C Programs for engineering applications

The C++ Programming Language Special Edition

Plotting Polar Functions

Suppose you have a polar function in the form:

r = f ( ø )
where r is the length of line emerging from the origin to a point at an angle of ø.

and you need to plot it using a C program. All we need to do is to simply use the methods we used previously after converting polar coordinates into quadratic ones.

Converting polar coordinates to quadratic coordinates
and vice versa

The figure above shows the relationships between polar and quadratic coordinates. From this figure we can derive the following relations:

Thus, our 3-step strategy for plotting any polar equation shall be as follows:

1. Get the value of r corresponding to the various ø values (remember that ø values in polar functions are always in radians not degress).

2. Convert the polar point (r , ø) into a quadratic point (x , y). This is done by the C functions P2Q_x() and P2Q_y() in the code shown below.

3. Use the functions defined previously to plot the equation.

We shall now apply the above strategy to plot the function

r = sin(2ø) + 2 cos(3ø);

Here's the C program to do it.

/* This program is supplied from https://c4engineering.hypermart.net
   visit us for more sources */

#include <graphics.h>
#include <conio.h>
#include <math.h>

/** Change the values below to suit your screen resolution.
	These values will probably suit most users.   ***/
#define MAXX 640
#define MAXY 480

/* Co-ordinate conversion functions, prototypes and declarations */
float screen_y(float, float, float);
float screen_y(float, float, float);
float P2Q_x(float, float);
float P2Q_y(float, float);
/**********************************************************/

float screen_x(float xb, float x, float xe)
{
	return ( (x - xb) / (xe - xb) * MAXX );
}

float screen_y(float yb, float y, float ye)
{
	return ( MAXY - (y - yb) / (ye - yb) * MAXY);
}

/***********************************************************/
/****** The 2 functions below convert a polar **************
*********************  point into a quadratic point ********/
float P2Q_x(float r, float phi)
{
	return r * cos(phi);
}

float P2Q_y(float r, float phi)
{
	return r * sin(phi);
}

/**********************************************************/
void main(void)
{
	/* Change the values of 'drv' and 'mode' if you change MAXX and MAXY */
	int drv = VGA, mode = VGAHI;
	float phi, r, xb, xe, yb, ye, x, y;

/* You can play with the parameters below to determine the viewable
	   area of your graph */
	xb = -3;
	xe = 3;
	yb = -3;
	ye = 3;
	/* Stop playing !!! */

initgraph(&drv, &mode, "");

/* Draw the X and Y axes */
	setcolor(15);
	line( 0, screen_y(yb, 0, ye), MAXX, screen_y(yb, 0, ye) );
	line( screen_x(xb, 0, xe), 0, screen_x(xb, 0, xe), MAXY );

moveto( screen_x(xb, 0, xe), screen_y(yb, 0, ye) );
	for(phi = 0; phi < 2 * 3.1415; phi += 0.02)
	{
		r = sin(2 * phi) + 2 * cos(3 * phi);
		x = P2Q_x(r, phi);
		y = P2Q_y(r, phi);
		lineto(screen_x(xb, x, xe), screen_y(yb, y, ye) );
	}
	getch();
	closegraph();
	return;
}

Here's the result of this program

If you wish to download a compiled version of this program that can run under DOS/Windows environments, click here (50 KB). You will also need this file (5.5 KB) in the same folder as the executable.

Effective C++: 50 Specific Ways to Improve Your Programs and Design
by Andrei Alexandrescu (Paperback)

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