S206E Lecture 15, 4/27/2018, Rhino 3D, Grasshopper, Shanghai Tower modeling

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1 S206E Lecture 15, 4/27/2018, Rhino 3D, Grasshopper, Shanghai Tower modeling Copyright 2018, Chiu-Shui Chan. All Rights Reserved. Creation of high-rise building models has a typical algorithm, which is covered in this lecture by an example. Shanghai Tower by Gensler: The structure is 632 Meters (2073 feet) height, with 121 floors and 120 Meter square of the base. The body twisted 120 degrees, rotated one degree per floor, and tested by 1/85 model in a wind tunnel. Result shows that it would reduce 24% of wind load. For every 5% of wind reduction, it will save roughly 12 million of US dollars (some sources: save more than $55 million in building material and construction process). Shanghai Tower s twisting, tapering, triangular form without a typical look-at-me cap on top will appear as if it could continue skyward forever. In this exercise, we will create a simplified version of the Tower from GH algorithm to serve as the beginning of modeling high-rise building models. The algorithm is a typical high rise building modeling technique. Version A: Sequences of form generation 1. Generate a Series of numbers first, with 6 units (the number of 6 is not representing Meters or Feet but just units) of the interval number of 121 counts. The number of 121 represents 121 floors of the tower, and numbers are spaced according to the step value of N (could change it to 15 to match the total height, if the system unit is in feet). 2. The list of number [0, 6, 12, 18 ] is converted by Unit Z component to the list of coordinates with Z value of the coordination number on the list (converting the number list of 0, 6, 12, 18 to the coordination lists of [0, 0, 0], [0, 0, 6], [0, 0, 12], [0, 0, 18] etc.). 3. This coordination list will be defined as XY plane (XY Plane or type xy) to provide mathematical representation of orientation and serves as the base plane (P) input for horizontal Polygon component. 4. The Polygon component has three number sliders defining the distance from center to tip of Radius (R), the number of segments (S, use 3 to represent a triangle), and the polygon corner fillet radius (Rf). Page 1 (4/20/2018)

2 5. The polygon output of (P) represents the floor. There are 121 polygons created and each will be rotated. The rotation angle starts from 0 to Here, each plane s rotation angle is controlled by Construct Domain component to build up a domain ranged from 0 to 0.75 and distributed 121 times. The range component will take the list from Domain output as its input to generate a list of 121 numbers evenly spread out (or cut) from 0 to For instance, the interval between two numbers is obtained by 0.75 / 121 = , and * 121 is In GH, the unit of angle always is treated as radian (1 degree = radian). Here, each number is multiplied (Multiplication) by PI to get the number of 0, 0.019, 0.038, for 0, , , etc., to simulate a close value for rotation. Accordingly; each plane will be rotated along the number given by this AxB component. If we divide the R from AxB component by 180 to get a real representation of radian unit, we will get a very small rotation angle. This explains the notion of representation in data input. 6. The rotated plane will also be scaled from bottom floor to the top floor with non-uniform factor (ScaleNU) component. In ScaleNU, G is the geometry obtained from Rotate. The X and Y axis of each plane will be scaled by a Series of numbers; the number will gradually be reduced by the interval of , 121 times. In this example, we don t want the original shape on the ground to be scaled by , so the starting number of the series is forced to be 1 instead of the default value of 0. The negative number determines the reducing factor that versus the positive number to increase the size (width) of the polygon. 7. Finally, the rotated triangles are lofted (Loft) to create the tower skin, which will be baked to Rhino as Rhino model. 8. We could put a cap (Cap) to close the top of the tower. Page 2 (4/20/2018)

3 Second version B the real simulation 1. In GH, the rotation angle is required to show in radians instead of degrees. The conversion is done by the method of getting the number in Range output times Pi and divided by 180, which is the formula of turning a degree to radians. See the formula below. In this coding example, we had not divided it by 180 yet. You should modify it to get exact results. RRRRRRRRRRRRRR = DDDDDDDDDDDDDD ππ 180 Changing the degrees to radians is done by the following formula. DDDDDDDDDDDDDD = RRRRRRRRRRRRRR 180 ππ 2. There is a method of using Radian directly to convert degree to radian quickly, which is the focus on this version. Similarly, we could also use the function of Degrees to turn radian to degrees. In this case, the Range component creates a list of 122 items of numbers (0 and 121 represent the ground and roof levels respectively), which is arranged by the value coming from Domain component to make appropriate list. As a result, it will have 122 items of consecutive number representing one degree of rotation angle for each floor and which are converted into radian for rotation input. 3. In this version B example, each floor will rotate one degree from the first floor to the 121th floor. So, this is a real simulation of the building rotation. The resulting image and codes are shown below. Page 3 (4/20/2018)

4 Version C: Calculate the pre-defined rotation angle In this version C, we could pre-define the maximum number of rotation as 121 degrees (or 90, 180 degrees etc.) for all 121 floors. So, the program calculates the radians unit by π / 180 (Division), which is , and multiplies it by the number of 121 to determine the Domain of rotation range (0 to ). The value of is the total rotation angle in radian. Thus, the Range component sets up the boundary ranging from 0 to In other words, the Range component will calculate 121 units of rotation angles individually. The coding is attached here for reference. The resulting image is provided below next to the real photo for comparison. Final exercise requirements: 1. Apply the second version to modify and change the rotation orientation to clock wise direction, see the images below. 2. Again, apply the second version to make the base size wider to match the real base size of around 120 Meter square units of distance with the height around 3.3 meters. 3. Make the tower as a circular shape instead of a triangular shape. You have to find out the most efficient way (number) to create it? 4. Bake the Loft component and save it to a particular layer. Render the image and save the Rhino image to JPG file. Please load both image and GH file to my.files server for completing today s exercise. Page 4 (4/20/2018)

5 Version 4: Construct solid floor planes and envelop 1. Use Boundary Surface to make surfaces from the un-uniformed scale list, which represents each floor and extrude each along Z axis with 1 foot distance to create the floor plane and the roof plane (which is created by the Cap Hole component, see the following GH algorithm). 2. From the Loft (or Cap) output, apply Extrude to extrude the surface along X axis to create the form of exterior walls. Footnote on the differences between range and series and assignment #2: Range is to evenly divide (or distribute) the given domain (from X to Y) by the given N counts and make a list. Series is to define the starting point, and make (the number of) a list of counts by a defined intervals (or step size). Compare the available GH modeling algorithms covered in lectures with the Rhino algorithm you developed for Assignment #2-1, and further implement a workable GH plan for Assignment #2. Page 5 (4/20/2018)