I then started thinking about this question, again. The idea of the question was to see what tables and columns would you set up to make this feasible. I wanted an easy solution with minimal work, so I avoided the polymorphism concept and went to a simpler definition of a shape (polygon).
I figure I would make 1 table called SHAPE with 2 columns and make the assumption that the shapes are defined as "simple polygons":
ID int, COORDINATES varchar
The ID is obviously the primary key for each shape.
The Coordinates is a order list of Cartesian coordinates going counter-clockwise.
Now, given a shape, the most common questions asked would be what is the perimeter and area of said shape. I could easily make 2 store procedures to find the perimeter and area.To figure out the perimeter, I just need to add up the distance from each point, simple enough.
To figure out the area of the polygon, I knew there had to be a formula that would do this for me, and thanks to wikipedia I found one:
"The formula was described by Meister in 1769 and by Gauss in 1795. It can be verified by dividing the polygon into triangles".
I was looking around, to see if others seen this question. I did find something similar at http://lists.mysql.com/mysql/207823
If I needed to query the table for certain shapes, then it would be good to add an additional column called: Points int
So, if I needed to query the table for triangles only then I can do a search on points = 3.