ProE Puzzle 001

I thought it would be nice to learn if its put in the form of Puzzles. This is nothing but a modelling requirement. How would you do it?

Puzzle No: ProE_Puzzle_001
Puzzle type: Basic.

Here is the Qn. See the diagram. We have 2 sets of points. each set has 4 points. they are A1 to A4 and B1 to B4.

The puzzle is to create a curve through the mid points of the lines A1-B1, A2-B2, A3-B3 and A4-B4.

The Modelling method should be such such that the values of x, y and the no of points in each set can be parametrically controlled.

How would you solve it? Leave your answer as comment.

I will post my answer in three weeks time.

[Edited on 15th Sep 2008]
Click here to get the answer for the puzzle.
[End of Edit]