## 4 Conceptual Framework for Augmented Reality Application
### Modeling
#### 4.3.3 Geometric Modeling  
In turn, geometric models are used for representations in two or three dimensions to provide critical information for industrial systems' design, construction, operation, and control. Specifically, in the case of technical drawing for the process industry, the diagrams are built based on the ISA 5.1 standard [64], which defines all the elements and lines that can and should be used so that there is a standardized understanding of the symbology. Different models are used during the operation of an industrial plant, including floor plans, isometric diagrams, control diagrams, and instrumentation. Additionally, each subsystem of the industrial plants has specific designs and points of interaction with the other subsystems. Still, in the context of geometric designs, the 3D geometric model can be characterized as a set of information of an object stored in a computer. This information concerns the topology of the object, such as connections of vertices, edges, surfaces, and volumes, as well as their dimensions, contours, and tolerances, and there may also be derivations of the shape to specify materials and other properties [65]. The principal types of geometric models include wireframe, surface, solid, or point cloud models. * Wireframe: Also known as wireframe models, these are 3D representations consisting solely of lines and edges without any surface presence. These models are useful for visualizing the basic structure of the object but do not provide detailed information about its form [66]. * Surface Models: In this type of model, in addition to lines and edges, the surfaces of the object are represented. However, these surfaces are considered \"empty\" or without thickness, meaning they lack volume. Surface models are commonly used in design and visualization applications. * Solid Models: Solid models are 3D representations with volume that define the object's complete shape, including its surfaces and interior. These models are more complex and provide detailed information about the object's geometry, making them widely used in engineering, manufacturing, and simulations. The complete modeling calculates mechanical properties such as weight and center of gravity [67]. * Point Cloud Models: The object's surface is represented as a collection of three-dimensional points in this model type. Each point has X, Y, and Z coordinates, and together, they form a point cloud that describes the external shape of the object. Point cloud models are useful for capturing the geometry of complex objects and for detailed analyses such as surface reconstruction and precise measurements [68]. The choice of geometric model type depends on the specific purpose of the application and the level of detail required to represent the object adequately. Each model type has its advantages and limitations, and the decision of which one to use will be based on the needs and requirements of the project. Specifically for process industry applications, 3D models are primarily used in manufacturing sites' design and construction stages. Despite the advanced digitization of industrial processes and the use of advanced process simulators, 3D models and the construction of digital twins for iterating and managing industrial processes lack development and boosting of applications. Good practices during the modeling process require a cyclical approach to building, validating, and using models [69]. Regardless of the type of model used, the steps involve the proposition of the model, choice of parameters when applicable, evaluation of the prediction or representation capacity, validation, and final adjustments before use. In this sense, Figure 1 presents a closed cycle that indicates that the model can be entirely reconstructed if it does not meet the requirements.