(**************************** DERIVATIVES  *******************************)

TYPE
  RealNeighborhood = ARRAY [-1..+1] OF ARRAY [-1..+1] OF REAL;
  (*
    A single-layer 3x3 neighborhood of a texel. *)

TYPE
  StateDerivatives = ARRAY [0..State.N-1] OF RealDerivatives;
  (*
    The six partial derivatives of order 0..2 at some texel
    of a texture. *)

  RealDerivatives = ARRAY [0..5] OF REAL;
  (*
    Partial derivatives for one layer of the texture:
    in order, $f, f_{x}, f_{y}, f_{xx}, f_{xy}, f_{yy}$. *)

PROCEDURE DerivativesFromNeighborhood(
    READONLY t: RealNeighborhood;
    VAR v: RealDerivatives;
  );
  (*
    Computes the six spatial derivatives "v[s]" of order 0..2 
    from a 3x3 neighborhood "t[y,x]", for a single layer of a texture. *)