## 4 Discussion and Conclusions  
A comprehensive methodology for creating an immersive environment for advanced modelling in AR has been presented and discussed in the paper. The methodology adopts freeform design through subdivision surfaces and incorporates a hand-tracking-based natural interface with sophisticated gesture recognition. The development of modelling software based on subdivision surfaces within an AR environment enhances the process of creating, interacting with, and optimising complex models. The use of pass-through, which allows virtual objects to be inserted into the real world, provides real-time spatial awareness and helps reduce sizing errors. Additionally, linking real and virtual objects enables the visualisation of mating errors in the physical environment. Mixed reality, combined with the use of hand tracking that replaces controllers, enhances immersion by reducing the gap between the virtual and real worlds, which is more noticeable with traditional modelling software. Hand tracking is essential for ensuring natural interactions. The ability to control the position, direction, and angles of each finger's phalanges and joints allows for the development of customisable gestures that translate the user's intent into commands for the software. The GAF/OAF methodology has been adapted to manage interactions between the user and virtual objects. This approach has been particularly employed to facilitate selection and grasping actions, ensuring more stable connections through the definition of virtual constraints that improve grip control. The approach has once again proved to be not only easy and general to use, but also highly capable of integration with tracking, visualisation, and modelling algorithms. The algorithm used for sculpting with subdivision surfaces is the Catmull-Clark algorithm, which has been adapted for use with triangular meshes in software designed for developing mixed-reality environments. These tools efficiently represent 3D objects and surfaces by leveraging the flexibility of triangular meshes. The choice of this algorithm is based on its general flexibility, straightforward implementation, and its ease of converting models from mesh to NURBS, enabling the models to be imported into traditional modelling software. This functionality also allows for the addition of further traditional operations to the model. The use of indices to identify the faces of the base cubes enables control over the transition between quadrilateral and triangular meshes, and vice versa. Also, the extrusion function is presented in this case, but the methodology can be generalised to other modelling functions. The entire proposed procedure has proven to be easy to learn even for users who are not very experienced in AR due to the ease of natural interaction with hand gestures. The use of high-end devices such as the Varjo XR-4 and Ultraleap Motion Controller v2 has made it possible to obtain excellent performance in terms of visual feedback and immersivity of the scene, in accordance with the usability study. The usability study also suggested working on an easier and more robust system for recognising hand poses which, despite having received discrete scores, is still the most critical aspect detected by users. At the moment, we have limited the evaluations to 5 min tests and, therefore, the usability study must be considered preliminary. Test will be extended in the continuation of the research. We believe that the proposed methodology can be generalised for the development of software for advanced modelling using subdivision surfaces, comprising all modelling functions and the ability to import the final design into traditional feature-based CAD software to convert meshes into NURBS. The interactive modelling phases should be intended as initial and not detailed design. This means that the user models initial three-dimensional shapes benefiting from the support of AR and then the laborious and time-consuming detailing of the geometry takes place on standard feature-based CAD platforms.