Using Formulas to Generate a Base for Our Seat surface

Screenshot: Seat with Base

If cosine lends itself for deriving a desired seat section could a similar formula lend itself to creating a seat base?  We asked ourselves this question hoping to find an equation that could possible play the role of both seated surface and as a support.  After reverting back to high school algebra II/trig we were reminded that formulas with Asymptotes were similar to the section of our seat base.

Several attempts to finding a formula that would be appropriate for representing the points that defined our seat base brought us to polynomial functions.

A quartic function (x^4) has the right number of degrees necessary for providing the section we needed.  We once again used this formula with number sliders attached to the variables associated with this function to the derive the base height and width. 

Screenshot: Entire Script

Screenshot: Seat base Script

Now that we have a seat base using the x^4 function and a seat surface using a CosX function, it is important that these two surface will be able to intersect in a manner that will allow them to share curvature.   Our next step is to go into the Seat portion of our script and replace it with the X^4 function so that the two separate surface will have the same curvature at the place where they overlap.

Once we have successful achieved this we should be able to output this chair at 1/2 scale and then finally at 1:1.