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.
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fe6a474f6-5f7b-4fcb-b775-0103176f44c4%2FUntitled.png?id=89d0a716-c098-4eeb-bc9c-c4c69db0459d&table=block)
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fd13bf3e0-de53-4180-9502-9c22f9ce0529%2FUntitled.png?id=9fc4050b-a576-4c68-9724-3bc3a804b4f4&table=block)
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F4a3710e5-fbab-4431-a872-3c3a933cdfdd%2FUntitled.png?id=f6ce5f02-7ae2-4ab8-aed8-2cd3b78528c0&table=block)
Inputs
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F62a72b59-3146-461e-82ef-de785b9e3281%2FUntitled.png?id=3cfb0d58-113a-44e0-9279-890a0e9d3aad&table=block)
The inputs for my canopy are number of points, height, and depth.
Creating Parabolic Lines
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F99300ee7-cc5a-45cb-a2e0-9341e183448a%2FUntitled.png?id=d906028e-004f-4fa1-b315-7b4da870371c&table=block)
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.
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F2aa35151-79ef-4186-9dc9-640c772f3c63%2FUntitled.png?id=56e6f95e-592a-41a8-9794-8ff9ceed326d&table=block)
For curve #2, I modeled the curve as flat, so the z-values were all zero.
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F5798e0fd-9965-4310-a0b1-edfaa15c5873%2FUntitled.png?id=26101bbe-27bf-40c0-aa00-8902d947c98b&table=block)
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:
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F67db4f09-ba7c-4d57-8cee-8de93d71a7d7%2FUntitled.png?id=ca3fbb83-cc3f-48f5-ba37-0a3fd45b156b&table=block)
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F93a0ecd5-0eb4-4bed-9c87-6fcc70b8bbc3%2FUntitled.png?id=0c549bd7-7e1b-4e16-be5e-57454efd6611&table=block)
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.
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F084ccb05-affe-4389-b4bf-352f8a6bc68e%2FUntitled.png?id=fdde8f90-8c08-4d19-9435-45c440934cd3&table=block)
![image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F8549dfdc-927c-4370-a219-3bee97915173%2FUntitled.png?id=76433c4b-f306-4778-b87c-bc340634781d&table=block)
I repeated the process shown above 10 times.