Desargues Projections

Desargues Projections are an application of Desargues theorem applied to projective geometry. By using Desargues projections, one forms an axis of perspectivity based on any two triangles.

Creating a Desargues Projection:
1: Given 3 lines that go through a single point, called the center of perspectivity.
2: Take 2 sets of three points, each point being on a separate line (ABC,DEF)
3: Draw lines which form the sides of ∆ABC (d,e,f)
4: Repeat this process for ∆DEF (g,h,i)
5: Find the intersection point for each corresponding triangle's side: AB and DF, AC and DE, BC and FE, to get points G,H, and I.
6: G, H, and I all lie on a common line, the Axis of Perspectivity.

Davis Gibson, March 7, 2011, Created with GeoGebra