Assuming I have 10 points (M1 , M2 .... Mn=10) that form a curve in three-dimensional space. Thus, Mi (XMi , YMi , ZMi).
To determine the distance from M1 to Mn, I have used the summation of the euclidean distances from i=1 to i=n using the normal Euclidean distance equation:
$$d= \sum_{i=1}^n \sqrt{(X_{i+1}-X_i)^2+(Y_{i+1}-Y_i)^2+(Z_{i+1}-Z_i)^2}$$
I would like to know if this function is a smooth function along these 10 points. Can someone present me with a reference on how to support the claim if it's either yes/no?