modify __eq__ method for Point class, the original == for float is no…

[jianantian]

modify eq method for Point class since the original == for float is not robust.
add set_epsilon function to change EPSILON value.

[TaipanRex]

I know the epsilon approximation for equality is used in papers, I wondering what problem it solves though? If two points differ by less than epsilon, does it matter if eq returns false? I guess my question is, what problem does adding epsilon solve?

Adding a call to abs and the additional arithmetic is a cost to performance, so must weigh that against what benefit it adds.

[jianantian]

In my example (at end), there is an exception,

UnboundLocalError: __lt__() in vis_graph.py

but as you can see in the graph, no polygon is overlap with other.

The debug info is the following: (this is the __lt__ method in EdgeKey)

self.edge: {Edge}((-3.51, 1.60), (-2.22, 1.60))
p1 = {Point} (-3.51, 1.60)
    polygon_id = {int} 0
    x = {float} -3.5101999999999998
    y = {float} 1.5981
p2 = {Point} (-2.22, 1.60)
     polygon_id = {int} 0
    x = {float} -2.2232
    y = {float} 1.5981
 

other.edge: {Edge} ((-3.51, 1.95), (-3.51, 1.60))
    p1 = {Point} (-3.51, 1.95)
    polygon_id = {int} 0
    x = {float} -3.5101999999999998
    y = {float} 1.9467000000000003
p2 = {Point} (-3.51, 1.60)
    polygon_id = {int} 0
    x = {float} -3.5101999999999998
    y = {float} 1.5981000000000005

as you can see, the keypoint is

{x = {float} -3.5101999999999998, y = {float} 1.5981} 

and

{x = {float} -3.5101999999999998, y = {float} 1.5981000000000005}.

I think this is caused by the float number precisition.

this is my example data, and you can see the graph in the attachment png file.

polygon_list = [
    [[-5.3231999999999999, 5.9744999999999999], [-5.3231999999999999, 5.0061], [-3.5101999999999998, 5.0061],
    [-3.5101999999999998, 4.5061], [-3.5101999999999998, 3.8466999999999998],
    [-3.0069999999999997, 3.8466999999999998], [-3.0069999999999997, 3.3466999999999998],
    [-3.0069999999999997, 2.4467000000000003], [-3.0069999999999997, 1.9467000000000003],
    [-3.5101999999999998, 1.9467000000000003], [-3.5101999999999998, 1.5981000000000005],
    [-3.5101999999999998, 1.5981000000000001], [-2.2231999999999998, 1.5981000000000001],
    [-2.2231999999999998, 1.0981000000000001], [-2.2231999999999998, -0.90189999999999992],
    [-2.2231999999999998, -1.4018999999999999], [-2.7231999999999998, -1.4018999999999999],
    [-5.8231999999999999, 1.0981000000000001], [-6.4231999999999996, 5.9744999999999999],
    [-6.4231999999999996, 6.4744999999999999], [-5.3231999999999999, 6.4744999999999999]],
    [[3.5348000000000002, 8.5561000000000007], [3.5348000000000002, 8.0561000000000007],
    [3.0348000000000002, 8.0561000000000007], [-0.66520000000000001, 8.0561000000000007],
    [-1.1652, 8.0561000000000007], [-1.1652, 8.5561000000000007],
    [-1.1652, 9.7561], [-1.1652, 10.2561], [-0.66520000000000001, 10.2561],
    [[3.5348000000000002, 7.0980999999999996], [-0.66520000000000001, -1.4018999999999999],
    [-1.1652, -1.4018999999999999], [-1.1652, -0.90189999999999992], [-1.1652, 4.7980999999999998],
    [-1.1652, 5.2980999999999998], [0.23480000000000001, 5.2980999999999998],
    [0.23480000000000001, 6.0980999999999996], [0.23480000000000001, 6.5980999999999996],
    [0.73480000000000001, 6.5980999999999996], [0.73480000000000001, 7.0980999999999996],
    [0.73480000000000001, 7.5980999999999996], [3.5348000000000002, 7.5980999999999996]]]   

out_polygon = [[  3.2848,   8.3061],
    [  3.2848,   7.3481],
    [ -0.9152,  -1.1519],
    [ -2.4732,  -1.1519],
    [ -5.5732,   1.3481],
    [ -6.1732,   6.2245],
    [ -6.1732,  10.0061],
    [ -0.9152,  10.0061]]
   
start_point = [-1.6942, 1.3481]
end_point = [-3.2442,  5.0561]