] other times. Since this is the basic level, you might not use functions. Your program might look something like the following. Examine carefully how the matrix multiplication goes; think it through to see how it does correspond to what you do when you multiply matrices by hand.

//   (some or all of these include files may not be needed, depending
//    on the compiler)
#include <math.h>
#include <stream.h>
#include <fstream.h>
#include <stdlib.h>

const int x = 0;
const int y = 1;
const int z = 2;
const double pi = ...;

void main(int argc, char** argv)
{

// -------------- get args, convert to radians -----------

    double view_lat_deg  = (argc>1) ? atof(argv[1]) : 0.0;
    double view_long_deg = (argc>2) ? atof(argv[2]) : 0.0;

    double view_lat_rad = ...;
    double view_long_rad = ...;

// ----- find rotation  R  taking viewplane to north pole ------

    double rot_long[3][3];
    double rot_lat[3][3];
    
    rot_long[x][x] = rot_long[y][y] = cos(view_long_rad + pi/2);
    rot_long[x][y] = ...;
                //etc. to complete rot_long

    rot_lat[x][x] = ...
                //etc. to complete rot_lat

    double R[3][3];

    for (int i=0; i<3; i++)
        for (int j=0; j<3; j++)
        {
            R[i][j] = 0.0;
            for (int k=0; k<3; k++)
                R[i][j] += rot_long[i][k]*rot_lat[k][j];
        }

// ------------------------------ draw circle -----------------

   for (int i=0; i<=60; i++)
   {
        double t = 2*pi*i/60.;  // better use 60., not 60  (why?)
        cout << ...   // write out cos(t), space, sin(t)
   }
   cout << endl;

// ------------------------------ main loop -------------------

    int connect;
    double data_lat_deg, data_long_deg;
    double data_lat_rad, data_long_rad;
    double data_pt[3];
    double p[3];

        // -------------- read in data, convert to Euclidean -----

    (open stream  fin  to read continents file)

    if (!fin)
    {
        cerr << "can't open continents file for reading" << endl;
        exit(-1);
    }
    
    while ( fin >> connect >> data_lat_deg >> data_long_deg )
    {

                // convert to data_lat_rad, data_long_rad  in radians;
		/  expressions on right will involve sines, cosines

        data_pt[x] = ...
	data_pt[y] = ...
	data_pt[z] = ...

		// rotate the data point: p = data_pt * R

        for (int j=0; j<3; j++)   
        {    // call outer index j since entry of row vector is column
            p[j] = 0.0;
            for (int i=0; i<3; i++)
                p[j] += data_pt[i]*R[i][j];
        }
        // ------------ check visibility, etc. ------------------

        // (see earlier part of this handout)
    }
}

Even if you intend to work at the 10A level, please read the next part.