A final remark relates to the fact that if the essential matrix is determined from corresponding image coordinate, which often is the case when 3D points are determined in this way, the translation vector \ mathbf { t } is known only up to an unknown positive scaling.
32.
In the case of symmetry groups in the plane, additional parameters are the direction of the translation vector, and, for the frieze groups with horizontal line reflection, glide reflection, or 180?rotation ( groups 3 7 ), the position of the reflection axis or rotation point in the direction perpendicular to the translation vector.
33.
In the case of symmetry groups in the plane, additional parameters are the direction of the translation vector, and, for the frieze groups with horizontal line reflection, glide reflection, or 180?rotation ( groups 3 7 ), the position of the reflection axis or rotation point in the direction perpendicular to the translation vector.
34.
For each of the types " D " 1, " D " 2, and " D " 4 the distinction between the 3, 4, and 2 wallpaper groups, respectively, is determined by the translation vector associated with each reflection in the group : since isometries are in the same coset regardless of translational components, a reflection and a glide reflection with the same mirror are in the same coset.
35.
Where \ textbf { a } ^ * and \ textbf { b } ^ * are the primitive translation vectors of the 2D reciprocal lattice of the surface and \ textbf { k } ^ { | | }, \ textbf { k } _ 0 ^ { | | } denote the component of respectively the reflected and incident wave vector parallel to the sample surface . \ textbf { a } ^ * and \ textbf { b } ^ * are related to the real space surface lattice in the following way:
