If we are to do this, what if we just linearly interpolate between all the points. Say, the points are p1= (x1,y1), p2 =(x2,y2),..., the line segment from point [LaTeX ERROR: Convert failed] to [LaTeX ERROR: Convert failed] is just [LaTeX ERROR: Convert failed] for [LaTeX ERROR: Convert failed] , from the slope-intercept form of the line passing through [LaTeX ERROR: Convert failed] and [LaTeX ERROR: Convert failed] . You can see that this will be a continuous function if [LaTeX ERROR: Convert failed] .