Modeling the Conceptual Mass

The parametric mass model for the Hearst Tower is comprised of 10 conceptual masses stacked and aligned to one another. Of the 10 masses, there are three different shapes for the conceptual mass shown in Figure 5-Figure 8. Each shape has its own unique feature, for example the top level shape has corner void extrusions that slope inward from the top face.

Figure 5: Conceptual Mass	Figure 6: Conceptual Mass
Figure 7: Top Level Shape	Figure 8: Bottom Level Shape

Top Level Shape:

To create the top level shape, I initially started with a rectangular block that is defined by 6 reference planes, and two reference levels that have two parametrically controlled dimensions, Width W1 and Width W2, which correspond to the larger width and the smaller width of the Hearst Tower respectively and the Height Hi of the level. The two reference planes that cross the center point of the grid are pinned to help enforce the alignment of all the masses (Figure 9).

Figure 9: Base Reference Planes

Once the initial mass is created, the void forms for the corner cuts need to be made in order to replicate the corner geometry that the Hearst Tower has due to the Diagrid system. To do this, I drew a trapezoid made up of reference lines on each face of the rectangular block and to connect each the corners of the shorter length of the trapezoid, I used a single 3D reference line (Figure 10). The dimensions of the trapezoid were controlled by:

1.       Height Hi: Controls the height of each of the shape and will be linked to the height determination from the user defined parameters and the host mass.

2.       Bot W1/Bot W2: Controls the bottom or shorter base length of the trapezoid. This parameter is a function of the main widths W1 and W2 of the structure.

3.       The angles of the trapezoid were kept symmetric by the aligned base lengths to the reference levels and also the “EQ’ed” dimensions from a center point intersecting reference plane to the ends of the Bot W1/Bot W2 reference lines.

Figure 10: Trapezoidial Reference Lines

Figure 11: Void Forms

Once all of the trapezoids and 3D connection lines have been drawn, I selected each corner triangle reference line to create the aforementioned void form (Figure 11). In the completed mass model, there are a total of 4 Top level shapes which are aligned with the Base level and Bottom Level shape masses. As previously mentioned, in the host family the Width W1 and Height Hi parameters of the Top level shape are linked to calculated widths and heights from the user defined parameters and their corresponding trigonometric equations.

Bottom Level Shape:

The method of creating Bottom Level Shape mass is the same as the Top Level Shape mass. The only differences between the two shapes are the angles at which the corner void forms are shaped. Also instead of the Bot W1/Bot W2 parameters, the Bottom Level mass has Top W1/Top W1 which is still a linked function of the Width W1 and W2 of the host family. There are 5 total Bottom Level Shape masses.

Base Level:

The 20 mega-columns supporting the Diagrid system of the Hearst Tower are modeled in this mass. Instead of making a large rectangular mass and creating a façade that looked like the mega-columns, I went ahead and created an extrusion for each of the 20 mega-columns as well as a thin walled mass connecting between the columns to use as a dividing surface for the façade (Figure 12). To create the masses, I drew rectangular reference lines on the sides (front, back, left, and right) of the model and set the dimensions of the rectangles to its corresponding widths and heights. Once they are drawn, I selected the rectangles and created a solid form, making an extrusion into the plane in which the rectangle was drawn on. I assumed that the columns were square and that the depth of the column was equal to a quarter of the column spacing.

Figure 12: Column at Base Level

Parametric Paths:

In the conceptual mass model of the Hearst Tower, I have set up the “parametric paths” that were mention previously within the properties of the family type. Whenever the window for the family properties is open, and under Constraints there are the options:

1.       Parametric Width: When you choose this option you will change the column spacing of the model and in turn change the widths of the model.

2.       Parametric Total Height: Choose this option to set the total height and the long width of the model. It will calculate Calc_Weq and Calc_Heq

3.       Parametric Height: This option will let you set the height of each level including the base level.

4.       Parametric Angle: Choosing this option will set the angles of the corners or isosceles triangles of the masses.

In the properties window, to select an option you change the value of the option to 1 otherwise to deselect it, you set it to 0.

In order to define all of the parameters of the mass model you would need to select two options, unless you select the Parametric total height in that case there are two dimensions (width and height) already set in that one option. If the user doesn’t select two different options or the Total option than under “Definition Check” a value of ERROR will be outputted (Figure 13). Below the Constraints parameters the Text parameters tells the user which Dimension parameter he/she needs to define depending on the options they have selected.

Figure 13: User Defined Parametric Options With Error

So depending on what option the user selects, the user will need to define the corresponding values under the dimension parameter category. In most cases, it is pretty straight forward which dimension you will need to define based on the option you choose. However the Base Level dimension parameter will need to be defined if the user doesn’t select the Parametric Total Height option.

When the user is done selecting the parameter options and inputting the corresponding dimensional values for the options, I’ve set up an if statement for the calculated values of heights and widths that are necessary for the mass to form.  I used an “OR” statement in each of the “IF” statements because I needed more than one condition to apply for the “IF” statement to be true. In short, Revit determines the parametric option combination that the user defines and then from whatever combination number it is, the calculated heights and widths (Calc_Hi or Calc_Wi) are determined. The progression of “IF” statements is as follows:

1.       If User selects options… Parameter Width, etc... Combination = ???

a.       Combination = 1 if Height and Width are selected

b.       Combination = 2 if Height and Angle are selected

c.       Combination = 3 if Width and Angle are selected

d.       Combination = 4 if Total is selected

2.       If Combination (Or PC) = 1, 2, 3 or 4

a.       Calc_Hi =  Hi (user-defined) or ½*Width*tan(Ai) or Calc_Heq

b.       Calc_Wi = Width or 2*H2/tan(A2) or Calc_Weq

c.       ***The exact equation can be found in XXX