## 1 Introduction
Mesh sculpting is well-suited for creating complex and organic surfaces; however, it is not ideal for precision modelling. To address this, precision CAD models have been integrated with virtual and AR tools, using solid modelling algorithms such as B-Rep [30] and Constructive Solid Geometry (CSG) [31]. B-Rep defines a solid by its geometric boundaries using NURBS [32] curves and surfaces, while CSG builds complex solid objects by applying topological operations to primitive solids like cubes, spheres, and cylinders [33]. In [PERSON] et al. [34], haptic gloves were introduced for force feedback, providing a much more immersive virtual experience, and deep learning was applied for more intuitive reverse engineering based on CSG algorithms. [PERSON] et al. [35] defined a procedure for conceptual design and freeform modelling using hand gestures based on NURBS surfaces. The use of hand gestures enhances the interactivity and intuitiveness of the application [35; 36]. Despite the state-of-the-art applications for qualitative modelling through mesh sculpting and precision CAD modelling using NURBS, all these methodologies may be inadequate where there is a need to model complex organic shapes with geometric accuracy. To combine the advantages and versatility of mesh sculpting with the mathematical accuracy and generalisation of the B-Rep approach using NURBS, freeform modelling through subdivision surfaces using refinement algorithms can be employed [37]. Subdivision surface algorithms are able to create smooth, high-resolution surfaces by iteratively refining a coarse polygonal mesh (control cage). The user acts on these control cages, relocating its entities (points, edges, and faces) or adding/removing entities, and the final surface is changed accordingly. These approaches are increasingly widespread and included in computer-aided modelling environments, becoming an alternative to history-based parametric modelling. Subdivision surface modelling has the extreme advantage of simplifying the modelling of complex organic shapes, but it is limited in creating exact functional fit surfaces (such as cylindrical holes, cylindrical pins, and flat surfaces). However, the complete modelling procedure always involves a final phase of modifications and detail of the geometries built with feature-based approaches. The great advantage compared to sculpting methodologies based on polygonal meshes is that a recursive subdivision scheme can tend to surface patches with high geometric continuity up to G2 (curvature continuity), allowing a final conversion into NURBS patches and a direct integration with geometries modelled with the standard B-Rep approach. Another important aspect of modelling complex shapes is the ability to act on the geometry to be sculpted through direct gestures, without the use of wearable devices, controllers, or pointers, to directly accept the user's intent, and transform it into actions. This approach is often called natural interface and has gained relevance in both the scientific and industrial communities, especially for assisted assembling and interactive simulations [38; 39]. From this background, the study aims to develop a novel integrated methodology, implementing an immersive modelling environment based on freeform modelling through subdivision surfaces in AR, and implementing an ad hoc natural interface based on hand tracking and advanced gesture recognition. The sculpting algorithm implemented in the methodology is based on adapting the well-known Catmull-Clark surfaces algorithm. It combines the effectiveness of the direct modelling approach with the capability of post-processing the outcome of the modelling with a B-Rep geometrical kernel to finalise the design into an exact NURBS patch. The interaction with the geometry to be sculpted is implemented as an extension of the Grasping Active Feature/Object Active Feature methodology (GAF/OAF) [40], adapted for the grasping and manipulating of subdivision control cage entities.