GeoGebra/Perspective Drawing on Mirror

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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]

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.

Mirror-Basic

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.

Paper location as mediator between 3D and 2D world of projection

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.

Projection on Mirror

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.

Z-Construction

X-Construction for Point on a Surface[edit]

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

X-Construction

I-Construction for a Vertical Line[edit]

The I-construction creates the perspective image of vertical line segment by using 2 X-constructions.

I-Construction

3D-Object generated with Z-,X- and I-Construction[edit]

3D-Object

External Resources[edit]

See also[edit]

References[edit]

  1. 3D Construction with Geogebra (2017-2019) Engelbert Niehaus, URL: https://github.com/niebert/3D_Construction_Geogebra (accessed 2019/06/12)
  2. 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