Table 2 Landmarks, mathematical reconstruction and measurements of the analyzed data

3D landmark position

Anterior nasal spine (ANS)

Most anterior point of the ANS

Posterior nasal spine (PNS)

Most posterior point of the PNS

Greater palatine foramen (GPF)

Geometric center of the GPF

Mesial pulp horn (MPH)

Highest occlusal point of the MPH of U6

Distal pulp horn (DPH)

Highest occlusal point of the DPH of U6

Palatal pulp horn (PPH)

Highest occlusal point of the PPH of U6

Mesial root apex (MRA)

Geometric center of the MRA of U6

Distal root apex (DRA)

Geometric center of the DRA of U6

Palatal root apex (PRA)

Geometric center of the PRA of U6

3D reconstruction and rendering

First permanent Molar (U6)

Rendered pyramid trunk solid formed by MPH-DPH-PPH base and MRA-DRA-PRA base

First molar center (U6-C)

Center of mass of U6

First molar axis (U6-A)

Line passing through the centroid of the upper and lower bases of U6

Pulp horn line (PH-L)

Line passing through MPH-PPH

Hemimaxillary plane (Hmx-P)

Plane passing through the ANS-PNS-GPF

Sagittal plane (x-P)

Plane passing through PNS and ANS, perpendicular to the respective right or left Hmx-P

Coronal plane (y-P)

Plane passing through PNS, perpendicular to right or left Hmx-P and x-P, respectively

Axial plane (z-P)

Plane passing through the PNS and parallel to the right or left Hmx-P

Hemimaxillary and maxillary measurements

Mesiodistal angulation (MD-angulation)

Angle between U6-A and coronal plane

Buccolingual inclination (BL-inclination)

Angle between U6-A and sagittal plane

Rotation (Rot)

Angle between PH-L and sagittal plane

Intermolar distance (Intermolar)

Sum of distances between right and left U6-C to x-P

Interforaminal distance (Interforaminal)

Sum of distances between right and left GPF to x-P