How to prepare a digital geometric model which is enclosed by an assembly of surfaces for 3D printing
Abstrakt
In this article we address the process of manufacturing 3D geometric models on 3D printers for educational purposes. The manufacturing of the geometric model includes the design, 3D computer modeling with Constructive Solid Geometry (CSG), 3D computer modeling of parametric surfaces based on differential geometry, 3D scanning of real objects, and the process of fabrication itself.
Students can join the whole process of designing the models for 3D printers or its parts and the printed models can be included in teaching and learning geometry at every stage of education (at the university and the secondary school in our case). We present the possibilities how to model geometric objects in 3D computer modeling software; including commercial ones and open-source software like the free dynamic geometry system, Geogebra.
We present particular constructions of selected geometric models whose boundary consists of parametric surfaces. All examples of printed geometric models presented in this article are intended to be used in mathematics instructions at the secondary school and in the undergraduate courses on descriptive geometry at Charles University (mandatory courses for secondary pre-service mathematics teachers who study teaching mathematics and descriptive geometry).
All phases of designing the models for 3D printing together with physical 3D printed models bring new opportunities for teaching and learning geometry. It engages students in real-world problem solving and promotes students' knowledge in geometry while introducing them into 3D computer modeling and 3D printing technologies. 3D virtual models and 3D printed models themselves can serve as the educational manipulative aids.