1. Now let P be the plane {x ? R3 : u · x = a} for some unit vector u and scala

1.  Now let P be the plane {x ∈ R3 : u · x = a} for some unit vector u and scalar a, where P does not necessarily contain the origin. Derive the 4 × 4 matrix that represents the transformation reflecting points across P.[

2.  Prove that every rigid, orientation-preserving affine transformation is a glide rotation.[

3.  Work out the correspondence between the two ways of representing the dimensional projective space.

4.  Prove the correctness of the formula above for the shadow transformation and the homogeneous matrix representation.

 

 
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