Table 1 Definition of the cephalometric measurements performed in the present study

Maxillary length (PNS-A): the distance between the posterior nasal spine (PNS) and point A

SNA: the angle formed between points S, N, and A, indicating the anteroposterior projection of the maxilla

Mandibular body length (Go L/R–Me): the distance between left and right gonion (Go) and menton (Me)

SNB: the angle formed between points S, N, and B, indicating the anteroposterior projection of the mandible

Anterior cranial fossa length (S–N): the distance between sella (S) and nasion (N)

ANB: the angle formed between points A, N, and B, indicating the anteroposterior intermaxillary relationship. In 3D analysis, unlike traditional cephalometrics, the difference between SNA and SNB could differ from the value of ANB

Total anterior facial height (N–Me): the distance between N and Me

Maxillomandibular (intermaxillary) angles (PNS–ANS–Go R/L–Me): the angles between the palatal and mandibular planes

Upper anterior facial height (N–ANS): the distance between N and the anterior nasal spine (ANS)

Total gonial angle (Cd R/L–Go R/L–Me): the angle between the mandibular ramus and body

Lower anterior facial height (ANS–Me): the distance between ANS and Me

Cranial base angle (Ba–S–N): the angle between basion (Ba), S, and N

Posterior facial height (Go L/R–S): the distance between S and left and right Go

Craniomaxillary angle (SN–PNS–ANS): the angle between the floor of the anterior cranial fossa and the palatal plane

Mandibular ramus height (Go L/R–Cd L/R): the distance between left and right condylion (Cd) and Go

Craniomandibular angle (SN–LGo–Me/SN–RGo–Me): the angle between the floor of the anterior cranial fossa and the mandibular plane, measuring mandibular divergence

Upper incisor midline and lower incisor midline to sagittal plane (UI–Sag P, LI–Sag P): the distances between the superior and inferior dental midlines and sagittal plane