Two-Dimensional Geometric Transformations

 When a real life object is modelled using shape primitives, there are several possible applications.  You may be required to do further processing with the objects.  For example, suppose you have created a chair model.  You may then like to view it from different angles, or you may like to create another chair model with a slight variation in its shape or size.  Similarly, you may want to show an object moving from one position to another along a path, or rotate it about a given pivot point.  All this can be achieved by using simple mathematical transformations called affine transformations.  Since these transformations help change the geometry of the object in terms of shape, size or position, we call them geometric transformations.  Present section deals with two-dimensional (2D) geometric transformations.  2D geometric transformations can be broadly classifies as - (i) Rigid body transformations (ii) Non-rigid body transformations.  Rigid body transformations do not change the object dimensions, while non-rigid body transformations modify the dimensions of the object.  For example, when you resize a rectangle, the transformation is non-rigid body, but when you rotate an object its shape or size does not change, hence it is rigid body transformation.