GeoGebra/Perspective Drawing on Mirror
This learning resource is about perpective drawing of 3D objects on a mirror and learn about geometric principles of construction. Together with this learning resource a GitHub repository with Geogebra Files was created that can be opened with dynamic geometry software Geogebra. The construction is based on a german article in the journal Mathematica Didactica 26 (2003) Bd.1 43, Experimenteller Umgang mit Spiegelung und Perspektive unter Verwendung von Dynamischer Geometriesoftware, Engelbert Niehaus
3D Construction of Projections in Geogebra[edit | edit source]
The repository contains Geogebra files for learning 3D projections on a mirror Z-, X, and I-construction of 3D point and lines. This repository has additional learning material for the Open Source software Geogebra and the file are bundled in a GitHub repositopry created for the Wikiversity Learning Resource about Perspective Drawing - https://en.wikiversity.org/wiki/Perspective_Drawing_on_Mirror
Basic Situation in Front of a Mirror[edit | edit source]
The following image shows the basic situation of a 3D projection on a mirror. The perspective image of the box is painted on the mirror.
Use a Paper as Mediator between 3D and 2D Construction[edit | edit source]
You can use a paper as mediator between the 3D world and the 2D projection on the paper.
Basic Geometry in Front of the Mirror[edit | edit source]
The perspective drawing creates an image of an object in front of a mirror. The eye observes the projective image from a point Z. Assume the observer is painting the perspective image of a vertical line/stick on the surface of the mirror. Considering the perpective construction from the side will lead to the following situation.
Z-Construction for Lines on a Surface[edit | edit source]
We unfold the paper mediator between 2D and 3D construction and transfer the folding to two parallel lines in Geogebra. A Z-construction generates perspective image of a half-line.
X-Construction for Point on a Surface[edit | edit source]
The X-construction creates the perspective image of a point by using 2 Z-constructions.
I-Construction for a Vertical Line[edit | edit source]
The I-construction creates the perspective image of vertical line segment by using 2 X-constructions.
3D-Object generated with Z-,X- and I-Construction[edit | edit source]
External Resources[edit | edit source]
- GitHub Resources with Geogebra Files as ZIP-File
- GitHub Repository for Wikiversity Learning Resource
See also[edit | edit source]
References[edit | edit source]
- 3D Construction with Geogebra (2017-2019) Engelbert Niehaus, URL: https://github.com/niebert/3D_Construction_Geogebra (accessed 2019/06/12)
- Niehaus, Engelbert (2003), Experimenteller Umgang mit Spiegelung und Perspektive unter Verwendung von Dynamischer Geometriesoftware, Mathematica Didactica 26 (2003) Bd.1 43, http://www.mathematica-didactica.com/altejahrgaenge/md_2003/md_2003_1_Niehaus_Spiegelung.pdf