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.
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Figure 6:
Conceptual Mass
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Figure 7:
Top Level Shape
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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
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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