Representing Celestial Coordinate Systems - 6

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• The 1981 prescription of linear coordinates reserved keyword CROTAj to define a rotation, but usage was not formally defined.



• General linear transformation matrix introduced in 1988 (Hanisch & Wells):
  
  
  • Form without scales (CDij matrix):
    X = X₀ + c₁₁ (I - I₀) + c₁₂ (J - J₀),
    Y = Y₀ + c₂₁ (I - I₀) + c₂₂ (J - J₀).
  
  
  
  • Form which retains scales (PCij matrix):
    X = X₀ + d_X [ p₁₁ (I - I₀) + p₁₂ (J - J₀) ],
    Y = Y₀ + d_Y [ p₂₁ (I - I₀) + p₂₂ (J - J₀) ].
  
  
• Allows general affine transformations to be defined - scale, rotation, skew.



• Additional FITS keywords:   CDij (c_ij), PCij (p_ij).