Just found that the creation of a Sankey chart can be made a bit easier, mainly in the data prep stage. Let me use his same example and streamline the procedure a little bit.

I will describe 2 options here. One is for all recent Tableau versions. The other is for 10.2 or above, which doesn't need any SQL script.

For recent Tableau versions

1.Load the Superstore data set into Tableau via Legacy Connection.
2.Create this Custom SQL:
This will create the data set necessary. Here [Point] is equivalent to [ToPad] in Chris' example. Those rows are for respectively point 1 and point 49 in the curve. Then we can proceed to create [Padded] bins and trigger data densification upon it.

For Tableau 10.2+

1.Load the Superstore data set into Tableau
2.In the data source editor, add another 1-column x 2-row table  as follows (in Excel)
3.Join them as follows
This takes advantage of the new "Join Calculation" feature in 10.2 to create join conditions. The 1=1 condition results in a cross join between the superstore data and the above 2-row table. We get thus the data set we need for creating Sankey or any Sigmoid based charts.
This method doesn't need SQL script.

4. BTW, Sigmoid expression can be written a bit more concise:
Sigmoid(t) = 1/(1+EXP(-t))

Voila, I created a little Sankey chart similar to the example of Chris.
Click the above image to access the interactive version.