get angle of position vector wrt to initial line.

angle.cpp

/* 

angle.cpp 

compute angle given sine and cosine

*/
#include <cmath>
#include <cstdio>
#include <cassert>
#include <cstdlib>

int quadrant(double x, double y);
void usage(FILE *fp);

#define PI       3.14159265358979323846

int main(int argc, char *argv[])
{
    if (argc == 1)
    {
        usage(stderr);
        return 1;
    }

    if (argv[1][0] == '-' && argv[1][1] == 'h')
    {
        usage(stdout);
        return 0;
    }

    if (argc != 3)
    {
        usage(stderr);
        return 1;
    }

    char *endptr;
    double x = strtod(argv[1], &endptr);
    double y = strtod(argv[2], &endptr);

    double diag = _hypot(x, y);
    if (diag == 0)
    {
        fprintf(stderr, "hypotenuse has zero length\n");
        return 2;
    }

    double xHat = x/diag;
    double yHat = y/diag;
    int quad = quadrant(xHat, yHat);
    switch(quad)
    {
        case 1:
            printf("%f\n", asin(yHat));
            break;
        case 2:
            printf("%f\n", acos(xHat));
            break;
        case 3:
            printf("%f\n", 2*PI - acos(xHat));
            break;
        case 4:
            printf("%f\n", 2*PI + asin(yHat));
            break;
    }

    assert(false);
    return 0;
}

int quadrant(double x, double y)
{
    if (y >= 0)
    {
        if (x >= 0)
            return 1;
        if (x < 0)
            return 2;
    }
    else if (y < 0)
    {
        if (x < 0)
            return 3;
        if (x >= 0)
            return 4;
    }

    assert(false);
    return 42;
}

void usage(FILE *fp)
{
    fprintf(fp, 
            "usage: angle x_coordinate y_coordinate\n"
            "prints the angle between (x, y) and the initial line\n");
}

get angle between point and initial line in [0,2pi]