Design Idea - Background

In this module, I began by hand-sketching the design for my shelter. I opted for a shape that could be adjusted parametrically to suit different requirements. The sketch below illustrates my specific objectives, as in, being able to:

• make the shape longer (adjusting the length l along X direction, sketched in magenta)
• make the shape wider (adjusting the depth d along Y direction, sketched in blue)
• make the shape taller (adjusting the height h along Z direction, sketched in orange)
• change the curvature and/or length of the main controlling curves (by adjusting length l, depth d, height h)

In the initial design, I established a fixed offset w of at least 1 foot (sketched in light orange), which serves as the minimum height for the vertical beams supporting the shelter's roof. Additionally, I introduced an extra parameter t to elevate the height of points A” and C” (sketched in green), thereby introducing a new lateral curvature in the direction of the depth d. The primary controlling curves for this design are:

• The primary Nurbs defined along the length direction (Nurbs(A’B’C’), Nurbs(A’’B’’C’’) Nurbs(A’’’B’’’C’’’), black in the picture below.
• The secondary Nurbs defined along the depth direction (LateralNurbs(A’,A’’,A’’’), LateralNurbs(C’,C’’,C’’’), violet in the picture below.
• The secondary Nurbs(B’B’’B’’’) defined by the adjustable parameter height h. Note that the height of B” was set to a fixed height of 2h/3.

These curves were defined by 9 control points A’, B’, C’, A’’, B’’, C’’, A’’’, B’’’, C’’’, marked with red dots in the image below.

In the final stage of my planning, I intended to cover the roof with solid panels featuring glass openings. To determine the size of these panels, I have utilized two adjustable parameters, namely, "geometry divisions" along the depth and length directions. These parameters will divide the NURBS into n equal parts along each direction, impacting:

• The quantity of structural supports, including vertical columns and ribs (tubes).
• The quantity and dimensions of panels on the shelter surface.

Note that changing the number of geometry divisions along the u direction will also affect the number of vertical columns. This approach ensures both structural integrity and aesthetic appeal in the shelter design.

Modelling Approach - 2 Units

I have used the following logic for modelling my design in Dynamo:

• Step 1: Define the adjustable parameters (length l, depth d, height h, lateral curves’ height t, geometry divisions along x, geometry divisions along y)
• Step 2: Define fixed parameters, like the minimum height w of the columns supporting the roof (which I set to 1’), and the height of the middle point of the roof B’’ (which I set at 2h/3).
• Step 3: Use the information at steps 1 and 2 to define the 9 control points A’, B’, C’, A’’, B’’, C’’, A’’’, B’’’, C’’’.
• Step 4: Use the 9 control points to define the three primary curves Nurbs(A’B’C’), Nurbs(A’’B’’C’’), and Nurbs(A’’’B’’’C’’’).
• Step 5: Use these three primary curves to create a Surface by loft.
• Step 6: Divide the surface into x geometry divisions along the u surface direction (corresponding to the x axis) and y geometry divisions along v surface direction (corresponding to the y axis). This will generate a series of equally distributed points on the surface created at step 5.
• Step 7: Group the points on the surface by 4 and place adaptive panels.
• Step 8: Create the projections of points along (LateralNurbs(A’,A’’,A’’’) and LateralNurbs(C’,C’’,C’’’) on the XY plane. Then, use the projected points and the points on the lateral nurbs to add the vertical beams that will sustain the roof. The radii of these beams were adjusted so that the base radius was bigger than the top radius. Such adjustment was thought both in terms of structural integrity and easthetical reasons.
• Step 9: Use the points created at step 6 to define the lateral and trasversal nurbs dividing the surface. The control points of these nurbs (start, middle, end points) were manually selected to add 3pt tubes along both the x and y direction. The radia of these curves were adjusted so that the the middle radius of each tube was smaller than the radius at the extremities.
• Step 10: Standardize the tube radii along LateralNurbs(A’,A’’,A’’’) and LateralNurbs(C’,C’’,C’’’) to ensure consistent structural integrity throughout the design.

The resulting design is depicted in the pictures below:

Modelling Approach - 3 Units

For this task, I have changed the the curvature of the middle curve by replacing the Nurbs(A’’B’’C’’) with a sinusoidal curve. I achieved this by updating the Z values of the points belonging to the original curve with the computed values resulting from the sinusoidal function. Initially, the implementation of the sine curve resulted in a curvature that lacked symmetry around its midpoint. To rectify this asymmetry, I added the “absolute value” function to the Sin function, ensuring that both positive and negative oscillations of the sine wave contributed equally to the curvature. This adjustment not only restored balance to the curve but also improved its overall aesthetic and functional characteristics.

The formula I have used is:

newZ = originalZ + Amplitude × Math.Abs(sin⁡((curvePosition × 360 × numberOfWaves) − phaseShift)) 

• newZ: Final modified position (Z coordinates of points) of the curve.
• originalZ: Original position (Z coordinates of points) of the unmodified curve.
• Amplitude: Magnitude of the sinusoidal variation.
• Math.Abs(): Ensures positive output, hence achieving symmetry.
• sin(): Generates the sinusoidal variation.
• curvePosition: Position along the curve (0 to 1).
• 360: Converts position to degrees for a full cycle.
• numberOfWaves: Determines the frequency.
• phaseShift: Adjusts phase for symmetry around the middle point. I calculated this as phaseShift = 0.5 * period; with period = 1.0 / numberOfWaves

The resulting design is depicted in the pictures below:

The adjustable parameters in this formula are the number of waves and the amplitude.

Testing the limits of the parameters in the formula can provide valuable insights into the behavior of the resulting curve:

• Minimizing Parameters:

When minimizing the number of waves and the amplitude, the curve will undergo fewer oscillations with smaller magnitudes of variation. Minimizing number of waves and the amplitude to 0 returns a null newZ value, and hence the code will not run. By using minimum non-zero values like 1 for both amplitude and number of waves, the shape will not change too much from the original shape defined by the nurbs curve.

• Maximizing Parameters:

Maximizing the number of waves and the amplitude will result in a highly oscillatory and exaggerated curve. The form can be reshaped extensively, with pronounced bends and undulations, like in the picture below, where amplitude and number of waves were set at 100. This design specifically, looks like a futuristic skyscraper. 😎👽


• Negative Parameters:

Negative amplitudes can invert the direction of the curve, while negative frequencies can reverse the oscillations. An example with Amplitude and Number of Waves set at -10.

Modelling Approach - 4 Units

For this task, I have decided to apply a scale factor to both length and depth measurements. Specifically, I have categorized the scales as follows:

• Small Scale: With a length and depth of 30 feet, this scale is suitable for projects like a cozy gazebo in a backyard or a compact outdoor seating area for a café.
• Medium Scale: Spanning 150 feet in both length and depth, this scale accommodates larger structures such as a mid-sized concert venue, capable of hosting hundreds of attendees for live performances or events.
• Large Scale: At a substantial length and depth of 420 feet, this scale is ideal for expansive projects like an exhibition area or an arena, capable of accommodating thousands of visitors for trade shows, sports events, or large-scale conventions.

Note: as the scale increases, it's important to incorporate additional vertical supports to ensure structural integrity. In both the medium and large-scale designs depicted below, relying solely on vertical beams positioned at the edges would compromise the structural integrity of the overall structure.