Hi! Players!

To form a preliminary Smooth S-Curve with available Cost Vs Time period of the project we can use some smooth curvature formulas (thus how we can make the curve smooth)
According to that,
One third of the time and one forth of the cost which gives us one parabolic curve
Assume Axis X - As Duration and Y- as Cost
Say the first parabolic curve Y = 0.0225 X2 è (1) (which 33.33%)
Secondly two third of the Time and three forth of the cost
Say the curve as Y = 1.5X - 25 è (2) (which is between 33.33 % to 66.66%)
Remaining portion say the curve as
Y= -125+4.5 X - 0.0225 x X2 è (3) (which is remaining upto 100%)
Likewise this method of drawing S-Curve likely we can get some Smooth S - Curve, But especially the equation (2) that is Between the one third and two third of the duration (which is between 33.33 % to 66.66%) there is no cost increment which remains as same for the entire period.
Take an example if the Period of the project as 12 months
While applying above
a) Equation (1) for the first 4 months, the Y value will be 1.56%, 4.69%, 7.81% and10.94%
b) From equation (2) that is from month 4 to 8,the Y value will be 12.5%, 12.5%, 12.5% and12.5%
c) From equation (3) that is from month 8 to 12,the Y value will be 10.94%, 7.81%, 4.69% and1.56%
Result b) shows 12.5% constant value for those 4 months -
My ultimate question is if there are any other possibilities to make the curve smoother then the above said way.