Evaluate minimum points required to define polygons based on an error threshold

I need to build a model or write an algorithm to do this.

here is my cadastral problem: I have plenty of polygons and I need to make a report of coordinations of their vertices. This is pretty easy: I can extract vertices using ArcGIS toolbox and add XY coordinate to each point again using ArcGIS toolbox. However, since each polygon has 20-30 vertices, I need to condense the information. I need to make reports of the most important vertices which define a polygon. The problem here is that these are polygons with irregular shapes. Some can be defined by using 4 points and some require 10 for example. Moreover, my datasets are huge and I definitely need an automated approach to this.

Here is what I thought I have to do:

1) Polygone to vertices > add XY to vertices

2) for each set of polygon vertices use an iterative approach as follows:

2.2) calculate area

2.3) evaluate area error percentage (area error/correct area = abs(real area-calculated)/correct area)

2.4) if area error < desired threshold (say 0.05)

then end step 2, go to next polygon

else add one vertex, go to 2.2

3) Make a report of selected vertices

However, I have a problem with this. How should I select the correct vertices in step 2.1 and 2.4. For example, a polygon having 20 vertices, may not be defined using 4 of its vertices, while it can be very well defined using another 4 vertices.

I have access to Arcinfo+python, Xtools, and Matlab+Mapping toolbox. I don't know if I have to use Matlab for this problem or not, since I doubt the efficiency of ArcPy in calculation of new polygon areas.

• You mentioned this was cadastral information. Removing vertices will likely violate the shared borders of the cadastral polygons. You'll end up with overlapping polygons or gaps between polygons (theoretically, if you were to recreate polygons from the resultant vertices), unless you're careful to remove the same vertices from adjacent polygons. Is this not a concern for the report you have to create? – user3461 Apr 13 '13 at 13:09
• What is the purpose of this analysis? Would it be beneficial to define each polygon by its centroid? – Aaron Apr 13 '13 at 13:37
• A report in form of a table, should be added to each cadastre map, which contains coordinations of the parcel's critical points. (We produce maps for each parcel separately). However, the reason behind this is not recreating the exact polygons. Prior to using LIDAR, we had smooth parcels which could be defined by using few points. Now parcels have far more details and some are redundant. Nevertheless, we must make map reports with the same map template we were using before: a handful of points should be reported on it. – Edi Gosilbang Apr 13 '13 at 18:56
• @Aaron So the centroids would not be that "representative". The centroids have no "area" information, unless there be no gaps and polygons can be recreated using thiessens. – Edi Gosilbang Apr 13 '13 at 18:57