Graphics function to calculate offset from line

I need a function that takes a set of points that makes up a line and an offset (+ or -) and returns a new set of points that are offset perpendicularly by the offset distance from the original set. If the angle between the adjacent line segments is convex then a new segment should be added. If concave then the intercept between the two new lines. If a short segment gets "reversed" in the new line then it should be removed. See the attached sketch. The line is open - i.e. this is not a closed shape. The number of points is 6 to 10. Ideally I would like this done in Swift but any variety of c would be ok. C++, C, C Sharp, Objective C. Please specify which language you will use in your bid. Something like the following: class Line { var points : [Point] init( Points : [Point] ) { points = Points } func GetPointsAtOffset( offset : Double) -> [Point] { // Fill this in :) } }