Fig. 2.

a Parametrization of the genioplasty osteotomy: α is the angle, H is the distance of the osteotomy plane from the lower incisal plane b Parameters of bony segment repositioning: horizontal translation (U_H, negative in the anterior direction, positive in the posterior direction), vertical translation (U_V, negative in the caudal direction, positive in the cranial direction) and pitch rotation (ϑ, positive when counterclockwise, negative when clockwise when viewed from the left side). C Bony segment repositioning (using the parameter set H^S, α^S, UH^S, UV^S, ϑ^S) to match the postop mandible-chin relative position (in gray the postoperative chin shape extracted from CBCT; in transparent pink the simulated surgical result for a representative patient)