Convex hull and shortest path problem

Hi,

I'm not so much after answers here as an explanation of what the second question is asking:

Quote:

**3.** There is a fenced area in the two-dimensional Euclidean plane in the shape of a convex polygon with vertices at points

P1(x1,y1), P2(x2,y2), ...., Pn(xn,yn)

(not necessarily in this order). There are two more points, A(xA, yA) and B(xB,yB), such that xA < min { x1, ..., xn } and xB > max { x1, ..., xn }. Design a reasonably efficient algorithm for computing the length of the shortest path between A and B, and the shortest path itself.

** 4.** Under the conditions of question 3, design a reasonably efficient algorithm for computing the shortest among all piece-wise linear paths between A and B having the least number of angle points.

Now I've done question three by effectively finding the convex hull of { P1, ..., Pn, A, B } and then using Dijkstra's algorithm to find the shortest path through them. I've drawn a diagram to illustrate what I mean:

http://img291.imageshack.us/img291/9764/q34wb5.png

What I'm not sure about is what question 4 is asking. They're after the path that is shortest AND has least angle points? Or some kind of compromise? Aside from the angle point restriction Q4 looks identical to Q3...

Does anyone have any ideas as to what Q4 is asking? This is fairly urgent and I'd really appreciate the help.

Thanks,

Rob