# 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^{[1]} 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^{[2]}

## Contents

- 1 3D Construction of Projections in Geogebra
- 2 Basic Situation in Front of a Mirror
- 3 Use a Paper as Mediator between 3D and 2D Construction
- 4 Basic Geometry in Front of the Mirror
- 5 Z-Construction for Lines on a Surface
- 6 X-Construction for Point on a Surface
- 7 I-Construction for a Vertical Line
- 8 3D-Object generated with Z-,X- and I-Construction
- 9 External Resources
- 10 See also
- 11 References

## 3D Construction of Projections in Geogebra[edit]

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]

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]

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]

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]

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]

The X-construction creates the perspective image of a point by using 2 Z-constructions.

## I-Construction for a Vertical Line[edit]

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]

## External Resources[edit]

- GitHub Resources with Geogebra Files as ZIP-File
- GitHub Repository for Wikiversity Learning Resource

## See also[edit]

## References[edit]

- ↑ 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