Viewing Transformations

• WCS is supported by , the World Frame.
• WF is usually orthonormal, i.e. , the Cartesian Standard Frame.
• VCS is supported by . the Viewing Frame.
• Express VF relative to the WCS: .
• Use Change of Basis to derive V, the Viewing Transformation.
• If VF was an orthonormal frame in WCS, then

  

• Note:

  

• Not usually given an O.N. frame for VF; might have
  • Position of camera C.
  • Direction of view of camera (or lookat point L, ).
  • Up vector .
• Convert C, , and to left-handed O.N. frame:

  

• For a right-handed frame, use .
• Slight problem if is parallel to ...