C++ Primer Plus

Next, let’s try something more ambitious and write a function that converts rectangular coordinates to polar coordinates. We’ll have the function accept a rect structure as its argument and return a polar structure to the calling function. This involves using functions from the math library, so the program has to include the cmath header file (math.h on older systems). Also on some systems you have to tell the compiler to load the math library (see Chapter 1, “Getting Started with C++”). You can use the Pythagorean theorem to get the distance from the horizontal and vertical components:

distance = sqrt( x * x + y * y)

The atan2() function from the math library calculates the angle from the x and y values:

angle = atan2(y, x)

(There’s also an atan() function, but it doesn’t distinguish between angles 180 degrees apart. That uncertainty is no more desirable in a math function than it is in a wilderness guide.)

Given these formulas, you can write the function as follows:

// convert rectangular to polar coordinates

polar rect_to_polar(rect xypos)   // type polar

{

    polar answer;

    answer.distance =

        sqrt( xypos.x * xypos.x + xypos.y * xypos.y);

    answer.angle = atan2(xypos.y, xypos.x);

    return answer;      // returns a polar structure

}

Now that the functions are ready, writing the rest of the program is straightforward. Listing 7.12 presents the result.

Listing 7.12. strctfun.cpp

// strctfun.cpp -- functions with a structure argument

#include

#include

// structure declarations

struct polar

{

    double distance;      // distance from origin

    double angle;         // direction from origin

};

struct rect

{

    double x;             // horizontal distance from origin

    double y;             // vertical distance from origin

};

// prototypes

polar rect_to_polar(rect xypos);

void show_polar(polar dapos);

int main()

{

    using namespace std;

    rect rplace;

    polar pplace;

    cout << "Enter the x and y values: ";

    while (cin >> rplace.x >> rplace.y)  // slick use of cin

    {

        pplace = rect_to_polar(rplace);

        show_polar(pplace);

        cout << "Next two numbers (q to quit): ";

    }

    cout << "Done.\n";

    return 0;

}

// convert rectangular to polar coordinates

polar rect_to_polar(rect xypos)

{

    using namespace std;

    polar answer;

    answer.distance =

        sqrt( xypos.x * xypos.x + xypos.y * xypos.y);

    answer.angle = atan2(xypos.y, xypos.x);

    return answer;      // returns a polar structure

}

// show polar coordinates, converting angle to degrees

void show_polar (polar dapos)

{

    using namespace std;

    const double Rad_to_deg = 57.29577951;

    cout << "distance = " << dapos.distance;

    cout << ", angle = " << dapos.angle * Rad_to_deg;

    cout << " degrees\n";

}

Note

Some compilers require explicit instructions to search the math library. For example, older versions of g++ uses this command line:

g++ structfun.C -lm

Here is a sample run of the program in Listing 7.12:

Enter the x and y values: 30 40

distance = 50, angle = 53.1301 degrees

Next two numbers (q to quit): -100 100

distance = 141.421, angle = 135 degrees

Next two numbers (q to quit): q

Program Notes

We’ve already discussed the two functions in Listing 7.12, so let’s review how the program uses cin to control a while loop:

while (cin >> rplace.x >> rplace.y)

Recall that cin is an object of the istream class. The extraction operator (>>) is designed in such a way that cin >> rplace.x also is an object of that type. As you’ll see in Chapter 11, “Working with Classes,” class operators are implemented with functions. What really happens when you use cin >> rplace.x is that the program calls a function that returns a type istream value. If you apply the extraction operator to the cin >> rplace.x object (as in cin >> rplace.x >> rplace.y), you again get an object of the istream class. Thus, the entire while loop test expression eventually evaluates to cin, which, as you may recall, when used in the context of a test expression, is converted to a bool value of true or false, depending on whether input succeeded. In the loop in Listing 7.12, for example, cin expects the user to enter two numbers. If, instead, the user enters q, as shown in the sample output, cin >> recognizes that q is not a number. It leaves the q in the input queue and returns a value that’s converted to false, terminating the loop.

Compare that approach for reading numbers to this simpler one:

for (int i = 0; i < limit; i++)

{

    cout << "Enter value #" << (i + 1) << ": ";

    cin >> temp;

    if (temp < 0)

        break;

    ar[i] = temp;

}