Graphics & Media Lab. >> Курсы >> Курс Ю.М.Баяковского 1999

Introduction to Projection Transformations

Mapping: 
Projection: Mapping with m less than n
Planar Projection: maps 3D object onto plane

Parallel Projection

  • parallel lines preserve relative length

Perspective Projection

  • produces foreshortening
  • non-linear

A Taxonomy of Projections


A Basic Projection Matrix

Let's use the following example to construct a matrix that performs a perspective transformation:
From similar triangles, we can see that  y'/d = y/z
Thus, y' = yd/z
Similarly, x' = xd/z

We can express this in matrix form by altering the value of the homogeneous parameter, h:
 

  •  non-linear because of divide by h
  • can incorporate scaling

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