S206E Lecture 17, 5/1/2018, Rhino & Grasshopper, Tower modeling

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1 S206E Lecture 17, 5/1/2018, Rhino & Grasshopper, Tower modeling Copyright 2018, Chiu-Shui Chan. All Rights Reserved. Concept of Morph in Rhino and Grasshopper: S206E057 Spring 2018 Morphing is a technique that could stretch and distort geometry precisely. Here are the steps of turning a sphere into a deformed box geometry. 1. We could use Transform Tag > Morph panel > Box Morph (type either Morph or Box Morph) to put a morph component in GH. 2. Create a sphere in Rhino, generate a geometry component in GH. 3. Right click on Geometry > Set one Geometry > Select the Sphere > right click the geometry component again > Internalize Data. This step would apply the sphere to the geometry component, and copy the sphere into the GH definition through the internalize data function. We could delete the Rhino geometry to display the original Geometry component in GH format. This way, the sphere geometry is a part of the GH data. 4. Connect the geometry output to Morph Geometry input. 5. In Morph component, it requires a reference box; which is the bounding box of the original geometry of the sphere. One method of setting up the reference box is to plug in the geometry parameter into the reference box input. GH will automatically figure out the proper bounds of that reference box. The other method, which is more flexible and visible, is to use a Bounding Box component between the geometry and the box morphs reference box input. Surface > Primitive > Bounding Box (or type BBox). Results of the BBox are to have a bounding box around the basic geometry created, which also visually helps to preview the possible framework. Note: In this BBox data management, C is the geometry to contain in a list format; P is the orientation plane, which has the world xy plane as default plane but it could also be defined by users. The first output parameter of B is the aligned bounding box in world coordinates. The second box output B is the bounding box in orientation plane coordinates, which is the defined plane by P. 6. The last input needed by the Morph component is a Target box for T, which determines how the base geometry of (the sphere) is morphed. A simple Center Box component could set it up and serve the purposes. Surface > Primitive > Center Box > (Type Center Box) Center Box will create a box, which is centered on a base plane defined by B input. Here the degault base plane is the world coordinate of X, Y plane on the ground. 7. Define the output of the Box component to the Target of Morph to see the result. The values of X, Y, Z will control the Morph results. Page 1 (4/20/2018)

2 Coastal Fog Skyscraper, Huasco City, Chile High-rise building GH construction methods: Step one: Generate four spiral lines first. 1. Create a rectangle in Rhino with the following values for X: -40 to 40; Y: -40 to 40; and R: Create a series of list. Here, Series will create a series of number as a list. Values inside the input components are established by Set Number. a. S is the first number in the series, it is 0 by default. b. N is the step size for each successive number: c. C is the number of values in the series: 30 numbers. 2.2 The numbers on the list will be calculated by multiplying the step size of 0.26 (or the length of an edge of a box) by itself twice through Cube (for instance, the second number on the list is 0.26 * 0.26 * 0.26 = ). 2.3 Turn this list to a list of 30 coordinates along Z axis by Unit Z, i.e., (0.0, 0.0, ) 2.4 Move the 30 rectangle up along the given Z values (Figure 1 below). 3 Convert the list of the moved 30 pieces geometry to a plane parameter, which creates the list of moved 30 rectangles 2D data to 3D data and use them as the rotation (Rotate) plane. 4 The rotate geometry input is from the Move geometry output, and its rotation angle of the 30 planes is determined by another list Series, which has 30 numbers with increment of 0.4 (degree). (Figure 2 below). 5 The rotated rectangle will be divided (Divide) into four segments (N in divide component is 4). (Figure 3 below) 6 Flip the data matrix (Flip Matrix) by swapping rows and columns to make spiral shapes. 7 Create an interpolated (Interpolate) curve through the swapped set of points curve degree is 3. (Figure 4 below) 8 Make the four curves into four pipes, with pipe radius of 4. (Figure 5 below). Page 2 (4/20/2018)

3 Step two: Create faces for the four curves. 1. Flatten Tree function to remove all branching information to flatten the data tree. 2. List Item to retrieve the data item back to the list, by increasing the output number from 1 to +3 (zoom in to the component and click the + sign three times to add three more output items). 3. These four outputs will serve as the four input data for the Curve parameters. 4. These four spiral curve lines will be connected to 4 sets of Ruled Surface to generate four faces. Each Ruled Surface will create a surface between two curves A and B. Step three: Creating the skin to be assigned to the exterior Page 3 (4/20/2018)

4 Draw triangular shapes (TriGrid) 1 by 60 with size of 10. Make these rectangles to curves (Curve) representation. Set up a Graft Tree component, (Note: in this example, we have a number of items generated. If we want to attach the data items of the shape to a structure, we want these points to be able to flexibly attach to the points in the structure. Grafting allows each data item to create a new branch for every single data item.) Apply Pipe to make these triangles as pipes. The radius of the pipe is 3. Put these pipes into a bounding box (BBox) and turn off the Preview on BBox to make it invisible. Step four: assign the framework in step three to the surfaces created in step two. 1. Create 4 sets of Divide Domain 2, separate the U and V direction of the vertical spiral face into surfaces. Their inputs of I are from the RuleSrf. U is from the step 3 of Extend Y, and V is from the Extend X. 2. Use 4 surface boxes (SBox) to create twisted box on the curved spiral surface patch. Its basic surface is the curved spiral surface (Rulesrf) output, Domain D is from the Divided output, Height is from the Number slider of number Apply Morph Box (Morph) to morph an object into a twisted box. Inside this component, the base geometry is the pipe in step 3. The reference box is the BBox in step 3. Target box is the resulting surface of the twisted box SBox on item 2 in this step. Do one Morph at a time. Do the second one after the first one is done to save time. 4. Finally, apply BREP Join component to join these four spiral surfaces together into one big tower. After the objects were joined together, the dot edges will be erased to get a better result. Note: It took around 2 for the first three components and 5 minutes for the fourth one of the morph to complete the operation in my machine, due to that each surface will go through the sequences of dividing it into 60 subversions, and morph them into a triangle target shape. So, it takes huge computational power with time to complete the task. Thus, constantly save the GH file. If the program doesn t work, then hit ESC key to stop it. Page 4 (4/20/2018)

5 Step four coding: Final coding: Examples of different kinds of skin compositions: Page 5 (4/20/2018)

6 Apply a series of mesh grid to construct the façade of a high rise building. 1. Draw an enclosed NURB curve, set it up as the Curve parameter input. 2. Apply Series to generate a list of a series of numbers, which has two number sliders to define the N input of 5 and the number of Counts as 20. The series of number will be [0, 5, 10, 15 ]. This means the tower will have 20 floors with 5 units as level interval. 3. Apply the Unit Z to generate a unit vector that is the World (Z) axis. Export the list from the Series to the Unit Z to generate a series of coordinates of [0, 0, 0], [0, 0, 5], [0, 0. 10] 4. Move the geometry from the Curve parameter along the imported translation vector, which is the list of coordinates, up 20 times. 5. After planes are moved up, each plane will be rotated (rotate) along World XY Plane (XY Plane) by certain angles. 6. We could apply Loft to create the skin. 7. We could apply Morph to create a complicated shape. 8. We could also apply Twist to manipulate the final form. Summaries of GH: There are many functions, components, and plug-ins available in GH, and many different ways to complete the same tasks. Please do more research on the use of GH, particularly the newly developed plug-ins, for getting a good control of the system. Reminder for Assignment #2 For assignment #2, here are the requirements: 1. Please modify and improve your Rhino model. 2. Apply GH to operate features and/or shapes for form generations. 3. After the project is completed, write a project summary to reflect the entire executing sequences. It is required to clearly (descriptively) describe the major GH components you applied and the sequential steps that you used to generate the form. The summaries could be saved as either PDF or PPT file format. Happy Rhino modeling and GH programming Page 6 (4/20/2018)

7 Last example 1: Results (see the image on the lower left): Last example 2 (see the image above right): Page 7 (4/20/2018)

8 Last example 3 (see the image below): Questions: Is it really true to apply extrude for creating thickness of the morph object? In these examples, which variable controls the real thickness of the façade? Shall we use BBox and DeBox to find the H for the SBox? Page 8 (4/20/2018)