Problem 2219. Wayfinding 2 - traversing

This is the second part of a series of assignments about wayfinding. The final goal is to be able to calculate the fastest route through a terrain of areas with different properties. The assignments will build on top of each other, gradually increasing the complexity, but guiding you stepwise towards the final goal. You can re-use code from preceding assignments to save some work. See [1].

How many times does AB cross the boundary of area F?

For this second assignment in this series you have to calculate how many times we cross the boundary of a single area while going from A to B. Our path from A to B is a straight line. And the area boundary is a closed polygon consisting of a finite number of straight segments.

The inputs of the function WayfindingBoundaryCrossing(AB,F) are a matrix AB of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a matrix F of columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is connected to the first.

 AB = [
   xA xB
   yA yB
 ]

 F = [
  [ x1 x2 ... xn ;
    y1 y2 ... yn ]

Your output n will be the number of times the line AB crosses the boundary of F. Note that AB may cross the boundary of F at a corner node of F.