RANARCH

The Prada epicenter building is wrapped by a perfect Diagrid system that provides an enclosure envelope as well as external structure system to the building. To correctly model this system, we started by its analysis to find out that there were two main aspects that needed to be considered: First is the ratio within the single diamond module of the grid, each diamond has the ratio of x:y=3:2. Second is the relation between the grid and the building edges, where all the diamonds intersect and perfectly fit together when meeting at the building edges, producing a one continuous grid that perfectly wraps around the whole building. For this to be achieved, the grid must always start and end at the corners of each of the building faces, where each face must have an integer number of diamonds. In other words, the x dimension of the grid must always be a multiple of 3, and the z direction must always be a multiple of 2.

In order to achieve that, the method was to create 2 overlapping identical grids, where one is offset by half a diamond in the x and y directions. Both grids have 3 points for the x-step, and 2 points for the y-step, creating an ordered list of points. By trial and error, it was also discovered that the 2 grids must have equal number of rows equal number of columns, for the matriculation of points to work correctly. The logic is to join the ordered list of points from grid one with the ordered list of points from grid two.

Different order of starting points and directions were used to create the remaining lines in the diamonds.

One of the initial challenges for modeling the Prada building in grasshopper lies in finding the most convenient method for constructing its irregular geometric mass.

Since the architect provided the façade drawings as a series of surfaces connected together in a single flat foldable envelope, therefore it seemed more compatible to also model it in grasshopper the same way. Therefore, the process began with referencing the given unfolded building façade drawing in Rhino and then constructing points with x, y, and z coordinates in Grasshopper that represents the corners for each of the nine folded surfaces. Each surface had 3 or 4 predefined corners with one of its edges (or the crease lines) as the axis of rotation for that single face. Just like the way a sheet of paper can be folded, the parameters in this grasshopper algorithm was mainly controlled by the 3D rotational angles (0 to 360 degrees) in either straight vertical, diagonal or horizontal axes depending on the shape of that predefined face or surface.

What seemed to be the most significant factor about this method is the level of precision in the size and dimensions of modeling the existed building mass accurately, yet it doesn’t give the needed flexibility in controlling its parameters. In other words, it is possible to generate multiple of variations using these parameters like the fold angles or the size area for each of the surfaces, but it doesn’t guarantee that the result will be a closed folded envelope or volume for the building. Therefore, we needed to explore a different method in re-modeling the Prada 3D mass without losing the ability or the flexibility of producing multiple of functional design variations from its parameters.

Thus we started off with creating 5 vertices to construct 5 lines aligning from the base floor plan. On one condition when creating the vertices was the distance between each vertex which needs to be multiples of 3 due to the ratio of the diagrid system. Then the vertices are connected to create lines and divide the length of the line by 3 to get the precise integer only and orient the measured line by utilizing Circle component and Curve Closest Point component. When the 5 lines are created, extrude them to the height where it reaches the lowest part of the roof. This is to make the base façades of the building. The method in creating the roof is to continue extruding the lines from the lowest part and to the highest part of the roof. In other words, there is two separate extrusions, one creating the façades and one creating the roof portion. When the mass is created, make the angled surfaces to cut down the extrusion. The angled surfaces are made from the referencing lines of the edges of the mass. Extrude a line to a surface and offset to scale up the size of the surface. Angle them with the Rotate component and use the surfaces to split the extrusion. The roof is formed with 4 sloped surfaces which connect the edges of the extrusion. This defines as one edge to remain as an extruded surface from the bottom to the top of the roof. Of all the surfaces that forms the roof, the north oriented surface is rotated twice. In order to cut down the extrusion, the mass needs to be deconstructed and selected separately with List Item component to split with the surfaces by using Solid Difference component.

After the diagrid was created as 2D lines, it was taken as a merged pattern to be projected onto the 3D building mass. Since the building is a 5-sided polyhedral form, this process was a little complicated. The diagrid pattern was projected on each face separately, by 3D-rotating the pattern to be on a plane parallel to the surface and projecting it with a direction vector that is perpendicular to the surface being projected on. Once this process was repeated for the 9 different surfaces of the building, the output was a perfectly wrapped building by the diagrid pattern.

Then as part of our 3D-mass study, we explored some options to produce more variations from the original design by simply changing some of the parameters that we have defined within our algorithm. First, we changed the building footprint to regular pentagon, where each side is 12 meters, to maintain the diagrid proportions intact. The second variation was done by changing the parameter angles of the roof cutting planes and the building height, producing a much more dynamic and vibrant output. Lastly, we explored the option of simplifying the building geometry by changing the footprint into a square, again with maintaining the diagrid proportions, and playing a little more with the roof angles, thus producing 3 very different and interesting mass variations.

One of the most significant aspects of the project was the integration of the building façade and the building structure into a single designed framework. Since the diagrid system is the focal point of the project, the other systems follow that order accordingly by design including the structure components of the building that consist of the slabs and the vertical cores; however, the three cores locations are determined based on the structural framing plan of the slabs to be extruded vertically along the z- axis. The slabs are spaced out based on the height of two diagrid modules where the boundary of each slabs takes the shape of the building geometric mass. Structurally, these slabs transfer the weight from that diagrid façade system to the cores of the building. The 3 generated design variations for the structural system complement the 3 design variation for the building envelope while it varies in the sizes and dimensions of the cores as well as the height between each of the building floors.

The horizontal cores are made based on the diagrids that are utilized as envelopes of the building structure. Where the intersection of the diagrids and the second, fourth, fifth level slabs meet are the pivots for each horizontal cores. Brep Curve component is used to find the intersecting vertexes, and List Item component is used to distinguish the centroid of the core. From the centroid, the left intersecting vertex becomes the left corner of the diamond core, in which the right intersecting vertex becomes the right corner of the diamond core. The top and the bottom vertexes are also the top and bottom points from the centroid which makes the size of 4 diamonds put together. From getting the four vertexes on the other side of the façade, the two facing diamonds are connected by creating horizontal surfaces and making them as solids by joining and capping. These surfaces are offsetted to create the thickness by 0.

Lastly, each corners have been rounded by using the FilletEdge component with the radius of 0.3.

RECLAIMING A LOST LEGACY