ABSTRACT

This chapter explains geometric transformation that forms the fundamental of computer vision and graphics. Geometric transformation, in general, means transforming a geometric entity to another. Linear transformation is a special kind of transformation. Linear transformation also implies that a line transforms to a line and a plane transforms to a plane. In fact, this can be generalized to higher orders of functions. Affine transformation preserves the ratios of lengths and angles. Therefore, a square can be converted to rectangle or a rhombus by an affine transformation, but cannot be transformed to a general quadrilateral. The chapter explores the different Euclidean and affine transformations. Scaling is the transformation by which a point is scaled along one of the axes directions. Shear is a transformation where one coordinate gets translated by an amount that is proportional to the other coordinate. The coordinate system remains local to each transformation and changes from one transformation to another.