## 2 Materials and Methods
### Calculation of Anatomical Planes and Bone Axes  
The files with the 3D bone models, in STL format, were imported in Matlab R2021b (Mathworks Inc., Natick, MA, USA) to be processed with original scripts according to an established technique [22]. The first step was the definition of the anatomical reference frame for the entire foot, with the vertical axis orthogonal to the ground plane, the antero/posterior axis on the ground plane joining the projections of the most plantar points of the calcaneus and the second metatarsal head, and the medio/lateral axis orthogonal to these two axes. All bone models were then realigned to this anatomical reference frame.  
A reference frame with three anatomical axes was also defined for the tibia (TI), calcaneus (CA), talus (TA), navicular (NA), and 1 st metatarsus (M1) according to the standard Principal Component Analysis [22]. Starting from the 3D coordinates of the bone surface points, this statistical analysis implies a one-shot calculation of the three orthogonal axes with the highest variance. For each of these bones, this results in the definition of the longitudinal axis, i.e., the antero-posterior, as well as the medio-lateral and the dorsi-plantar axes. However, for the following angular measurements, only the former was used and projected into the three anatomical planes of the foot, as defined above. Moreover, the plane orthogonal to the ground and passing through the longitudinal axis was defined, to report the most correct inclination, exactly in the spatial plane containing the axis, thus hereinafter called the \"3D angle\".  
For the assessment of relevant bone alignments before and after the operation, the following ten angles were thus calculated (Figure 2), according to the nomenclature in [22].  
IL_TA; IL_CA: the inclination angle in the lateral anatomical plane of the talus (TA) and of the calcaneus (CA), with positive being down to the ground and negative being up.  
I3_CA: the inclination angle in 3D of the calcaneus, with negative being up from the ground.  
RF_TICA: the relative angle in the frontal anatomical plane between the tibia (TI) and the calcaneus (CA), i.e., varus (negative) and valgus (positive) of the calcaneus.  
RL_TACA; RT_TACA; R3_TACA: the relative angle between the talus (TA) and the calcaneus (CA), respectively, in the lateral and transverse anatomical planes, and in 3D.  
RT_TANA: the relative angle in the transverse anatomical plane between the talus (TA) and the navicular (NA).  
In the transverse anatomical plane, positive values indicate inclinations of the bone toward the lateral side and negative toward the medial side.  
RL_CAM1: the relative angle in the lateral anatomical plane between the calcaneus (CA) and the first metatarsal (M1), i.e., the Hibb angle in traditional X-ray pictures [13]; it is the value of the apex dorsi angle.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{13}{c}{**Post-Op**} & \multicolumn{13}{c}{**Clinical Scores**} & \multicolumn{13}{c}{**Bone Alignments**} \\ \hline \multirow{2}{*}{**Patient**} & \multirow{2}{*}{**FPI**} & \multirow{2}{*}{**TT**} & \multirow{2}{*}{**TT**} & **Valigins** & \multirow{2}{*}{**Calcaneal**} & **FFI** & \multirow{2}{*}{**IL\_TA**} & \multirow{2}{*}{**IL\_CA**} & \multirow{2}{*}{**B\_CA**} & \multirow{2}{*}{**RF\_TICA**} & \multirow{2}{*}{**RL\_TACA**}  
RL_TAM1: the relative angle in the lateral anatomical plane between the talus (TA) and the first metatarsal (M1), i.e., the Meary's angle in traditional X-ray pictures [13]; it is the value of the apex dorsi angle and is negative when it is an apex plantar angle.