Find out projection matrix for oblique projection, Computer Graphics

Find Out Projection Matrix for Oblique Projection

To find out projection matrix for oblique projection, we want to find out the direction vector d. Because vector PP' and vector d both contain the same direction. Hence, PP'=d 

 So, x'- 0=d1= f.cosθ

       y'- 0=d2= f.sinθ

       z'-1=d3

 Since z'=0 on the xy-plane, d3 = -1, 

Because, Oblique projection is a particular case of parallel projection, hence, we can transform the common transformation of parallel projection for Oblique projection as given:

792_Find Out Projection Matrix for Oblique Projection.png

Here, f=foreshortening factor, that is the projected length of the z-axis unit vector. When β is the angle among the Oblique projectors and the plane of projection so,

1/f=tan (β) , that is f= cot(β)

θ=angle among the projected line along with the positive x-axis.

Posted Date: 4/4/2013 2:27:43 AM | Location : United States







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