Simple Algorithms - Parametric Architecture

Marco Antonio Zoch Souza . LSBU

MSc Digital Architecture & Robotic Construction

ADVANCED DIGITAL DESIGN TECHNIQUES TUTOR : HUNBAI JUN

PARAMETRIC STUDIES_

I CASE STUDY_ VORONOI SPHERE SPHERE PACKING NEGATIVE ELEMENT EXTRACTION

II PSEUDO CODE_ VORONOI ANALYSIS SPHERE STUDIES JOINT ELEMENT

III APPLICATION OF THE CODE_ GRASSHOPPER APPLICATION AND EXPLANATION

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VORONOI ANALYSIS | CASE STUDY

About: The project consist of the joint work of researchers in Poland to demonstrate on a workshop the possibilites that digital technologies can bring for complex shapes. No form of traditional architectural assemble was used, only digitally assisted solutions.

Project Facts: Name: Voronoi Cupola Pavilion Location: Gdansk, University of Technology, Poland Who: Margaret Zboinska (Morfotactic) + Jan Cudzik, Kalina Juchnevic, Robert Juchnevic, Kacper Radziszewski (Gdansk University of Technology) Why: Parametric Architecture II workshop When: 2014

It uses Voronoi Diagram, a pattern developed by Georgy Voronoy, that through an algorithm divide a surface into its optimal polygonal cells solution, based on point distribution.

It was exhibited at the Gdynia Design Days 2014, polish summer design festival and on the University o Gdansk Nantechnology Center exhibition.

Extraction: _ The Voronoi Pattern and its optimal solution for translating curved shapes in polygonal cells. _ The Skin Panels Fabrication system. _ Possibility of translating porosity through layers within voronoi grid.

Key Information

Voronoi

Exclusively Digitally Assisted

Digital Fabrication

Computational Optimization

Skin

Perforated Timber Panels

TheVoronoi Cupola Pavilion - Gdansk Unversity of Technology, Poland - Parametric Architecture II Workshop- 2014 - Images from morfotactic.wordpress.com

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CIRCLE SPHERE PACKING | CASE

About: Packed is a pavilion designed by the MAS CAAD researchers on ETH, designed for the 3d paperArt EXPO 2010 in the Museum of Arts and Crafts in Shanghai. It is made of cardboard,

Project Facts: Name: Packed Location: ETH, Zurich, Switzerland and Shanghai, China.

Who: MAS CAAD researchers Why: Shanghai world EXPO 2010 When: 2010

It is a digitally designed project that consist of a spherical dome circle packed by ‘rings’ of cardboards. Variable truncated cones (409 cones of different sizes), assembled together strievng to fill the entire surface of the dome.

The corrugated cardboards are made of 28 layers, that were cut, glued and labelled by computer-controlled machinery.

Extraction: _ The Circle packing of a spherical surface to achieve the most optimized pattern. _ The Portability of the elements that made reassemble easy. _ Possibile structural gains on material density. _Low cost materials.

Circle Packing

Exclusively Digitally Assisted

Digital Fabrication

High-Low

Compact Solution

Geometrical Optimization

Packed Pavilion - MAS CAAD - ETH - Triumph Pavilion Competition 2010 - Zurich, Switzerland- Exhibited in Shanghai Expo , China 2010 - Images from dezeen.com

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PACKING | CASE STUDY

About: It is an expansion of the cinpaosan necropolis in Taipei. t has being awared LEED platinum and is the new arrival hall as well as a pavilion on the complex.

Project Facts: Name: Ocean Pavilion Chinpaosan Necropolis Extension Location: Taipei, Taiwan Who: Steven Holl Architects Why: New Program - Extension of the necropolis When: to be completed in 2018

Sphere Interesction

The symbology of the circle was used and later translated to spheres,. The resultant circulation between the nodes was considered the most appropriate approach. It also uses the reflection of the water for better vizualization of the concept. the result brings a complex shape with different light directions.

Digitally Assisted

Extraction: _ The sphere intersection study for its analytical and geometrical value _ The Regular fixed geometry solution _ Better understanding of packing spheres.

Light and Porosity

Sphere Subtraction studies

Ocean Pavilion | Chinpaosan Necropolis Extension | Hotel - Steven Holl Architects - Taipei, Taiwan - Images from designboom.com

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JOINT ELEMENT | CASE STUDY

About:

Project Facts: Name: Voronoi Sky Pavilion Location: East London, UK Who: Nonscale CO Why: Arch Triumph Competition When: 2012

Negative Geometrical Elements

it resembles ‘smattering of stars’, and cast reflection on its mirrored plate base, operating like a giant sundial. It was assembled in the Museum Gardens, neighbour to the V&A Museum of childhood.

It was part of the program to investigate how the sky changes architectural structures.

It is assembled with 17 twinkling stars, pointing towards the North Star. the structure is pinned to a series of interlocking circular mirrors, It has a solid steel core that join the elements on the ground.

Geometry Rationalization

Extraction: _ The geometrical rationalization that can be obtained through a combination of other geometries _ The dynamic value that relate the project with the sky

Digital Fabrication

Computational Optimization

Sky Pavilion - Nonscale Co - Triumph Pavilion Competition 2012 - East London - Images from dezeen.com

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PSEUDO CODE

VORONOI ANALYSIS { Generate sphere; >Populate sphere with points

>Produce voronoi diagram

>Cut voronoi cells to fix sphere shape; Connect the polyline of the cells

>Scale the cells.

>Cut the cells with scaled element; Join the elements into a single shape

>Scale shape

>Extrude shape between scaled element

and original shape Smooth result; }

SPHERE STUDIES IRREGULAR PACKING { Generate sphere or box or brep;

>Populate sphere with points

>Define sphere sizes

>Solve packing equation Turn vertices into spheres

>Scale the spheres Send to Rhinoceros

>Boolean difference against initial element Analyze result; }

CIRCLED PACKED SPHERE STUDY

REGULAR PACKING

{ Generate tetrahedron; >Extract points and normals

>Generate smaller sphere

>Project circles from extracted points on sphere; Join the curves

>Scale the circle packed sphere.

>Generate line from original sphere to scaled; Join the elements into a single shape

>Pipe curves }

{ Define Rectangle; >Generate 3 layers from rectangle

>Create equal size grid

>Connect points with triangulation Turn points into spheres

>Scale the spheres Send to Rhinoceros

>Boolean difference against 3d box from rectangle Analyze result; }

JOINT ELEMENT { Define Rectangle; >Generate 3 layers from rectangle

>Create equal size grid

>Connect points with triangulation Turn points into spheres

>Select colliding spheres on a single area

>Find center of the spheres group Generate sphere in center

>Subtraction of geometries against central sphere

>Extract external shape Deform with relaxation

>Smooth result }

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*PLUGINS USED INSIDE GRASSHOPPER: WEAVERBIRD & FOX.

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STEP 1

STEP 2

VORONOI SPHERE Create a sphere and populate its geometry with points that will define the 3d voronoi diagram, limit the boundary of the 3d voronoi with a boundary box that covers the initial sphere.

Cut the geometry with brep | brep, beware that the curves from the cells will need to be reconnected, use discontinuity and polyline (set true to closed curve).

After this define the cell aperture scaling the polyline of the cells (you will need the average to define the scaling centroid for each cell). Join the breps 1Sphere 2Populate Geometry 3Blounding Box 4Voronoi 3d

5Brep | Brep 6Discontinuity 7Polyline 8Average

STEP 3

Now it is possible to loft the external shell of the voronoi sphere.

To make it thicker, scale both the voronoi cell and its aperture (with sa,e scaรงomg factor,) loft and join the brep Join all of the breps and deconstruct it so you can turn it into a mesh. Using mesh surface connect the faces and the define the grid of the mesh (u v).

For a more elegant result use weaver bird parameters in this order: join the mesh with wb join, add the iamount of subdivisions of your interest in catmull clark subdivision (so to get a more smooth curved element), than finally add thickness with wb thicken for 3d printing.

9Scale 10Loft 11Brep Join 12Area

To visualize I used parameters from Fox (a very interesting aggregation plugin): Fox preview mesh colors, that allow a soft view of the final elment (necessary to flatten the mesh for better result) You will need a color picker, rgb, cmyk or any color parameter of your preference. .

Fox preview mesh edges, which helps to see te quality of the model with a sharper precision.

13Deconstruct Brep 14Mesh Surface 15Wb Join 16WbCatmullClark Subdivision

17Wb Thicken 18Mesh 19Fox Preview Mesh Edges 20Fox Preview Mesh Colors

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*PLUGIN USED INSIDE GRASSHOPPER: ELEMENT

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STEP 1

STEP 2

CIRCLE PACKED SPHERE Start with a Tetrahedron from Element plugin and extract the face normals as well as deconstruct the mesh.

This will allow to use the limiting vertices (end of edges and central positions ) and the tetrahedron normals of the vectors to produce circles facing towards the area of interest. With 2 circle CNR parameters use the first to connect the points from edges towards its curves. On the second use the vectors and normals from the deconstructed mesh. Apply same radius to both circle CNR’s parameters.

1Tetrahedron 2Face Normals 3Deconstruct Mesh

4Circle CNR 5Sphere

Create a sphere of smaller size than the tetrahedron. This sphere will be used to project the circles along it. Use double parameters of project area, on the latter flatten the curve input, so circles wont overlap and will project on both the top and bottom.

Join the curves into a single circle-packed sphere.

Deconstruct both the original circle-packed-sphere and its scaled version, allowing to connect the vertices from each with a line, flatten the data for accurate result.

Create a pipe from the the circle-packed-sphere, its scaled version and the connecting lines between them to get the final result.

Scale the element to allow s multilayered pattern

6Project Area 7Join Curves

8Scale 9Deconstruct Brep

10Line 11Pipe

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*PLUGIN USED INSIDE GRASSHOPPER: KANGAROO.

STEP 1

STEP 2

IRREGULAR SPHERE PACKING To start, create a sphere (and later other elements such as box and breps to apply the algorithm).

Apply populate geometry on the desired element and use parameters kangaroo Solid point collide and sphere collide.

On Kangaroo point collide connect the geometry and its populated points and set true on inside so points will be inside the shape. Let strength around 1.0 1Sphere 2Brep

3Box 4Boolean Toggle

On sphere point collide, connect the populated geometry points, define a radius for the spheres and leave the strength no less than 1.0.

Use kangaroo solver to calculate results, apply both sphere collide and point collide on the goal objects and add a reset button to restart calculation when necessary.

Get the final resulting vertices as spheres. For a more interesting result, scale them so they will connect better. Bake it.

5Kangaroo Solid Point Collide 6Kangaroo Sphere Collide

After baking use boolean difference between the sphere (or box, brep), and the spheres from kangaroo to get the result.

Although possible to do boolean difference inside grasshopper it’s undesirable, heavy and generally may result in flaws.

Create an arch shape on rhinoceros, revolve it along its center to create a dome; revolve away from element to produce a toruslike shape; and finally extrude the arch to produce a simple curved shape. Now apply them inside grasshopper and reuse the plugin to produce different results.

7Populate Geometry 8Kangaroo Solver

9Area 10Scale

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*PLUGINS USED INSIDE GRASSHOPPER: LUNCHBOX, STARLING AND WEAVERBIRD.

STEP 1

STEP 2

STEP 3

For the regular sphere packing, bake the soheres and an extrusion of the initial rectangle. Apply boolean difference on them to get the result.

REGULAR SPHERE PACKING + NEGATIVE ELEMENT EXTRACTION Define a rectangle of same size and move it producing 3 layers of equal heights (keeping in mind a straight grid of even sides).

Create a double paramenter of Lunchbox Spacetruss Structure 2. Use the first with the middle and top rectangles, and the other with the bottom and middle. Apply the same uv grid for both parameters.

Remove the duplicate points (reduce accuracy of pattern a bit just for possible mistakes). Extract the points and create spheres of same radius on them.

1Rectangle 2Move 3Unit Z 4Lunchbox Spacetruss Structure 2

5Extrudde 6Remove Duplicate Points 7Points 8Sphere

Now to extract the negative 3d element between the spheres, use the same algorithm, selecting from a list item some spheres that produce the possible element, check the point list for faster analysis.

After selecting the elements find the center of all the elements with a line, divide the curve to get the middle point which is the center of the element Add a sphere of same radius as the others on it.

Do a solid difference from the external spheres to the inside sphere and visualize the negative element from it. A possible solution is another solid difference from a scaled sphere inside of it to reduce mass in the central area Instead, lets deconstruct brep and extract the external faces so produce a lighter element..

9List item 10Area 11Point List 12Divide Curve

Using a list item of multiple items, select all the external area and join it on a single brep.

For relaxation, turn the brep into an slFastMesh (starling) graft te brep, as the grid inside of it will give better results.

Apply Starling slRelax and define a slider to test relaxation of the element and see variation of iterations.

For a finer result use weaverbird join, add weaverbird thickness (for 3d printing purposes) and Catmull clark for extra smoothness.

13Solid Difference 14Deconstruct Brep 15Brep Join 16Starling slFastMesh

17Starling slRelax 18Weaverbird Join 19Weaverbird Thicken 20Weaverbird CatmullClark Subdivision

Marco Antonio Zoch Souza MSc.Digital Architecture & Robotic Construction

TUTOR _

Hunbai Jun

LSBU