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# 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(θ) and Y = r*sin(θ) or for ellipse X = rx*cos(θ) and Y = ry*cos(θ) where rx and ry are radius in X- and Y- direction and θ is the angle.
If we vary θ 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 θ (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 θ 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``#include``#include` `// 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();``}`

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