Discrete Variable Conditional 3D Models in Computer Extended Descriptive Geometry (CeDG): Preliminary Study on Cylindrical Polygonal Sheet-Metal Elbow

Computer extended Descriptive Geometry (CeDG) technique has demonstrated its ability to build parametric computational models of 3D systems supported by Descriptive Geometry procedures in previous studies. When a parameter causes a non-continuous and qualitative change in the 3D model, it requires an additional logic. The treatment of visibility is a well-studied example of qualitative changes that are associated with continuous parameters. We are interested in qualitative changes associated with discrete parameters (discrete variable conditional 3D models). This work deals with the preliminary study of a methodology for the construction of such 3D models. A cylindrical polygonal sheet-metal elbow model of n ferrules (neutral surface) with the ability to cater for the change of variable n (n > 2, discrete) is used in this work as a target system to study the limits and accuracy of CeDG based on GeoGebra in the construction of discrete variable conditional models. We successfully achieved a conditional CeDG model (3D), including the flat pattern, for any number of ferrules. This model overpasses the scope of the polygonal elbow model from LogiTRACE v14, which is restricted to \(n\le 12\) . In addition, flat patterns in CeDG are exact in opposition to that of LogiTRACE, which are prismatic approximation with a given number of generatrices.