Module 5 Refresher
For Module 5, I designed a twisting building structure that was based on four parameters: height, twist factor, number of sides, and radius. After setting base values in each category, I created a list of all 560 possible permutations. In Grasshopper, I created a loop that tested each of the 560 buildings and returned the resulting volume, surface area, and floor area.
New Evaluation Metrics
The first metric I calculated was the total cost to build each building based on floor square footage and height. I used the previously calculated sqaure footage of each floor and multiplied that by a linear cost scaling factor that went from $700/sqft at the base to $1,500/sqft at 750 ft.
The second metric I calculated was a bit more complicated. First, I created a pool/lake feature next to the building (the ellipse in the picture below). The rooms that face the pool/lake would have a premium view, allowing them to sold for a higher price. So, created a relative factor that would allow me evaluate how much of the building has pool/lake views compared to the other options.
First, I panelized the building to create “windows”. Then, I created normal vectors from each window with a z coordinate of 0 (because you can look down at the pool no matter what height the window is, so z direction didn’t matter). Finally, I created a vector from the center of each panel to the center of the pool/lake (again, with a z coordinate of 0).
To find the direction factor, I took the dot product between those two vectors. Any dot product that was less than 0 was converted to 0 (since it didn’t matter how opposite you were to the lake, only that you couldn’t see it) and then summed them all up to get the final direction factor.
Manipulating Data
After running all 560 options, I exported the data to Google Sheets to further manipulate. https://docs.google.com/spreadsheets/d/15df08hGsZ97jowvhZBGRmXXBh9C7ez5oKbxUiVTo6ZM/edit?usp=sharing
I started by filtering out any buildings that did not satisfy the 1,200,00-1,500,000 sqft requirement. That left me with 106 different building options.
I created two new columns: comparative direction value and comparative cost. Each of took the desired variable (direction or cost) and divided it by the minimum variable in the list. This helped to compare how the different buildings differed from each other by relative scale. The final score was calculated by multiplying the two comparative values.
Final Score Explained
My logic behind the final score was based on a cost/benefit principle. The more directional views a building has, the more we would be able to charge for those units, which could justify a higher price. For example, if building B costs 2x more to build than building A, bit building B has a direction value that is 4x building A, it may be worth the extra cost to build building B because in the long run it will have more expensive units.
However score was not enough because I wasn’t sure exactly what the developers would prioritize. So, to aid in a multi objective optimization also created a graph between cost and direction factor.
The four points circled each represented a possible desired outcome. The point on the far left is the cheapest option, though it doesn’t have a huge direction value (final score: 1.12). The point second from the left is still very cheap, but has a higher direction value(final score: 1.37). The point third from the left almost looks like an outlier because it has a mid-tier cost but high direction value(final score: 1.70). Finally the point on the right has the highest direction value, but is the most expensive which would be ideal if cost is not an issue(final score: 1.68).
An important note to make is that each point I highlighted corresponded with 5 different buildings, each with the same height, radius, and sides, but a different twist factor. This made me think that though the twist factors (.02, .04, .06, .08, 1) have an effect on the aesthetics of the building, they do not have an effect on the cost or the direction value, so any twist may be chosen. However, after some testing, I realized that the twist should have an effect on not only those factors, but the volume and floor area as well (which it does not). When testing specific twist values, all those variables change, but they are not recorded, meaning there is an error somewhere in the loop recording. After much searching I couldn’t find the error, so for the ideal solution, I tested each twist value and eliminated any that did not fall into the surface area constraint. That left two values: .06 and .08.
For the final choice, I chose the point that was third from the left, since it had the best final score and seemed to be the best direction view for the price. It’s initial parameters were:
Height: 450 ft
Base radius: 150ft
Sides: 8
Twist: either .06 (left) or .08 (right). I chose .06 because I prefered the aesthetic.
Final Images w/ panel frames determined by direction factor:
