## 2 Materials and Methods
### The 3D Cephalometric Measurement  
The preoperative (T0), one-jaw, and two-jaw simulation images were exported as STL files and imported to Simplant O&O software (Materialize, Leuven, Belgium) for landmark location and 3D cephalometric measurement (Table 1). All landmarks were identified by the same investigator. Three reference planes were defined. Frankfort horizontal plane (FHP) was the plane passing through bilateral orbitales and the midpoint between the right and left portions. The midsagittal plane (MSP) was the plane passing through nasion and basion and perpendicular to FHP. The coronal plane was the plane passing through nasion and perpendicular to FHP and MSP. After landmark identification, the 3D linear and angular measurements were calculated. Comparisons of cephalometric measurement were conducted among T0, one-jaw, two-jaw designs, as well as normative Taiwanese data [17]. For further investigation in the one-jaw surgical simulation, the samples were divided into large advancement design (more than 6 mm) and regular advancement design (6 mm or less) according to the amount of maxillary movement.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline \hline
**Landmark** & **Definition** \\ \hline \hline Basion (Ba) & The most anterior point of the great foramen (foramen magnum). \\ \hline Nasion (N) & The midpoint of the frontonasal sutures. \\ \hline Sella (S) & The center of the hypophyseal fossa (sella turcica). \\ \hline Porion (Po) & The most superior point of each external acoustic meatus. \\ \hline Orbitale (Or) & The most inferior point of each infra-orbital rim. \\ \hline Anterior nasal spine (ANS) & The most anterior midpoint of the anterior nasal spine of the maxilla. \\ \hline A point (A) & The point of maximum concavity in the mid-line of the alveolar process of the maxilla. \\ \hline B point (B) & The point of maximum concavity in the mid-line of the alveolar process of the mandible. \\ \hline Pogonion (Pog) & The most anterior midpoint of the chin on the outline of the mandibular symbiosis. \\ \hline Menton (Me) & The most inferior midpoint of the chin on the outline of the mandibular symbiosis. \\ \hline Gonion (Go) & Dropping a perpendicular from the intersection point of the tangent lines to the posterior margin of the mandibular vertical ramus and inferior margin of the mandibular body or horizontal ramus. \\ \hline Upper incisors (U1) & The midpoint between the crowns of the maxillary central incisors. \\ \hline Lower incisors (L1) & The midpoint between the crowns of the mandibular central incisors. \\ \hline Upper canine (U3R/L) & The cusp tip of the maxillary canine on the right/left side. \\ \hline Lower canine (L3R/L) & The cusp tip of the mandibular canine on the right/left side. \\ \hline Upper first molar (U6R/L) & The meso-buccal cusp of the maxillary first molar on the right/left side. \\ \hline Lower first molar (L6R/L) & The meso-buccal cusp of the mandibular first molar on the right/left side. \\ \hline Anterior occlusal cant & Angle between the line of canines and Frankfort horizontal plane. \\ \hline Posterior occlusal cant & Angle between the line of first molars and Frankfort horizontal plane. \\ X axis & Frankfort horizontal plane. \\ Y axis & Midsagittal plan. \\ Z axis & Coronal plane. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Definition of the three-dimensional skeletal landmarks, angle and reference planes.