Basic Transformations in OPENGL

Transformations play a very important role in manipulating objects on the screen. It should be noted that here the algorithms will be implemented in code and the built-in functions will not be used to give a good understanding of how the algorithms work. Also, note that all transformations are implemented in 2D. There are three basic kinds of Transformations in Computer Graphics: 1. Translation 2. Rotation 3. Scaling

Algorithms:

1. Translation: Translation refers to moving an object to a different position on the screen.

Formula:  X = x + tx
          Y = y + ty
where tx and ty are translation coordinates

The OpenGL function is glTranslatef( tx, ty, tz );

2. Rotation: Rotation refers to rotating a point.

Formula:  X = xcosA - ysinA
          Y = xsinA + ycosA,
   A is the angle of rotation.
The above formula will rotate the point around the origin.
To rotate around a different point, the formula:
          X = cx + (x-cx)*cosA - (y-cy)*sinA,   
          Y = cy + (x-cx)*sinA + (y-cy)*cosA,   
                 cx, cy is centre coordinates, 
                 A is the angle of rotation.

The OpenGL function is glRotatef (A, x, y, z). 

3. Scaling: Scaling refers to zooming in and out an object on different scales across axes.

Formula: X = x*sx
         Y = y*sy,    sx, sy being scaling factors.

The OpenGL function is glScalef(float x, float y, float z)

Note: If combined transformations are to be applied, follow the order: translate, rotate, scale

Implementation: