Define Transformation and Projection

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’.
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