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:

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

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:

Figure: (g)