PARAMETRIC MASS – CANOPY

To achieve the parametric design of the canopy, it is necessary to start with the dimensions and positional relationships of the modules that make up the canopy. Each module consists of a roof and a tree-shaped column, and there are dimensional relationships and constraints between these two components as well. Thus, the parametric canopy is structured into three levels of families: Column Family – Module Family – Canopy Family.

1. Column Family:

1.1 Four-pronged Columns Family:

a. Using the Column Template, rather than a Mass Template, since mass cannot be designated as structural components in the Revit project.

b. The profile of one branch of the column is drawn on a vertical reference plane. The profile includes the following parameters:

• Lower Part Height: The height of the column's vertical section.
• Lower Part Height Outer = Column Height - 600: The outer height of the vertical section.
• Upper Part Height: The height of the column’s inclined section.
• Upper Part Length (L&S): The length of the column’s inclined section.
• The depth of the inclined section’s end is locked at 600mm.

c. Use Create Solid Form tool to generate solid geometry of the branch. Next, use the Rotate tool to copy the branch around the center to form the other three branches.

d. The base of the column is defined by a set of orthogonal reference planes, with an additional set of orthogonal planes rotated 30 degrees. Parameters set for the base include:

• Base Thickness: The thickness of each branch’s base and the core component.
• Base Length = Base Thickness: The length of each branch’s base protruding from the core.
• Base Dimension = Base Thickness / 2: The distance between the inner edge of each branch’s base and the reference planes, which is always equal to half the thickness of the core component. This ensures that all four branches remain connected to the core.

e. Associate the material of the four branches and the core component with the Column Material family type parameter. 

1.2 Three-pronged Columns Family:

The steps and parameter settings for creating the three-pronged column family are almost the same as for the four-pronged column family, while the key difference is:
a. Base Dimension = Base Thickness / 2 / tan (Reference Angle): The center point of the three-pronged column is not located at the centroid of the equilateral triangular roof (the reason will be explained in the Module Family). Therefore, the Base Dimension is calculated using a fixed angle from the roof component (Reference Angle = 49.11°) and the Base Thickness, determined by a geometric relationship.
b. Additionally, the profile of the core component is irregular, so Align Constrain and Angle Constraint are applied to ensure it remains connected to all three branches.

2. Module Family

2.1 Rhombus Roof Module Family

a. Start by creating a new family using the Conceptual Mass Template. Draw the profile of the rhombus-shaped roof and place a reference point at the center of the profile. Next, drag the reference point along the z-axis to define the roof's height. Finally, use the Create Solid Form tool to generate mass by forming planes based on the roof profile and the reference point. The following parameters are defined:

• Roof Angle: In this project, the roof angle is fixed at 60°
• Roof Width: The length of the shorter diagonal of the rhombus mass.
• Roof Length: The length of the longer diagonal of the rhombus mass.
• Column Branch Length L = Roof Width * cos (Roof Angle / 2) - Column Thickness / 2: The formula ensures the tip of the column branch doesn’t extend beyond the rhombus vertex.
• Column Branch Length S = Roof Width * sin (Roof Angle / 2) - Column Thickness / 2: Similarly, this ensures the branch remains within the rhombus boundary.
• Roof Depth: The vertical displacement of the center point.
• Column Height: The distance from the center point of the rhombus mass to the 0 level.
• Column Thickness: The thickness of the column.

2.2 Equilateral Triangular Roof Module Family

a. The steps and parameter settings for creating the three-pronged column family are almost the same as for the four-pronged column family, while the key difference is:

• Reference Dimension = Roof Width * cos (Roof Angle / 2) / 2: The displacement point of the triangular roof is not located at the centroid but at a point that is Roof Width * cos (Roof Angle / 2) / 2 away from the vertex. This is to ensure that in the canopy family, the two modules can align with each other.
• The Column Branch Length L = Roof Width / 2 / cos (Branch Angle) - Base Dimension and Column Branch Length S = Reference Dimension - Base Dimension are defined by Base Dimension rather than Column Thickness.

3. Canopy Family

a. Start by creating a new Conceptual Mass Family and load both the Rhombus Roof Family and Triangular Roof Family into it.
Arrange the modular roof families according to the design layout, using the Rotate and Mirror tools where necessary.
b. The modules labeled a and b can be treated as a group, using the center point of a1 as the origin, draw orthogonal reference planes and Pin them in place. The position of module labeled as a and b can be determined by its center point’s horizontal and vertical distances from the origin. These distances are controlled by Horizontal Spacing and Vertical Spacing, which can be calculated based on the Roof Width parameter and trigonometric relationships.

• Horizontal Spacing is calculated based on geometric and trigonometric relationships
• Vertical Spacing = Roof Width / tan (Roof Angle / 2) / 2

c. The modules labeled c and d can be treated as another group, with C1’s center point serving as the origin. To define their position, draw orthogonal reference planes rotated 30 degrees clockwise from the center point of a1 and lock them with the Pin tool. Similarly, draw another set of 30-degree clockwise rotated orthogonal reference planes at the center point of C1. The position of the reference planes at C1 is controlled by two distance parameters, Axis Spacing 1 and Axis Spacing 2, which also adjust according to the Roof Width:

• Axis Spacing 1 = 4 * Roof Width * cos (Roof Angle / 2)
  
• Axis Spacing 2 = 2.5 * Roof Width
  

d. Use the Align Constraint to lock module C1 to the 30-degree rotated orthogonal reference planes. The position of the other modules labeled c and d can then be determined by Diagonal Spacing and Vertical Spacing between their center points and the center point of C1.

• Horizontal Spacing is calculated based on geometric and trigonometric relationships
• Vertical Spacing = Roof Width / tan (Roof Angle / 2) / 2

e. On the vertical direction, the parameters include:

• Roof Depth = manually input value
  
• Column Height = manually input value