I write a mesher for special geometric forms to train Computer Aided Engineering with them.
I need to display a rectangular with rounded corners in 3d. It is a Stadium Shape/Obolong/Capsule Shape, like it named in this post.
The 2D form is no problem. 
But now I want to bend it around the y - axis. The extrema is a closed pipe, but what I want is more like a parabolic cylinder, like a taco shell or a Scutum.
The outer boundary is clear, it is like: $$ x_i = x_a + sin(\alpha)*r_c \\ y_i = y_a + i*l_c \\ z_i = z_a + cos(\alpha)*r_c \\ $$ with
$$ -\frac{\Pi}{2} < \alpha < \frac{\Pi}{2} \\ l_c = length\ of\ sheet\\ r_c = width\ of\ sheet $$
But now there are the corners. I don't know how to gave it a parametric shape and what where the name of these lines, is it a spline, a bspline or a bezierspline or something other?
In CAD-Tools you could use a fillet for rounding the corners or bend the 2d form afterwards, like in this example:
But I don't know how to calculate the rounded corners.
Please help me.
Thank you