OpenGL program for simple Animation (Revolution) in C

OpenGL is a cross-language, cross-platform API for rendering 2D and 3D Vector Graphics. Using this, we can make a lot of design as well as animations. Below is the simple animation made using OpenGL.
Approach :
To make a picture moving, we need to understand the working procedure of a function used to display i.e glClear(GL_COLOR_BUFFER_BIT). Its task is to clear screen with default value after a certain time (normally, after 1/30 sec or 1/60 sec). So, if any change of coordinate happens, then it will appear to be moving as human eye can distinguish image only which is separated by 1/16 second (persistence of vision).
Now, the coordinates of circle are X = r*cos(?) and Y = r*sin(?) or for ellipse X = rx*cos(?) and Y = ry*cos(?) where rx and ry are radius in X- and Y- direction and ? is the angle. 
If we vary ? from 0 to 2*pi (360 degree) at very small increase (say of 1 degree) and draw point on that coordinate, we can make a complete circle or ellipse. We can also make semi-circle or any arc of circle or ellipse by varying the starting and ending value of ? (angle).
These concepts are used to draw the following Animation: 

• 7 horizontal parts of ellipse and 3 vertical complete ellipse as well as 1 outer circle and one outer ellipse are used to visualise an orbit drawn by adjusting the ? as well as radius.
• One vertical line is drawn to make the figure. Then to make it move, an other loop is given where value of j changes with very small amount to make the motion smoother.
• Since, we had to make all point moving in same type of motion to keep the figure together, so equation of motion, that is, glVertex2i(x/2 – 600*cos(j), y/2 – 100*sin(j)) is given inside every inner for loop, so that it can be applied to all points altogether.

For working on Ubuntu operating system:

gcc filename.c -lGL -lGLU -lglut -lm 
where filename.c is the name of the file
with which this program is saved.

Below is the implementation in C.

C

// C Program to illustrate
// OpenGL animation for revolution

#include<stdio.h>
#include<GL/glut.h>
#include<math.h>

// global declaration
int x, y;
float i, j;

// Initialization function
void myInit (void)
{
    // Reset background color with black (since all three argument is 0.0)
    glClearColor(0.0, 0.0, 0.0, 1.0);

    // Set picture color to green (in RGB model)
    // as only argument corresponding to G (Green) is 1.0 and rest are 0.0
    glColor3f(0.0, 1.0, 0.0);

    // Set width of point to one unit
    glPointSize(1.0);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();

    // Set window size in X- and Y- direction
    gluOrtho2D(-780, 780, -420, 420);
}

// Function to display animation
void display (void)
{
    // Outer loop to make figure moving
    // loop variable j iterated up to 10000,
    // indicating that figure will be in motion for large amount of time
    // around 10000/6.29 = 1590 time it will revolve
    // j is incremented by small value to make motion smoother
    for (j = 0; j < 10000; j += 0.01)
    {
        glClear(GL_COLOR_BUFFER_BIT);
        glBegin(GL_POINTS);

        // Iterate i up to 2*pi, i.e., 360 degree
        // plot point with slight increment in angle,
        // so, it will look like a continuous figure

        // Loop is to draw outer circle
        for (i = 0;i < 6.29;i += 0.001)
        {
            x = 200 * cos(i);
            y = 200 * sin(i);
            glVertex2i(x, y);

            // For every loop, 2nd glVertex function is
            // to make smaller figure in motion
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        // 7 loops to draw parallel latitude
        for (i = 1.17; i < 1.97; i += 0.001)
        {
            x = 400 * cos(i);
            y = -150 + 300 * sin(i);
            glVertex2i(x, y);
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        for (i = 1.07; i < 2.07; i += 0.001)
        {
            x = 400 * cos(i);
            y = -200 + 300 * sin(i);
            glVertex2i(x, y);
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        for (i = 1.05; i < 2.09; i += 0.001)
        {
            x = 400 * cos(i);
            y = -250 + 300 * sin(i);
            glVertex2i(x, y);
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        for (i = 1.06; i < 2.08; i += 0.001)
        {
            x = 400 * cos(i);
            y = -300 + 300 * sin(i);
            glVertex2i(x, y);
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        for (i = 1.10; i < 2.04; i += 0.001)
        {
            x = 400 * cos(i);
            y = -350 + 300 * sin(i);
            glVertex2i(x, y);
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        for (i = 1.16; i < 1.98; i += 0.001)
        {
            x = 400 * cos(i);
            y = -400 + 300 * sin(i);
            glVertex2i(x, y);
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        for (i = 1.27; i < 1.87; i += 0.001)
        {
            x = 400 * cos(i);
            y = -450 + 300 * sin(i);
            glVertex2i(x, y);
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        // Loop is to draw vertical line
        for (i = 200; i >=- 200; i--)
        {
            glVertex2i(0, i);
            glVertex2i(-600 * cos(j), i / 2 - 100 * sin(j));
        }

        // 3 loops to draw vertical ellipse (similar to longitude)
        for (i = 0;i < 6.29; i += 0.001)
        {
            x = 70 * cos(i);
            y = 200 * sin(i);
            glVertex2i(x, y);
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        for (i = 0; i < 6.29; i += 0.001)
        {
            x = 120 * cos(i);
            y = 200 * sin(i);
            glVertex2i(x, y);
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        for (i = 0; i < 6.29; i += 0.001)
        {
            x = 160 * cos(i);
            y = 200 * sin(i);
            glVertex2i(x, y);
            glVertex2i(x / 2 - 600 * cos(j), y / 2 - 100 * sin(j));
        }

        // Loop to make orbit of revolution
        for (i = 0; i < 6.29; i += 0.001)
        {
            x = 600 * cos(i);
            y = 100 * sin(i);
            glVertex2i(x, y);
        }
        glEnd();
        glFlush();
    }
}

// Driver Program
int main (int argc, char** argv)
{
    glutInit(&argc, argv);

    // Display mode which is of RGB (Red Green Blue) type
    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);

    // Declares window size
    glutInitWindowSize(1360, 768);

    // Declares window position which is (0, 0)
    // means lower left corner will indicate position (0, 0)
    glutInitWindowPosition(0, 0);

    // Name to window
    glutCreateWindow("Revolution");

    // Call to myInit()
    myInit();
    glutDisplayFunc(display);
    glutMainLoop();
}