Intersection and Flattening of Surfaces in 3D Models through Computer-Extended Descriptive Geometry (CeDG)

Abstract

Computer-extended Descriptive Geometry (CeDG) is a new approach to solving and building computer models of three-dimensional (3D) geometrical systems through descriptive geometry procedures (thus inheriting invariant-symmetry properties from projective geometry) that have demonstrated reliability and accuracy. CeDG may calculate a parametric implicit functional form for the spatial curves generated in the intersection of two surfaces, as well as of the flattened pattern of any developable surface involved in those encounters. This study first presents the theoretical foundations and methodology to calculate those curves. Secondly, a compound hopper is defined and modeled through CeDG (implemented in GeoGebra) and CAD (Solid Edge© 2023) approaches to evaluate the advantages of CeDG against CAD. The results demonstrate the robustness and accuracy of the CeDG technique for he intersection and flattening of surfaces and the advantages of CeDG against Solid Edge 2023 in solving the hopper case study.