Continuity Types

Can someone help me out with understanding the continuity types?

When I need to find discontinuities or tangent changes etc. I generally just cycle through the list pictured until I get what I wanted, but I would like to gain an understanding of what each one means and how they differ from each other. 

This is the code that I am using to check though curves:


Curve c = (Curve) x.Duplicate();
double st = c.Domain.Min;
while(st >= 0){
double t = 0;
c.GetNextDiscontinuity(Continuity.C2_continuous, st, c.Domain.Max, out t);
if (t < 0){break;}
st = t;
Print(t.ToString());
}


or if you prefer VB:


Dim c As curve = x.duplicate
Dim t As New Double
Dim st As Double = c.Domain.Min
While c.GetNextDiscontinuity(Continuity.C2_continuous, st, c.Domain.Max, t)
st = t
print(t)
End While


It doesn't get the start and the end points (which I like) but I am curious about that because according to my logic the start and end points would be considered a discontinuity.