Stage 1

Evaluator Node 1 - Perimeter to Floor Area Ratio

The first evaluator node that I created computes the perimeter to floor area ratio. Inside the node, I computed the perimeter and floor area at each mass level, and then computed the perimeter to floor area ratio at each level. I then summed the ratios over all levels to get the total perimeter to floor area (P-A) ratio. A higher value indicates that there is more exterior surface of the building compared to floor area.

A greater P-A ratio could be interpreted as an advantage or disadvantage. An advantage of a high P-A ratio could be that there is more access to windows and this might improve the happiness of people living/working inside the building. A disadvantage is that the building may be less energy efficient since the exterior of the building is where heat transfer occurs.

Evaluator Node 2 - Curvature Complexity

The second evaluator node that I created computes the Gaussian curvature of the building surfaces. Inside the node, I extracted all of the surfaces from the building and then computed the Gaussian curvature for a specified number of points on each surface. Then I summed the absolute values of the Gaussian curvatures over each surface and over the all surfaces and called this “curvature complexity.”

A greater curvature complexity value means that the structure’s surfaces are more curved. This could be a disadvantage because the building would then be more difficult and more expensive to construct.

Summary Table

Points to Ponder

The new evaluation metrics that I have designed capture some of the meaningful differences, such between the building form alternatives. They capture the perimeter to floor area ratio and the curvature complexity of the building form. Other important metrics to consider might be the construction cost and the solar insolation potential.

Stage 2

My rationale for this single-objective optimization scheme is that the lower the combined score is, the better. Because higher values surface area, perimeter to floor area ratio, and curvature complexity are less advantageous, and higher values of floor area are more advantageous, I added together the surface area, P-A ratio, and curvature complexity weighted scores, and subtracted the floor area weighted score.

The best design alternative is when the mid rotation is 25 degrees. The second and third best design alternatives are when the mid rotation is 20 and 30 degrees (the next closest rotation angles to that of the best alternative).

The 25 degree mid rotation design alternative is the best because it is a well rounded design. It’s perimeter to floor area ratio, curvature complexity, and surface are lower than some design alternatives, while still having a gross floor area that is higher than other design alternatives.

Points to Ponder

The best alternative wasn’t really propelled to the top of the list, since it’s evaluation score is still close in value to the second and third design alternatives, but since the perimeter to floor area ratio category had the highest weighting, having a moderate to high ratio pushed this alternative towards the top.

There are some nuances that get lost in a single evaluation, such as preferences for how the floor area should be distributed across the height of the structure, or maybe how the volume should be distributed across the site. Another nuance that is more specific to the curvature complexity could be that this parameter computes a total or “average” value across the whole building form, but some curves could be more complex in specific areas the building form while other curves are nearly flat and these curves could average out and produce a similar total value when compared to another building form that has a moderately curved surface across the majority of the building form.

Remaining points to ponder are answered in the above Stage 2 paragraphs.