# Define Transformation and Projection

Computer Graphics
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**Define Transformation and Projection**

- The transformation of points from a coordinate system in
__n__ dimensions to a coordinate system in __m__ dimensions where m<n.
- There are fundamental differences between the true three-dimensional world and its pictorial description.
- For centuries, artists, engineers, designers, drafters, and architects have
__tried to represent a three-dimensional object or scene in a two-dimensional medium__ à called *projection**.*

- Projection plane- A 2D coordinate system onto which the 3D image is to be projected. We’ll call this the VRP for
__view reference plane__.
- Center of projection- COP- A point in space which serves as an end point for projectors. We’ll refer to this point as the COP. It is also called a PRP for a
__projection reference point__.

*Projectors* – a ray originating at the center of projection and passing through a point to be projected. Here is an example of a projection.
- Projection can be defined as a
__mapping of point __*P(**x,y,z**)*__ onto its image __*P’(**x’,y’,z**’)* in the projection plane, which constitute the display surface.
- The mapping is determined by a projection line called the
__Projector__ that passes through P and intersect the __view plane__. The intersection point is P’.