We start our journey with the curve C parameterized by
with the parameter t ranging in value from a to b (ie. 
.)
The curve is now said to be oriented since we have a definite direction of
travel along C.
Next, for those destructive gremlins out there, break the curve up into N
segements. The image below shows the curve broken into N = 5 pieces.
At each of the N + 1 points we need to compute two things: the tangent
vector 
and the vector field, 
.