INTERFACE Quaternion;

IMPORT Matrix4;

TYPE
  T = RECORD
    a, b, c, d : REAL;
  END;

PROCEDURE FromMatrix4 (READONLY M : Matrix4.T) : T;

FromMatrix4(M) takes an orthonormal matrix M and returns the corresponding quaternion q. q will have unit norm.

PROCEDURE ToMatrix4 (q : T) : Matrix4.T;

ToMatrix4(q) takes a unit norm quaternion and returns an orthonormal matrix M that corresponds to this quaternion.

PROCEDURE Interpolate (q : T; f : REAL) : T;

Interpolate (q,f) takes a unit norm quaternion q = (a,b,c,d) and a real f between 0 and 1, and returns a unit norm quaternion. Mapping Interpolate over the range [0,1] and applying ToMatrix4 to the results yields a series of matrices that describe a ``smooth'' rotation, with Matrix4.Id as the initial matrix and ToMatrix(q) as the final matrix.

END Quaternion.