A closed fence in the plane is a set of non-crossing, connected line segments with N corners (3 < N < 200). The corners or vertices are each distinct and are listed in counter-clockwise order in an array {xi, yi}, i in (1..N).
Every pair of adjacent vertices defines a side of the fence. Thus {xi yi xi+1 yi+1} is a side of the fence for all i in (1..N). For our purposes, N+1 = 1, so that the first and last vertices making the fence closed.
Here is a typical closed fence and a point x,y:
* x3,y3
x5,y5 / \
x,y * * / \
/ \ / \
/ * \
x6,y6* x4,y4 \
| \
| \
x1,y1*----------------* x2,y2
Write a program which will do the following:
- Test an ordered list of vertices {xi,yi}, i in (1..N) to see if the array is a valid fence.
- Find the set of fence sides that a person (with no height) who is standing in the plane at position (x,y) can "see" when looking at the fence. The location x,y may fall anywhere not on the fence.
A fence side can be seen if there exists a ray that connects (x,y) and any point on the side, and the ray does not intersect any other side of the fence. A side that is parallel to the line of sight is not considered visible. In the figure, above the segments x3,y3-x4,y4; x5,y5-x6,y6; and x6-y6-x1,y1 are visible or partially visible from x,y.