Discrete variable 3D models in Computer extended Descriptive Geometry (CeDG): Building of polygonal sheet-metal elbows and comparison against CAD

Abstract

The Computer extended Descriptive Geometry (CeDG) is as a novel approach based on Descriptive Geometry to build 3D models within the framework provided by Dynamic Geometry Software tools. Parametric CeDG models can be interactively explored when continuous parameters change, but this is not the case for discrete parameters. This study demonstrates the capability of the GeoGebra - CeDG approach to incorporate algorithms that build discrete variable 3D models with dynamic parameterization. Several 3D models and their flattened patterns (neutral fiber), based on a new developed CeDG algorithm, were compared to their LogiTRACE v.14 and Solid Edge 2024 (CAD) counterparts. The accuracy of the CeDG models surpassed that of CAD models for nearly all dimensions defined as metrics. In addition, the CeDG approach was the unique that provided an automatic solution for any value of the number of ferrules.

Keywords

• Computer extended Descriptive Geometry
• Computer aided design
• 3D discrete modeling
• Sheet metal
• Polygonal elbows
• Dynamic geometry software