## 1 Introduction  
Dentofacial deformities interfere with the quality of life, both psychologically and physically. Patients with dentofacial deformities require a meticulous assessment of the dentoalveolar position, facial skeleton, facial soft tissue surface, and their interdependency. The treatment plan must correct this triad in order to achieve an aesthetic and stable result with adequate function [1; 2]. The treatment plan is dependent on an in-depth physical examination, cephalometric analysis, patient age, and severity of the malocclusion. In complex cases, a combination of orthodontic treatment and orthognathic surgery is required [3; 4; 5]. A systematic review found that three-dimensional models are accurate tools that allow clinicians to identify and locate the source of the deformity as well as its severity. Moreover, 3D models are realistic tools for treatment planning and assessment of outcomes. Since these models can be manipulated in any direction, avoiding patient recall and decreasing the time of the appointment, the treatment simulation and pre- and post-treatment comparisons are easier, allowing the clinicians to assess facial changes following orthodontic and/or surgical treatments. Despite the progress in 3D imaging, the available imaging techniques still do not allow the representation of the three elements of the face (skeleton, soft tissue, and dentoalveolar) at the same time with optimal quality [6]. A correct diagnosis and surgical plan are fundamental to obtaining improved therapeutic results. To achieve this, the clinician can use a three-dimensional computerized virtual preoperative simulation using cone beam computed tomography (CBCT) [7; 8]. CBCT is a medical imaging technique that uses a cone-shaped radiation beam that rotates 180\({}^{\circ}\) to 360\({}^{\circ}\) around the patient [9], allowing the images to be reconstructed three-dimensionally [10]. It is currently an important tool in diagnosis, planning and postoperative follow-up of complex maxillofacial surgery cases [11]. It further complements conventional two-dimensional X-ray [12] imaging techniques, given that these have some limitations [13; 14]. Moreover, CBCT allows for detailed planning, not only by the creation of a virtual 3D craniofacial model, but also by the virtual simulation of the planned surgery. This process is based on a simplified anatomical virtual model with hard, soft, and dental tissues. The obtained model facilitates the construction of surgical splints using CAD/CAM techniques, thus rendering manually constructed splints unnecessary [15]. CBCT reconstruction with a digital dental cast is the most accurate model to visualize the facial dentition and skeleton. However, CBCT skin is untextured and to allow a more realistic visualization of the 3D facial model, a superimposition of the textured facial soft tissue surface (e.g., 2D photographs) is required. This process is easy and cheap, and uses a specific algorithm and software obtainable through surface-based registration [6]. It is possible to obtain 3D models by reconstruction of CBCT images using techniques such as multiplanar rendering, surface rendering, which includes contour-based surface reconstruction and isosurface extraction based on marching cube, and volume rendering [16]. Multiplanar rendering is a technique that displays intensity values on arbitrary cross-sections using volumetric data. The volume is projected onto three orthogonal spatial planes (coronal, sagittal and axial), allowing the user to navigate while changing the coordinates of the three planes [16]. Surface rendering allows for volume quantification through datasets that have common values, using voxels, polygons, line segments or even points. Marching cube has the ability to define about 15 intersection patterns, resulting in a detailed construction of a desired surface [16; 17; 18]. Volume rendering allows the visualization of the 3D model from any direction, making it possible to obtain a high-quality analysis of the various layers.