Table 1.

(a) The osteotomy parameters which are involved in the application of an ODCRO and their relation with (b) optimization parameters visualized in Figs. 1b and 5. In this example the distal plane is chosen by the algorithm, the proximal plane parameters can then be calculated. (c) Shows how these optimization parameters are calculated.

Description	(a) Osteotomy parameter	(b) Optimization parameter	(c) Calculation of optimization parameter based on osteotomy parameter
Distal plane location	pd	d1 (*)	d1 =|pd—p0|
Distal plane orientation	nd	φd, ψd	Azimuth (φd) and elevation (ψd) angles: ${\phi }_d=\arctan \left(\frac{{\mathit{n}}_d(y)}{{\mathit{n}}_d(x)}\right);{}_2=\arctan \frac{{\mathit{n}}_d(z)}{\sqrt{{{\mathit{n}}_d(x)}^2+{{\mathit{n}}_d(y)}^2}}$
Distal bone segment rotation	βd	βd
Proximal plane location	pp	d2 (*)	d2 =|pd – pp|
Proximal plane orientation	np	(#)	Azimuth (φd) and elevation (ψd) angles (np, see Eq. 4): ${\phi }_p=\arctan \left(\frac{{\mathit{n}}_p(y)}{{\mathit{n}}_p(x)}\right);{}_2=\arctan \frac{{\mathit{n}}_p(z)}{\sqrt{{{\mathit{n}}_p(x)}^2+{{\mathit{n}}_p(y)}^2}}$
Rotation of distal/middle bone assembly	βp	(#)	See Eq. (3)
In-plane sideward and upward translation of distal bone segment ($)	xd, yd	xd, yd
In-plane sideward and upward translation of distal/middle bone assembly ($)	xp, yp	xp, yp

(*) Measured along the gravitation axis of the target bone (see text).

(#) proximal plane follows distal plane (see Eqs. 3 and 4).

($) Measured along the two gravitation axes of the points describing the distal or proximal bone cross section (Fig. 5b).