Define geometric transformations and coordinate transformation.

Subject | Computer Graphics and Multimedia |
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NU Year | Set: 2.(a) Marks: 2 Year: 2009 |

**Geometric transformations:**

A geometric
transformation is any bisection of a set having some
geometric structure to itself or another such set. Specifically, "A
geometric transformation is a function whose domain and range are sets of
points. Most often the domain and range of a geometric transformation are both
R2 or both R3. Often geometric transformations are required to be 1-1
functions, so that they have inverses." The study of geometry may
be approached via the study of these transformations.

**Coordinate transformation****:**

A Cartesian
coordinate system allows position and direction in space to be represented in a
very convenient manner. Unfortunately, such a coordinate system also introduces
arbitrary elements into our analysis. After all, two independent observers
might well choose coordinate systems with different origins, and different
orientations of the coordinate axes. In general, a given vector a will have different
sets of components in these two coordinate systems. However, the direction and
magnitude of a are the same in both cases. Hence, the two sets of
components must be related to one another in a very particular fashion.