Transformations play a very important role in manipulating objects on 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:
- Translation : Translation refers to moving an object to a different position on screen.
Formula: X = x + tx Y = y + ty where tx and ty are translation coordinates The OpenGL function is glTranslatef( tx, ty, tz );
- 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 = cx + (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).
- Scaling : Scaling refers to zooming in and out an object in 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 is to be applied, follow the order: translate, rotate, scale
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