regions

determining whether a point is within a region, take the points of the region 

boundry that have the same x value as the point in question, and check that 

the main point's y value is within the two y values of the boundry points selected


in polar co-ordinates, points with the same theta and radius's greater and less than the point.



given a set of points P specifying a closed region, draw a line through the point A and determine the points B, C from the set P that

lie on the line. If the point A is on the line between the points B and C then the point is within the region, otherwise it is not.

More specifically, A is between the points B and C if the segments B-A and A-C make up the line B-C, the lengths B-A + A-C = B-C



in more detail

given a set of points P specifying (the boundry of a) closed region, draw a line through the point A and determine the points B, C 

from the set P that lie on the line. If the point A is on the line between the points B and C then the point is within the region, 

otherwise it is not. More specifically, A is between the points B and C if the segments B-A and A-C make up the line B-C, in practice

that the lengths B-A (length of the line from point B to point A) + A-C = B-C

The line may be in any direction.



closed region

a set points forming an irregular line, where starting at one point and tracing through the other points leads back to the starting position (the area enclosed by this line)

