Connect two points considering barriers between them

Discussion created by jose_luis_miguel_sanchez on Nov 4, 2011
I try to describe my problem as detailled as possible:

Initial point: I have a bounded area. This area has some angles. My area is saved as a polygon but if you tell me, that a line-feature would be better for my problem, this would be no problem.
Now assume, that I have two points within this area and want the shortest connection between them. But this connecting line has to be within the area. So in some cases the line would have a bend at an angle (or even more than one).

I've allready tried a lot of tools, but none of them did what I need. Here is a scetch of my problem:

A friend told me to use raster data but I don't really know how to manage my problem in a raster. I converted to area to a raster, setting the inside-area to a value of 0 and the outside i.e. to 100. I think I even managed to create a kind of surface showing the highest decline, some kind of potential like in physics respectively. But finally I was not able to create a line-feature out of this surface...

Actually I think the must be a way without using rasters.

I would really appreaciate your recommendations.