Determine the transformation matrix for cavalier projection, Computer Graphics

Determine the transformation matrix for:

a) Cavalier projection with θ=450, and

b) Cabinet projection with θ=300  

c) Draw the projection of unit cube for all transformations.

Solution: We familiar with cavalier and cabinet projections are a particular case of an oblique projection. For oblique projection, the transformation matrix is:

2035_Determine the transformation matrix for Cavalier Projection 1.png

(ii) To sketch the cabinet projection, we determine the image coordinates of a unit cube i.e.:

2329_Determine the transformation matrix for Cavalier Projection 2.png

The image coordinates are given as:

A' (0, 0, 0), B' = (1,0,0), C' = (1, 1, 0), D' = (0, 1, 0), E' = (√3/4, 5/4, 0) F' = (√3/4, 1/4, 0), G' = (1 + √3/4, 1/4, 0), H' = (1 + √3/4, 5/4, 0)

Figure (g) demonstrates a cabinet projection of a unit cube as given below:

2163_Determine the transformation matrix for Cavalier Projection 3.png

Figure: (g)

Posted Date: 4/4/2013 2:33:25 AM | Location : United States







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