## 1 Introduction and Related Work  
The application of Virtual Reality (VR) technology to 3D modeling was one of the first uses that VR pioneers gave to the primitive hardware that was available in the 1990s. 3 DM [1] was one of the first systems with the capability of creating 3D geometry. The system was implemented with a VPL EyePhone head-mounted display (HMD) with a 442 \(\times\) 238 point LCD screen, a field of view of 108\({}^{\circ}\)\(\times\) 76\({}^{\circ}\), and a price of around 99000 [2]. The resolution was so low that the text labels on the buttons were very difficult to read. The 3 DM system was able to create a 3D geometry by the direct construction of triangular facets, the extrusion of polylines, and the creation of a set of basic 3D primitives. Due to the important limitation on the resolution of the screens in the available commercial HMDs, other researchers opted for desktop VR solutions such as HoloSketch [3]. This early system used a regular high-resolution monitor (960 \(\times\) 680, 20 in screen) coupled with stereo shutter glasses to provide stereo vision at a 56.45 Hz refresh rate. It supported a set of primitive 3D objects, free-form tubes, 3D isolated line segments, and polyline wires, among others. The system was a wireframe modeler without any surface or solid representations. The hardware capabilities, both in terms of processing and visualization, were the limiting factors in the systems developed during these years. Fortunately, the development of low-cost HMDs that began with the DK1 and DK2 Oculus Rift development kits [4] in 2013 and 2014 fueled the development of novel systems that leveraged the affordability of the new generation of HMDs. The creation of precise geometry in a VR environment has followed two main routes [5]: create a VR front-end to interact with a commercial CAD system or provide 3D modeling functionality using a geometric kernel such as Open Cascade [6] or ACIS [7]. An example of the first approach (linking a VR front-end with a CAD system) is cRea-VR [8], where a middleware architecture was developed to interact with Dassault Systemes' CATIA V5 in VR [9]. Another prototype system [10] interfaced a CAD system (Autodesk Fusion 360 [11]) with a game engine (Autodesk Stingray [12]) with limited modeling capabilities that supported the creation of solid prisms and spheres, snapping them to a grid, and performing cuts of similar shapes. Instead of controlling a host CAD system to create 3D geometry, an alternative research line focuses on supporting 3D sketching for VR. For example, Multiplanes [13], provides a VR-based 3D sketching environment that supports 3D freehand drawing that automatically Beautifies strokes to compensate for the difficulty of drawing in 3D. Similarly, Smart3 DGuides [14] automatically generates visual guidance by analyzing the user's gaze, controller position and orientation, and previous strokes in the VR environment, to increase the overall quality of the drawn shapes. To help users create sketches with higher precision, VRSketchIn [15] combines a 6 DoF-tracked pen and a 6 DoF-tracked tablet as the input devices, supporting unconstrained 3D mid-air sketching with constrained 2D-surface-based sketching. Other researchers have used commercial VR applications to study the reaction of users when they have to perform sketching and modeling tasks in the virtual environment. The commercial success of some HMDs has created a market for this type of system. The most widely recognized applications include:  
* Gravity Sketch [16];
* Tilt Brush [17];
* Master Piece [18];
* Kodon [19];
* ShapeLab [20];
* Adobe Medium [21];
* flyingshapes [22]. The results are contradictory. For example, a user study [23] with Gravity Sketch and Kodon concluded that these VR applications do not provide significant advances compared to conventional 2D sketching tools. This study also reports that the use of these VR applications produced noticeably more physical fatigue than traditional 2D sketching.