Main Topics:

In Triangle Geometry we studied everything connected with 3 points / 3 lines.
However there are also points connected with 4 points / 4 lines.
For example there is a centroid in a figure with 4 points.
There is a point with least sum of squared distances to 4 lines.
There are lots of surprises.
For example the centroid in a figure of 4 points differs from the centroid in a figure of 4 lines.
When you are interested go to the  Encyclopedia of Quadri-Figures .
QA-QG-QL-Centroids-01                                         QA-P1                                               QG-P4                                                          QL-P12

  What are Perspective Fields ? 

Look at the resemblance between these 3 pictures:  


Why are there so many collinearities in Triangle Geometry?
Challenged by this question I developed a theory on Perspective Fields.