My model geometry is a station entrance - for example for a major train station, which is controlled by two parabolic equations; one denoting the top/peak of the entrance, and the other controlling the base/perimeter of the space. Both equations are a form of f(x) = 0.05x +b. I have walked past train stations with grand entrances, similar to the one attached below. For this assignment, I wanted to play around with mathematically informed geometries, and I found the double parabolic shape to be most interesting.

**Inputs**

The inputs for my canopy are number of points, height, and depth.

**Creating Parabolic Lines**

Creating the lines themselves was very challenging.

For Curve #1, I modeled a “flat” x-y parabolic relationship. Then, I computed the z-values as a function of the “height” of the canopy. Z increased linearly. I created an ascending list of z-values which was half the size of the number of points input into the system. I then reversed the list, and combined both lists, so that each pair of x-values would have the same z-value.

For curve #2, I modeled the curve as flat, so the z-values were all zero.

I created curves which represent each line, and then I joined them into a surface and created panels as well as thin rods (intentionally) along the edges of the panels. I did this by arranging points on each curve end-to-end, and then placing tubes along the lines:

I also have tubes along the panels in the vertical direction. I did this by creating a grid, and then individually connecting each point on vertical lines along the grid to one another. I placed rods along each of these lines.

I repeated the process shown above 10 times.