Ryan Fruehwirth

2 or More Units: Creating Forms with Revit Conceptual Masses

For Stage 1, I imported the Parametric Tower - Twisting Rectangular Mass family into a new Revit project configured for the Dubai project location and added mass floors to enable computation of Gross Floor Area, Gross Volume, and Gross Surface Area. The mass exposes several instance parameters that can be flexed: twist, building top width (200’), building top depth (100’), building base width (400’), building base depth (260’), and building height (755’). I held the dimensional parameters constant while varying the twist angle to isolate its effect on the building’s performance metrics.

The Dynamo graph automates the testing process: a select model element node identifies the Revit mass, an Integer Slider feeds a twist angle into an set parameter by name node that pushes the value into Revit, and three get parameter values by name nodes pull the resulting GFA, Volume, and Surface Area back out. As the slider is dragged, the mass flexes live in the Revit viewport while the Watch nodes update with the new metrics. I ran the graph across a range of twist values and exported the results to a summary table for analysis as shown below.

The results show that increasing the twist angle monotonically decreases all three metrics. While twist reduces usable floor area and reduces facade envelope, the GFA reduction is proportionally larger, meaning higher twist results in worse efficiency.

The second tower is a much more sophisticated mass family with three independent levels (Base, Mid, Top) each having their own rotation and dimensions. This three-profile lofted system allows the tower to twist progressively up its height (base rotation 0 degrees, mid rotation 35 degrees, top rotation 65 degrees) while also tapering: the form transitions from a 500’ x 260’ base, through a 480’ x 240’ mid-level at 380’ elevation, up to a 500’ x 250’ top at 755’. The result is a much more aesthetically differentiating building form than the simple base-to-top twist of Part 1. What’s super interesting is that altering the top rotation angle from 10 to 60 degrees actually has the opposite effective on the three measured metrics as Part 1. Other than the surface area bucking the trend from 10 to 20 degrees, all three metrics are increasing monotonically as the top rotation angle increases.

I found this result pretty odd so I dug into why this could be occurring. I believe the main difference is that the building in this configuration is barely tapering up to the top (certainly much less relative to the building from Part 1). When you twist a non-tapered building, the lofted surface between an un-rotated bottom and a rotated top creates floor plates that are actually larger at intermediate elevations than the base or top profiles, because the swept rectangle bulges outward as it rotates.

In practice, very few real supertall towers behave like Part 2. Most twisted skyscrapers (such as the Shanghai Tower) follow the Part 1 pattern of significant tapering combined with twist, where GFA decreases as twist increases. From a structural engineering perspective, the Part 2 geometry where the top footprint is nearly equal in size to the base is concerning, especially in combination with a twist. A non-tapered twisting tower carries enormous lateral and torsional loads at the top, where wind pressures are highest and where the rotational moment arm is greatest. In contrast, a tapered twisting tower naturally reduces both wind exposure and structural mass at the upper levels.

Point to Ponder: What’s the advantage of exporting the values to Excel?

Exporting results to Excel reduces human error and saves significant time when iterating through parametric designs. Manually copying values from Grasshopper or Dynamo into a spreadsheet works for a handful of test cases, but across dozens or hundreds of design variants it becomes tedious and increasingly error-prone. One of the core tenets of parametric design is the ability to explore and modify designs efficiently. Exporting further automates this process.

In addition, export to Excel allows you to sort, filter, compute new metrics, build pivot tables, generate charts, etc. All of these operations would be much trickier to do in Dynamo or Grasshopper.

3 or More Units: Creating Forms with Dynamo or Grasshopper Geometry (Combined with 4 Units)

4 Units: Summarizing the Testing Results (Combined with 3 Units)

My goal throughout this course has been to sharpen my skills in Grasshopper so I decided to take a stab at creating a building form from scratch in Grasshopper. This Grasshopper script generates a parametric twisted tower with controllable plan geometry and records key performance metrics for use in design optimization. The script is organized into eight labeled groups that flow sequentially from initial geometry generation through performance analysis and data export.

Workflow:

1. Set Up Initial Geometry
• Three polygons are first generated to define the tower’s base, mid-height, and top profiles. Each polygon is controlled by independent radius sliders and a shared number of sides slider that determines the polygon resolution. This three-polygon system allows the tower to bulge or pinch at the middle as opposed to tapering linearly, which ultimately gives more design flexibility.
2. Break Apart Polygons and Divide Vertices into Two Separate Lists
• Each of the three polygons is exploded into its constituent edges. The midpoints of each edge are extracted, and a series of operations divides the polygon vertices into two interweaved lists, alternating vertices and midpoints. This sets up the next step, where every other vertex can be flexed inward or outward.
3. Distort Every Other Vertex in Each Polygon
• Using the linear interpolation expression A + x*(B-A), alternating vertices are pushed inward or outward according to per-level distortion sliders. The current values create an interesting pinwheel-like star plan with positive and negative distortion magnitudes. The distorted vertices are then reconnected into closed polylines.
4. Set Tower Height
• The mid and top polygons are vertically translated based on the tower height slider. The maximum of this slider is 755 feet per the assignment requirements. The mid-polygon is placed at half the tower height while the top polygon is placed at the full height.
5. Rotate Tower
• The mid and top polygons are rotated about their respective centroids using another slider. The mid-polygon receives half the twist angle and the top polygon receives the full angle, producing the smooth corkscrew transition between levels.
6. Create Tower Boundaries and Loft
• The three distorted, vertically-stacked, rotated polygons are converted into planar surface boundaries, then lofted together using entwine and flip to ensure proper data tree structure. The result is a closed polysurface representing the tower envelope.
7. Split Up Tower into Floors per Story Height and Determine GFA
• The lofted tower is sliced horizontally using the contour component at intervals defined by the story height slider (set at 12 feet to match the 2 unit stage). Each contour generates a floor boundary, which is converted to a closed surface and its area calculated. Summing all floor areas yields the GFA.
8. Merge Tower and Output Volume and Surface Area
• The closed tower polysurface feeds into volume and area components, yielding the Gross Volume and Gross Surface Area of the building envelope.

Since I was having technical difficulties with Anemone on the Mac, I used Colibri to sweep through two parameters. I decided to choose the tower twist angle (0, 10, 20, 30, 40, 50, 60, 70, 80, and 90 degrees) and the number of sides (4, 6, 8, 10, 12) as the two input values that would be varied. This produces 35 unique design combinations. For each iteration, Colibri records GFA, Gross Volume, and Gross Surface Area into a CSV file. The Aggregator also captures a viewport screenshot of each design for visual reference. The full dataset allows for analysis of trade-offs between geometric efficiency (GFA/SA ratio), construction cost, and aesthetic beauty. Please see below for the output from the Colibri function:

Of these values, only the options with a GFA between 2.5 and 3 million SF could be considered per the assignment requirements. The table below is filtered out accordingly, with the highlighted options representing the greatest GFA to surface area efficiency (which would theoretically reduce construction costs).

Point to Ponder: Which of these inputs tested has the biggest effect on creating a desirable building form?

The number of sides has the biggest effect on the building’s overall form and performance. Across the parameter sweep, changing the number of sides shifts the GFA dramatically (from approx. 2 million SF for 4 sides up to 3 million SF for 12 sides —> 50% increase). It also fundamentally changes the building’s geometric figure: 4-sided towers are rectangular prisms, 6 and 8-sided towers are faceted polygonal massings, and 10-12 sided towers start to look more like cylinders (if the vertex distortions aren’t set too high). By comparison, the twist angle has a much smaller effect on the quantitative metrics. Within any fixed number of sides group, varying twist from 0 to 90 degrees changes the GFA/SA ratio by only 1-2%. However, twist has a disproportionately large effect on the visual character of the building. Even a 30% twist transforms an otherwise boring polygonal tower into a dynamic, more sculptural form.

Point to Ponder: Which of these pairs of input values gives the most desirable result? Which building form would you recommend to the developer and why?

Between all of the options with the highest GFA to SA ratio, I would advocate for the use of the 8 sided structure with a 30 degree twist angle as it provides the most dramatic silhouette, helping it to stand out in the crowded Dubai skyline. A pure-economics developer might push for an un-twisted 8-sided tower (also at 3.55 ratio) for slightly cheaper construction. However, in a market like Dubai where iconic architecture commands significant rental premiums, the 1-2% efficiency cost of a moderate twist is easily offset by the brand value and rentability of a more distinctive form. The 30 degree twist is the optimal balance: enough to create sculptural identity, not so much that it harms the bottom line. Below is what the 8-sided, 30 degree twist building looks like:

As an aside, these structures have the capability of looking far more interesting if the correct parameters are selected (however, they may not meet the client’s demands/be efficient enough). Below is a 12-sided, 90 degree rotation building:

Bonus Creativity Points:

Adding the midpoint distortion system allows the tower to flex into a distinctive star-shaped plan. Rather than using regular polygons (as the example node files demonstrate), I built logic that explodes each polygon into its constituent edges, extracts midpoints, and then displaces alternating vertices inward and outward using a linear interpolation expression. This helps the tower achieve an origami form rather than a conventional polygonal massing.

The entire Grasshopper script alone was developed by scratch without the use of templates or pre-built example files. Every component, data structure, and parameter relationship was designed manually based on the geometric logic of the tower.

To support the analysis with a more rigorous visualization, I plotted GFA against Surface Area for all 35 tested designs. The chart below clearly shows five distinct clusters, each corresponding to a different number of sides. The dramatic vertical separation between clusters, combined with the negligible horizontal spread within each cluster (representing the full 0 to 90 degree twist range), visually confirms the earlier assertion that the number of sides is the dominant driver of the building’s geometric response, while tower twist plays only a minor secondary role.