Let me ask about spline functions. I tried spline() function of Octave then I found it was almost I wanted , to draw a smooth curve through given 2D points. But for some points data , it plots unexpected lines. I think it does because each my data is allowed to have multiple values for an x-value.For example (x=1,y=1) , (x=1,y=10). To solve this problem , I plan to use the concept of parametric forms of functions. Namely I plan to apply the spline() function on respectively (t,x) values data and (t,y) values data. I expect it will work well for almost all cases. Question 1 , possibly will it? If yes,I have the 2nd question. I want any resultant curve has the minimum number of inevitable changes of the direction of curve.For example , the number for a circle is zero. Because if you travel along the line in one direction, you always turns right or always turns left. Question 2 , will my plan possibly satisfy the condition. If no , I have the 3rd question , is there any algorithm to satisfy the condition?