Table 1 Definitions of the facial global coordinate system, reference landmarks, translational deviations of the landmarks, and rotational deviations of the maxillary dentition

Facial global coordinate system

Origin

The deepest point of the nasal bridge on the facial soft tissue (soft-tissue nasion)

Horizontal plane

Constructed by three landmarks, the most superior point of infraorbital rim on right and left sides and the most superior point of right porion

Mid-sagittal plane

Constructed perpendicular to the horizontal plane, through soft-tissue-nasion and midpoint of both tragus points

Coronal plane

Constructed perpendicular to the horizontal plane and the mid-sagittal plane, passing soft-tissue nasion

Axis

X, transverse axis. Y, sagittal axis. Z, vertical axis

Landmarks

UI

The most mesial point of the tip of the crown of each maxillary central incisor.

A6

The most superior point of buccal groove of the crown of the right first maxillary molar.

B6

The most superior point of buccal groove of the crown of the left first maxillary molar.

Translational deviations of the landmarks

X

Transversal translation of the reference point, “> 0” indicates right movement of the reference point, “< 0” indicates left movement of the reference point.

Y

Sagittal translation of the reference point, “> 0” indicates anterior movement of the reference point, “> 0” indicates posterior movement of the reference point

Z

Vertical translation of the reference point, “> 0” indicates superior movement of the reference point, “> 0” indicates inferior movement of the reference point

Rotational deviations of maxillary dentition

Pitch

Pitch of the maxillary dentition, “> 0” indicates upward rotation of the maxillary dentition in the front around a horizontal axis, “= 0” indicates no rotation of the maxillary dentition on the sagittal plane around a horizontal axis, and “< 0” indicates downward rotation of the maxillary dentition in the front around a horizontal axis, in the global reference system

Roll

Roll of the maxillary dentition, “> 0” indicates rotation of the maxillary dentition around a horizontal axis, up on the left side, “= 0” indicates the maxillary dentition no rotation on the coronal plane around a horizontal axis, and “< 0” indicates rotation of the maxillary dentition around a horizontal axis, down on the left side, in the global reference system

Yaw

Yaw of maxillary dentition, “> 0” indicates left rotation of the maxillary dentition in the front around a vertical axis, “= 0” indicates no rotation of the maxillary dentition on the horizontal plane around a vertical axis, and “< 0” indicates right rotation of the maxillary dentition in the front around a vertical axis, in the global reference system