DISTRIBUTED DIRECTIONALITY AD Research Cluster 1 The Bartlett
Bartlett • AD • RC1 Madalin Gheorghe Arianna Di Pasquale Zhihao Li Huaibo Han
Research Cluster 1 || Soomeen Hahm, Daghan Cam, Andy Lomas Team Members || Arianna Di Pasquale, Madalin Gheorghe, Huaibo Han, Zhihao Li
CONTENTS 01. INTRODUCTION 01.1 RESEARCH REFERENCES 01.2 NATURE
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02. DECISION MAKING PROCESS
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03. BRANCHING CHAIR I 03.1 OVERVIEW 03.2 MATERIAL DISTRIBUTION 03.3 VOXELIZATION STRATEGY 03.4 FINAL PROPOSAL
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04. BRANCHING CHAIR II 04.1 VOXELIZATION STRATEGY 04.2 FINAL PROPOSAL
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05. HIGH RESOULTION VOXEL FACADE 05.1 OVERVIEW 05.2 MATERIAL DISTRIBUTION 05.3 COMPOSITE TOWER 05.4 VOXELIZATION STRATEGI 05.5 FINAL PROPOSAL
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06. DEFORMED FACADE 06.1OVERVIEW 06.2 MATERIAL DISTRIBUTION 06.3 FINAL PROPOSAL
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07. EMERGENT SUBDIVISION I 07.1 OVERVIEW 07.2 CELL GENERATION 07.3 PAVILLION I GENERATION 07.4 PAVILLION II GENERATION 07.5 WALL GENERATION
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08. EMERGENT SUBDIVISION II 08.1 VECTOR FIELD 08.2 FORCES OF GROWTH 08.3 MULTIPLE SEEDS 08.4 SURFACE 08.5 WALL GENERATION 08.6 WALL PROPOSAL 08.7 FINAL PROPOSAL 08.8 FABRICATION METHOD
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DISTRIBUTED DIRECTIONALITY
Arianna Di Pasquale, Madalin Gheorghe, Huaibo Han, Zhihao Li The project investigates a material distribution system in order to fulfill structural and functional requirements together via continuous 3D extrusion printing technique. In order to inform the growth, a vector field is used to generate either structure and aesthetic of the case study design. The material deliberately used for the project is a flexible filament: this solution have been studied in order to obtain soft parts where needed (ergonomics or responding to the environment) and stiff parts (structure). The current scenario in which the project laid can be refered to nature in terms of heterogeneous design and variation of mechanical properties, especially, compression resistance and flexibility.
Compared to the macro-micro hierarchical study approach, the research for a lightweight lattice structure is focus on single cellular voxel that aggregate and create regional patches, which results invariation of shapes, sizes, and spatial distribution.
INTRODUCTION
01.1RESEARCH REFERENCE
The current state in which our industry lies in is dictated by mass production. This implies that in order to achieve outputs with complex behaviors we need to design assemblies of different parts with distinct functions. In nature on the other hand, things are grown from the same material that adapts its behavior and shape according to local conditions. The way nature congragates from the smallest unit in a hierarchical way can be well referred in our projects in terms of material distribution, function and aesthetics. Instead of taking time and cost to assemble different materials and components, our goal is to investigate a continuous material system by designing material behaviors in order to achieve variations of material performance via 3D space extrusion method. Different designer, especially with the develop of new technology and new tools, have been looking into nature system in order to generate their designs. Reference in this field could be the work of Lilia Van Daal with her Biomimicry 3D printed soft seat (2015) (1) that starting from observing how plant cell structures are made in the natural world, the designer was able to produce a chair that features different levels of flexibility using one single material, normal Nylon for 3D printing machines.
Firstly she studied different patches in order to obtain variable flexibility related to the structure of the patch itself, and afterwards that she placed, related to the needs, different variation of the same geometry in different parts of the chair. Using one single material, and modifying the disposition of the cells, Lilian Van Daal creates a soft seat able to embrace the human body in the back of the seat and in the seat itself, and four rigid legs, able to support the human body. As declared by the dutch designer, nature grows and create different functions, from structural to protection, using one only material, avoiding like this the discretization of the object itself: especially in the actual industry, pieces like sofas and chairs are created by different parts all glue together.
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1. Representation of many components of a knife 2. Lilia Van Daal, Biomimicry 3D printed soft seat, 2015 3. Neri Oxman, detail of Waterbase digital fabrication, 20142015
Pioneer of designing with nature, not only as an inspiration but as main fundamental, is probably Neri Oxman. In a public conference for Ted9 in 2015 the designer questioned herself about heterogeneity in nature, using as an example the human skin: “Our facial skins are thin with large pores. Our back skins are thicker, with small pores. One acts mainly as filter, the other mainly as barrier, and yet it’s the same skin: no parts, no assemblies. It’s a system that gradually varies its functionality by varying elasticity.” A representation of this theory is the project, Water-based Digital Fabrication Platform (2013-2014), made with her collaborators at Harvard and MIT for a 3,65 meter long structure made by one single material, called chitin, traceable in organisms such as shrimps, crabs, scorpions and butterflies. Oxman’s group “were able to generate structures that would seamlessly transition from beam to mesh” in one single material, biodegradable and made out from insects and shellfish.
Experiments such as Lilian Van Daal’s 3DPrinted chair and Neri Oxman’s structures made by chitin suggest a new vision of design using two different approaches to create objects not only made out from parts and compositions but from one single material: in both case the final production is actually a merging of natural design and human innovation suggesting an harmonious compromise between nature and human. Lilian Van Daal’s experiment, explores the possibility to create objects that can be really complex even if made out by one single material, opening new possibility especially for furniture design. The materials used by the designer, normal nylon for 3D printers, is extremely common and is adequate to embrace the human body and can act as a strong and stiff material as well, thanks to her experimentation.
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INTRODUCTION 01.2 NATURE
H E T E R O G E N E I T Y As happens in nature, mostly of the organisms that we know are made by few single elements that aggregates between them, thanks to small changes in their geometry and properties, that can create intricate patterns and at the same time complex structures. Nature is in fact able to generate organism that have differentiations in their properties using variation of the same material. Case study such as the lobster have been studied and imported in the design field for the property of the exoskeleton’s lobster to be stiff and soft in different parts in order to embrace the delicate body of the lobster. The carapace is made out by different segments: the ones that comprise the abdomen are not fused, but are connected to each other in such a way as to allow flexibility. The shell that protect the lobster is extremely stiff and at the same time very light and versatile. In this concept laid the project, focused on finding a method to create a new typology of structure, aesthetic and function, using one single geometry and material. A differentiation in the voxels arrangement and dimensions, creates different areas of density, that relates to the deliberate choice to have different stiff and soft parts, and the possibility to create a considerable range of aesthetic composition.
tor field extracted from topology optimization. Approaching the grow with different input, the results achieved are aesthetically intricate and complex in terms of material distribution result.
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The project investigates different input to control density, such as manipulate vec-
6. Macro photograph of a Starfish 7. Macro photograph of a Starfish 8.Macro photograph of a Fungi
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The project move around the concept of flexibility, the main material used along all the year of research. The use of flexible material is related to the first approach of the project, that wanted to investigate the role of a chair. Considering the actual scene of the design and architecture industry, most of the object are made by different typology of materials, aggregated and composed together in order to obtain one single unit. However, as a initial research, a chair seemed a good example to speculate in discrete and variation of properties. Chair such as Lilia Van Daal Biomimicry 3D Printed Soft Seat has been a reference in order to understand how one single object could achieve flexibility (in terms of ergonomic) and structure at the same time, using one single material, in this case Nylon, in our case Flexible Filament.
More specifically, the voxels, considered as a cell, have been researched and studied during all the process, with three different fitness values: deformation in X,Y,Z direction, number of connection inside the voxels and between the other cells. These values, helped us to find a single cell that, related to its direction, could be structural where needed and flexible and able to embrace the human body on the surface.
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The reference for all the projects is nature: in fact, plants are organism that can stand and be stable and at the same time flexible and malleable in order to respond to environment, for example reacting to wind. In order to achieve an object that needs to be comfortable and responds to ergonomics and have a structure at the same time, we started to investigate the concept of cell and how this cell relates to other cells.
9. Macro photograph of a Sunflower 10. Cross section of a plant cell
INTRODUCTION 01.2 NATURE
D I R E C T I O N A L I T Y Directionality has always been a reason of researches during all the year research. All the cases studied tried to focus their application in how to better translate in geometry what firstly the agent’s result and lastly the growth. During the strategy, the main goal was to capture directionality without loosing high resolution quality and complexity in the structure. As nature teaches us in every organisms that she produces, the directionality of growth is clear and is the pin around which the whole shape and form finding process is created. As we are able to see in leaves and flowers, the veins that bring nourishment from the soil to the extreme point of the organism are visible and along them all the shape is created. There are many factor that can influence the directionality of growth within a surface: for instance, placing the initial seed in different position in the same vector field, can creates different results. Once the first seed is placed and is growing, its follows the direction of the nearest vectors in an organic and smooth way. However, in order to capture properly directionality, is necessary emphasise it setting some rules. One of these rules is related to the growth in height of one vein where more forces are acting in the same time.
acting in order to make it more visible. In this way the directionality is capture not only visually but creates a depth that can be fundamental for the structural parts (910).
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When two edges are attracted by each other and collapse, a new vain is created and a force that push them in height is
9. Pavilion II, detail 10. Pavilion II, detail
DECISION MAKING PROCESS
BRANCHING CHAIR I
VOXEL FACADE
BRANCHING CHAIR II
Small Scale Design Agent Based System
I TERM
DEFORMED FACADE
EMERGENT SUBDIVISION II
EMERGENT SUBDIVISION I
Large Scale Design Cellular Growth System
II TERM
III TERM
BRANCHING CHAIR I
BRANCHING CHAIR II
VOXEL FACADE
DEFORMED FACADE
EMERGENT SUBDIVISION I
EMERGENT SUBDIVISION II
BRANCHING CHAIR I 03.1 OVERVIEW
A simple algorithm records the distance between the trails of the agents and the center of each voxel. If the distance is larger than a certain parameter, then the voxels are turned inactive. If the distance is smaller, then the voxels are categorized as active. The distance between the center of the voxel and the closest trail point will influence the thickness of the geometry inside the voxel, creating a continuous differentiation. The closer the voxel is to the trail point, the thicker the geometry inside it. The thicker the geometry, the more structural the voxel becomes, but at the same time less flexible. The reason of differentiating the geometry is to create structural veins surrounded by flexible cells.
Detailed View of Branching Chair I
BRANCHING CHAIR I
03.2 MATERIAL DISTRIBUTION - AGENT BASED SYSTEM In order to achieve directionality and the overall shape of the chair, two values are taken into consideration: a mesh, which is derived from a 3d model of a sitted human body, and an agent based system that starts from randomly selected vertices of the mesh and advances towards the floor. The agent based system is manipulated by gradually increasing the cohesion range of the agents with the passing of time. This results into a structure that resembles the inverse of a branching algorithm.
Voxalized Chair
Agents Trail Curves
BRANCHING CHAIR I
03.2 MATERIAL DISTRIBUTION - AGENT BASED SYSTEM Agents are running into a box with precise dimention in X, Y and Z axes. The values took in consideration could be included in a range for each force used. Cohesion Range | 0.5 to 15 Cohesion Strenght | 0.5 to 15 Separation Range | 0.5 to 5 Separation Strenght | 0.05 to 10 Alignment Range | 20 to 200 Alignment Strenght | 0.001 to 0.01 Max Speed | 0.1 to 1 Gravity Z | 0.1 to 100
Case Study A Case Study B
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dimX = 90 | dimY = 90 | dimZ = 120 cohesion range = 10.75 cohesion strength = 0.16
dimX = 90 | dimY = 90 | dimZ = 120 cohesion range = 9 cohesion strength = 2
separation range = 1.4 separation strength = 10
separation range = 1 separation strength = 0.05
alignment range = 20 alignment strength = 0.06
alignment range = 120 alignment strength = 0.8
max speed = 0.4 gravity = 15
max speed = 0.6 gravity = 0.1
BRANCHING CHAIR I
03.2 MATERIAL DISTRIBUTION - AGENT BASED SYSTEM
Frames Captured From Simulation
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C dimX = 90 dimY = 90 dimZ = 120 cohesion range = 10.75 cohesion strength = 0.16 separation range = 1.4 separation strength = 10 alignment range = 20 alignment strength = 0.06 max speed = 0.4 gravity = 15
BRANCHING CHAIR I
03.2 MATERIAL DISTRIBUTION - AGENT BASED SYSTEM
D dimX = 90 dimY = 90 dimZ = 120 cohesion range = 9 cohesion strength = 2 separation range = 1 separation strength = 0.05 alignment range = 120 alignment strength = 0.8 max speed = 0.6 gravity = 0.1
BRANCHING CHAIR I
03.3 VOXELIZATION STRATEGY Considering the concepts of variation in stiffness and flexibility, the cell study firstly explores the relationship between line thickness inside the geometry and the voxel stiffness. The cell used at the very beginning is the simplest unit, created by connecting all vertexes in diagonals with a small inside volume.
Low Pipe Thickness Cell 0.10 | 0.50
By only changing the size of the volume of material inside one cell as is shown, it is clear that the larger the inner volume, the stiffer is the cell. Inversely, the less is the volume, the more flexible the cell appears to be. The material properties will always be intensified when many single cells congregate together. In nature, that is how cells gather into tissue. Based on the study of single voxel, the approach adopted to generate a chair with three layers remains to place stiffer cell closest to the main structural curves.
Medium Pipe Thickness Cell 0.10 | 0.50
High Pipe Thickness Cell 0.10 | 0.50
Voxel Placement according to curves extracted from the trialpoints of the agents
ATTRACTOR CURVES Curve extrected from the trialpoints generated by agents
VOXELS Voxels generated along the attractor curves
SPECIALIZED CELLS Specialized cells applied to each voxels
BRANCHING CHAIR I 03.4 FINAL PROPOSAL
Front and Back View of Branching Chair I Prospective View of Branching Chair I
BRANCHING CHAIR I
BRANCHING CHAIR II
VOXEL FACADE
DEFORMED FACADE
EMERGENT SUBDIVISION I
EMERGENT SUBDIVISION II
BRANCHING CHAIR II 04.1 VOXELIZATION STRATEGY
After testing how the cells could be organized in relation of their volume size and in terms of flexible perfomance, the project Branching Chari II concentrates the strategy on varying two other fitness values: density and proximity. Branching Chair II records the number of points in each voxel, thus the density. This strategy is more complex, as it varies both the thickness and the geometry of the cells. The first part of the algorithm categorizes the voxels as being active and non-active according to their density. The proximity towards the trail points indicates the thickness of the geometry and the density defines the geometry.
The denser the field, the geometry is more stiff and structural, the further away, the geometry becomes more open and thus more flexible. The final structure is the result of a negotiation between the cell shape and its thickness. This translates into an almost infinite number of variations of the cells which adapt in order to create a continuous macrostructure. Density (A): variation of volume related to density values extracted from the agents based system Proximity (B): variation of volume related to proximity to a curve extracted from the agents trial points.
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Phase 1
Phase 2
ATTRACTOR CURVES Curve extrected from the trialpoints generated by agents
DENSITY MAPPING Analyze and map the more and less dense parts of the design along attractor curves
SPECIALIZED CELLS Specialized cells applied to each voxels
BRANCHING CHAIR II 04.2 FINAL PROPOSAL
Front and Back View of Branching Chair II Prospective View of Branching Chair II
BRANCHING CHAIR I
BRANCHING CHAIR II
VOXEL FACADE
DEFORMED FACADE
EMERGENT SUBDIVISION I
EMERGENT SUBDIVISION II
HIGH RESOLUTION VOXEL FACADE 05.1 OVERVIEW
The project now switches from a small scale design to a large scale design, moving from furniture to architecture. The choice was to analyzed a facade. As first approach, a different series of facade are developed using agents form finding method, after setting different parameters, such as different percentage of open parts along the surface. Afterwards the solutions have been mixed together in order to have a more functional and satisfying design. Lastly, the voxel grid has been populated with three different types of voxels, each one with different geometry and flexibility. The agents drop along the surface of the building avoiding fixed particles in order to create void spaces, suitable for windows. Once the different levels of density have been setted, the voxels are placed in the surface analyzed.
Detail of High Resoluation Voxel Facade
Detail of High Resoluation Voxel Facade
High Resoluation Voxel Facade
HIGH RESOLUTION VOXEL FACADE
05.2 MATERIAL DISTRIBUTION - AGENT BASED SYSTEM Different case studies have been taken into consideration in order to create the final facade. Each of them has been studied in terms of porosity for light. Agents form finding values: number of agents = 200 cohesion strength = 0.18 cohesion range = 8 separation strenght = 0.1 separtion range = 7 max speed = 2 gravity strength = 4.5 predator range multiplier = 1.25 Case Study I Case Study II Case Study III Case Study IV Case Study V Case Study VI
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HIGH RESOLUTION VOXEL FACADE
05.2 MATERIAL DISTRIBUTION - AGENT BASED SYSTEM
Case Study I
Different Case Study
Case Study II
Case Study III
Case Study IV
Case Study V
Case Study VI
HIGH RESOLUTION VOXEL FACADE 05.2 MATERIAL DISTRIBUTION - DENSITY MAPPING Agents form finding values: number of agents = 200 cohesion strength = 0.18 cohesion range = 8 separation strenght = 0.1 separtion range = 7 max speed = 2 gravity strength = 4.5 predator range multiplier = 1.25
Case Study I Case Study II Case Study III Case Study IV Case Study V Case Study VI
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HIGH RESOLUTION VOXEL FACADE 05.2 MATERIAL DISTRIBUTION - DENSITY MAPPING
Case Study I
Different Case Study
Case Study II
Case Study III
Case Study IV
Case Study V
Case Study VI
HIGH RESOLUTION VOXEL FACADE 05.3 COMPOSITE TOWER V
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Case Study IV
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Voxel Organization
Voxel Placement
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HIGH RESOLUTION VOXEL FACADE 05.3 COMPOSITE TOWER
High Density - Voxel Typology I Med Density - Voxel Typology II Low Density - Voxel Typology III
Agent Trial Curves
Density Mapping
Voxels Organization along density mapping (dense to low dense)
Voxels Placement
Composite Tower
HIGH RESOLUTION VOXEL FACADE 05.3 COMPOSITE TOWER Frame 1
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HIGH RESOLUTION VOXEL FACADE 05.4 VOXELIZATION STRATEGY - RESEARCH During the year many typology of voxels have been studied in order to obtain the ideal voxel. Many factors have been taken in consideration, such as: Pipe Thickness Number of Connection Deformation in X, Y and Z axes. In particular, the variation of flexibility derives from several factors. The first factor is connection between cells. The cell with more connections is stiffer than the one with few connections. And the amount of connections derives from the position of this ones, for instance, the points from corners will definitely have more connections than those from surfaces. Another factor is the ratio of central geometry. The lower the ratio of width to height, the more flexible the cell is.
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The cell analizyed in High Resolution Facade (3) is made of 8 small units mirrord 3 times. By picking points from corners, edges and surfaces of each voxel and connecting each two points, the voxel achieves variation of flexibility thanks to its geometry. 3
1. Simple Voxels 2. Interlocking Voxels 3. Descrete Voxels 4. Exagonal Voxels
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1.1 Face Voxel
1. 2 Octagonal Voxel
3.1 Discretize Voxel
4.1 Exagonal Voxel
1. 3 Tetraedron Voxel
1. 4 Spring Voxel
1. 5 Interlocking Voxel
HIGH RESOLUTION VOXEL FACADE 05.4 VOXELIZATION STRATEGY - GEOMETRY
Generation of the discretize Cells Flexible Cell
Semi-Flexible Cell
Stiff Cell
c1: 10 connections e1:Flexible 4 connections Cell s1: 4 connections 10 connections s2:c1: 4 connections
c1: 16 connections e1: 6 connections Semi-flexible Cell s1: 4 connections c1: 4 16connections connections s2:
c1: 6 connections e1:12 connections Stiff Cell s1: 6 connections c1:46 connections connections s2:
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EXPLOSION
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HIGH RESOLUTION VOXEL FACADE
05.4 VOXELIZATION STRATEGY - TOOLPATH FOR FABRICATION In order to print the project using 3D spatial extrusion with robotic fabrication, a toolpath has been studied and illustrated. The complexity of the cells in terms of geometry make the printing a slow process, that could be optimized creating a toolpath that follows exactly the geometry and the process behind the design of each voxel. A. Flexible Cell B. Semi-Flexible Cell C. Stiff Cell
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HIGH RESOLUTION VOXEL FACADE
05.4 VOXELIZATION STRATEGY - PHISICAL TESTS ON FLEXIBILITY In order to test the different capacity of the cells to be flexible or stiff under setted condition, the group has done different experiment either physical either digital.
Flexibility in X axe
Flexibility 25 %
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Flexibility 33 %
Flexibility in Y axe
Flexibility 7 %
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Flexibility 33 %
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Digital Simulation
Flexible Cells | X, Y, Z
Semi-Flexible Cells | X, Y, Z
Stiff Cells | X, Y, Z
Phisical Simulation
HIGH RESOLUTION VOXEL FACADE
05.4 VOXELIZATION STRATEGY - STUDY OF THE PATTERN
Study of the pattern for a part of the facade
HIGH RESOLUTION VOXEL FACADE
05.4 VOXELIZATION STRATEGY - STUDY OF THE PATTERN
Study of the pattern for a part of the facade
HIGH RESOLUTION VOXEL FACADE 05.5 FINAL PROPOSAL
Back View
Bottom View
Front View
HIGH RESOLUTION VOXEL FACADE 05.5 FINAL PROPOSAL
Details Render of an interior with High Resolution Facade applied
Render of an interior with High Resolution Facade applied
BRANCHING CHAIR I
BRANCHING CHAIR II
VOXEL FACADE
DEFORMED FACADE
EMERGENT SUBDIVISION I
EMERGENT SUBDIVISION II
DEFORMED FACADE 06.1 OVERVIEW
As part of the new strategy shift which implies robotic extrusion and the increase in scale, the voxel field is deformed. The purpose of this strategy is to better approximate the directionality and orientation of the agent based system. By orienting the voxels along the trails of the agents, their orientation is more likely to coincide with the strains of the forces that pass through the structure. The deformation occurs between specified parameters and it is achieved by creating an additional vector field based on the density of the voxel field. The point of view is switched from a rectangular grid to a non-euclidean geometry, ruled by the application of a magnetic field, where the magnets are no longer points but pipes, the same pipes created by the agents in the design process.
Detail of Deformed Facade
DEFORMED FACADE 06.1 OVERVIEW
I Deformed Grid along Trialcurves
II Deformed Grid along Trialcurves
DEFORMED FACADE 06.1 OVERVIEW
The first approach in order to understan the deformation is based on the use of some planes: these are distributed in all the Z direction of the curve, and using a precise value they deformed near the attractor curves. The value that rules the deformation is the necessity to define structural and aesthetic variation.
Ideal Deformation Value
Low Deformation Value
Deformed Grid along Trialcurves
High Deformation Value
DEFORMED FACADE
06.2 MATERIAL DISTRIBUTION - AGENT BASED SYSTEM Using the agents as main attractors, the facade is developed in different steps, from the analysis of the density to the vector field. Lastly, the design is collocated inside a regular grid, that is deformed following the main strategy, in order to produce the final resault. Agents form finding values: number of agents = 200 cohesion strength = 0.18 cohesion range = 8 separation strenght = 0.1 separtion range = 7 max speed = 2 gravity strength = 4.5 predator range multiplier = 1.25
Agent Trial Curves
Composite Tower
Density Mapping
Vector Field
Grid Deformation
Geometry Deformation
DEFORMED FACADE
06.2 MATERIAL DISTRIBUTION - AGENT BASED SYSTEM High Density Low Density
Agent Trial Curves
Density Mapping
Vector Field
Grid Deformation
Geometry Deformation
Composite Tower
DEFORMED FACADE 06.3 FINAL PROPOSAL
Deformation in Y Direction Deformation in X Direction
Low and High Level of Deformation - Deformed Facade
DEFORMED FACADE FINAL PROPOSAL
BRANCHING CHAIR I
BRANCHING CHAIR II
VOXEL FACADE
DEFORMED FACADE
EMERGENT SUBDIVISION I
EMERGENT SUBDIVISION II
EMERGENT SUBDIVISION 07.1 OVERVIEW
The project investigates a system in order to generate geometry and the aesthetic, and then translates it into the fabrication method using a precise strategy: cellular growth in order to create voxels population. In order to inform the growth, a vector field is used to generate either structure and aesthetic of the case study design.
EMERGENT SUBDIVISION OVERVIEW
Pavilion I
Detail, Pavilion I
EMERGENT SUBDIVISION 07.2 CELL GENERATION
Inorder to achieve unconstrained orientation and break free from the rigidity of a rectangular voxel field, we opted for a botom-up approach in which we employ growth instead of manipulation. The FEM method provides the environment for growth. In other words, growth is directed by vector field coming from the FEM. Below is an illustration of the basic principles for the growth algorithm (1). In order to perform an initial test of my assumptions, we reduced the problem to two dimensions, for simplicity. After testing the rules of the algorithm, we started testing by modeling it manually (2). A. The seed cell is already oriented according to the vectors’ directions B. Its verices are moved outwards from the center. When the edges get large the cell splits into 4.
(1) Explenation of the iteration
C. In order to provide freedom of orientation, sometimes the cells split in less than 4 and trangles appear. D. The cells are growing at an almost exponential rate E. If the cellular structure reaches the end of the vector field, it stops growing. F. The structure seems to create small rows of cells between other rows, which help approximate the directionality better. G. The bottom right corner seems to become denser. Probably because the amplitude of the vectors decreased. H. The bottom right corner is denser, and the cells are elongated. I. The structure seems to capture the directionality of the vector field, but it is denser in the area of least force.
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(2) Manual Testing of the Algorithm
EMERGENT SUBDIVISION 07.2 CELL GENERATION
1. The algorithm adapts to the vector field by creating rows of cells betwen other rows of cells. This is a key feature that helps break free from the constrained uniform grid. Viewed from a computer graphics perspective,it’s safe to say that the 3D mesh topology is nonuniform. 2. The directionality is achieved, but the density is smaller where one would normally expect the contrary. This is because the amplitude of the vectors is directly proportional to the stress. By creating an inverse proportional relationship, higher density could be achieved in the areas with more stress.
3. The denser part is the one with less stress. Also because of the big difference of amplitude between the perpendicular vectors, the cells are grown elongated. This relationship should probably be adjusted so that fabrication constraints can be met. This will be decide after doing physical prototypes.
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EMERGENT SUBDIVISION DATA STRUCTURE
The data structure is important, as it defines the relationship between the different elements. The main elements are: vertices, vertex clusters, edges, faces and cells. Vertices represent the locations of the points. Vertex Clusters represent collections of points. When two points are very close to eachother, they snap together in the same Vertex Cluster. Vertex Clusters control the movement of the Vertices. Edges are collections of the two endpoints that define a line. Each edge has an axis, “X“, “Y“, “Z“..
Face are collections of 4 edges and 4 vertices. Each face has an axis “X“, “Y“, “Z”. Faces can have either one cell parent , meaning they are on the surface of the structure, naked or two cell parents, meaning they are inside the structure. Cells are collections of 6 faces, 12 edges and 8 vertices. The data structure is comprised of 2 faces with axis “X“, 2 with axis “Y”, 2 with axis “Z”, 4 edges with axis “X”, 4 edges with axis “Y”, 4 edges with axis “Z”. Cells are deformable to such degree that one of the faces becomes degenerate, resembling a line or apoint. The data structure always remains the same.
Data Structure
EMERGENT SUBDIVISION
07.2 CELL GENERATION - MOVEMENT The movement of the Vertices is controlled by the Vertex Clusters. The movement directions are inherited from the vector field. Step 1. Compute the normal vector, perpendicular to the Face and pointing outwards. This is performed for naked faces only. Step 2. Find the analog vector in the vector field by analyzing the voxel in which the center of the Face belongs to. Each voxel stores a “X“, “Y“ and “Z” vector. Step 3. Assign the appropriate vector to each naked Face. If the Face axisis “X”, pick the “X” vector from the voxel. Then compare them to make sure the pointing direction is not opposite to the normal. Step 4. Add all the vectors of the parent Faces each of the child Vertex of each naked Vertex Cluster. Normalize the vector magnitude to the mean magnitude of the added vectors. Then move.
Step 1
Step 2
Step 3
Step 4
Iteration 1 - 2 - 3
Iteration 4 - 5 - 6
Iteration 7 - 8 - 16
Iteration 24 - 32 - 40
EMERGENT SUBDIVISION
07.2 CELL GENERATION - EDGE COLLAPSING The convergence of vectors produces unwanted cell intersections and small edges. This results into a messy geometry. The small edges can also cause problems for fabrication especially if the preffered manufacturing technique is 3D printing by robot spacial extrusion. This is mainly because the extrusion nozzle will collide with the neighbor geometry. Taking into acount these reasons the next step is to introduce the second feature of the growing, which is colapsing edges. The edge lengths are checked every iteration. When one of the edges has its length smaler than a treshold, it send points snap togetherto the same position, becoming children of a common Vertex Cluster. The edge is not deleted, it is still accounted in the data structure. This helps keep the grid organized in rows and columns, a feature that will prove helpful when sorting the printing path for the robotic extrusion.
2. The collapsing of edges inside accounts for a less constrained arrangment of cells. By accounting the collapsed edges in the data structure, the unconstrained arranment is kepts sorted in rows and collumns. Aesthetically it creates branching structure. In the examples (3) below the branching structures reveal how they acommodate a regular grid that rotates 45 degrees from left to right. Notice the branches are slighlty diferent, but the general patterns are almost the same. This is probably due to the constant density.
1. The collapsing of the naked edges ensures a good density of faces and vertices, which is vital for the developement of the growth. The growth vectors areas signed only from the faces with two or more uncolapsed edges.
Edge Collapsing
(3) Branching structures
EMERGENT SUBDIVISION ALGORITHM SPLITTING
The grid of cells is organized in rows and columns. Each Cell has two identification numbers that represent its position in rows and columns. Step 1. The process of splitting is done in rows and columns. It starts by analyzing the lengths of the edges contained by the naked cells. In this case, a cell is naked if its position is either first or last in any row or column. Step 2. Each face is given a score depending on the lengths of its edges. The face with the highest score, that passes al conditions of spliting is chosen as a starting point in the splitting process.
Step 3. Depending on the face orientation, the splitting will take place in a row or a column. Once the splitting face is decided, al list of all the cells inside the row or column is assembled. Similar to nature, the cells receive a signal to prepare for reproduction. Step 4. Each of the cells that have been chosen for splitting will duplicate its DNA. In this case, the DNA of the cells is comprised by its relations with its neighbors, and its internal data structure comprised of Faces, Edges and Vertices. After this is done, a function checks the new DNA for mistakes, repairing it where possible. When the checking is complete, the cells split into two.
Step 1
Step 2
Step 3
Step 4
Splitting Process
EMERGENT SUBDIVISION 07.2 CELL GENERATION
In order to control the density of the grid, an atraction force was introduced. When two vertices are closer than a treshold to each other, they are attracted one to the other. This paired with the variation in the collapsing treshold created the following results: the less the grid collapses, the less homogeneous it becomes. By varying the two parameters dense parts of the grid can be emphasized.
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The orientation of the grid is becomes more visible if one sees the two directions separately, as ilustrated below. This feature can become interesting when one orientation is more visible to one side and the other on the other side of the grid.
Snaptreshold Force 0.02
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0.002
Attraction Force 0.0002
0.000002
Variation of different forces combined together
EMERGENT SUBDIVISION 07.2 CELL GENERATION
In order to control the density of the grid, an atraction force was introduced. When two vertices are closer than a treshold to each other, they are attracted one to the other. This paired with the variation in the collapsing treshold created the following results: the less the grid collapses, the less homogeneous it becomes. By varying the two parameters dense parts of the grid can be emphasized. The orientation of the grid is becomes more visible if one sees the two directions separately, as ilustrated below. This feature can become interesting when one orientation is more visible to one side and the other on the other side of the grid.
Growth in X
Growth in Z
Growth in Both Direction
Cellular Growth
Frame 1, Growth in Both Direction
Frame 20, Growth in Both Direction
Frame 60, Growth in Both Direction
Frame 100, Growth in Both Direction
Frame 20, Growth in Both Direction
Frame 40, Growth in Both Direction
Frame 80, Growth in Both Direction
Frame 120, Growth in Both Direction
EMERGENT SUBDIVISION 07.2 CELL GENERATION
Position A, Growth in Both Direction
Position B, Growth in Both Direction
Position C, Growth in Both Direction
EMERGENT SUBDIVISION FORCES OF GROWTH
Growth in Both Direction Diagonal Vector
Laplacian Vector
Attraction Vector
Smooth Edges Vector
Cell Center
EMERGENT SUBDIVISION 07.3 PAVILION GENERATION I
Frame 20, 40, 80
Frame 120, 140, 160
Frame 180, 200, 260
Frame 180, 200, 260
Growth in X Growth in Y Mesh
Frame 450
EMERGENT SUBDIVISION 07.3 PAVILION GENERATION I
Pattern, Pavilion I
Detail, Pavilion I
EMERGENT SUBDIVISION 07.3 PAVILION GENERATION I
EMERGENT SUBDIVISION 07.4 PAVILION GENERATION II
As nature express especially in trees, structures are often negotiation between dense parts and lose ones. The same strategy has been adopted for the pavilion designed: the growth starts in fact from the bottom part of the pavilion, in order to create a cantilever structure able to stand without any support. The result is a branching shell structure more dense where the structure is more stressed and less growing in hight. Once the vector field is imported, with the relative boundary of grow (in this case a mesh modelled in Rhinoceros) the cellular grow creates its own topology, moving according to vectors that influence the process since the beginning. The growth is controlled by the vector field and by internal forces, controlled in order to obtain precise dense areas related to the necessity of having resistant parts or not.
Frame 60, 120, 180, 200
Frame 60, 120, 180, 200
Frame 220, 240, 260, 380
Frame 400
EMERGENT SUBDIVISION 07.4 PAVILION GENERATION II
Top View
Single Module
Module Aggregation
EMERGENT SUBDIVISION 07.4 PAVILION GENERATION II
Pavilion I
EMERGENT SUBDIVISION 07.5 WALL GENERATION
Frame 50, 80, 100
Frame 120, 140, 160
Frame 180, 200, 210
Frame 220, 240, 250
Growth in X Growth in Y Mesh
EMERGENT SUBDIVISION 07.5 WALL GENERATION
BRANCHING CHAIR I
BRANCHING CHAIR II
VOXEL FACADE
DEFORMED FACADE
EMERGENT SUBDIVISION I
EMERGENT SUBDIVISION II
EMERGENT SUBDIVISION II
EMERGENT SUBDIVISION II 08.1 VECTOR FIELD
Study of different Vector Fields. Different factors have been taken into consideration in order to create the vector field, with consequentely different impacts: I. Positive Charge, Negative Charge (70%) Perlin Noise (30%) II. Positive Charge, Negative Charge (50%) Perlin Noise (50%) III. Positive Charge, Negative Charge (30%) Perlin Noise (70%)
I
II
Study of Vector Fields
III
EMERGENT SUBDIVISION II 08.2 FORCES OF GROWTH
Attraction Angle 15
Attraction Angle 25
Attraction Angle 45
Multiplier 0.5 - 1.0
Multiplier 1.0 - 1.0
Multiplier 1.0 - 0.5
EMERGENT SUBDIVISION II 08.3 MULTIPLE SEEDS
In order to control more the growth, the algorithm has been modified and a snapping fore between two cells has been introduced. In this way, the design can be made out different seeds on a mesh.
Cell A
Cell B
Growth Of 2 Cells Simultaneously
Frame 100, 180, 300
Frame 300, Grwoth in Z
Frame 300, Grwoth in X
EMERGENT SUBDIVISION II 08.4 TEST ON SURFACE
Frame 20, 60, 110
Frame 120, 150, 175
Frame 255
Case Study I
Frame 20, 60, 110
Frame 20, 60, 110
Case Study II
EMERGENT SUBDIVISION II 08.5 WALL GENERATION
Starting Points - Point Charge Starting Point 1= 12876 Starting Point 2 = 17512 Starting Point 3 = 13220 Starting Point 4 = 6569 Starting Point 5 = 3154 Starting Point 6 = 3295 Starting Point - No Point Charge Starting Point 7 = 9994 Starting Point 8 = 9948 Starting Point 9 = 18570 Starting Point 10 = 12282 Move Angle = 15 Smooth Rows X = 6 Smooth Rows Z = 6 Laplacian Rows = 3 Attraction Angle = 15 Maximum distance from Mesh = 0.1 Initial Cell Edge = 2 Max Cell Edge = 3 Min Cell Edge = 1
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Starting Point
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9 10
Frame 80, 240
Frame 580, 1170
EMERGENT SUBDIVISION II 08.6 WALL PROPOSAL
EMERGENT SUBDIVISION II 08.6 WALL PROPOSAL
EMERGENT SUBDIVISION II 08.7 FINAL PROPOSAL
As a final mesh, the project moved into a complex surface that is actually modular. The single module (I) is composed by 6 surfaces, that if mirrored can compos a bigger module, actually inscrivibile in a cube. Once the cube is composed, it could be composed with other modules by mirroring along the diagonal or along the edge, creating like this a complex and continuos structure (II).
I. Single Module
II. Mirroring strategy
Double Module
EMERGENT SUBDIVISION II 08.7 FINAL PROPOSAL
Double Module, render
EMERGENT SUBDIVISION II 08.7 FINAL PROPOSAL
Multiple modules, Pavillion
EMERGENT SUBDIVISION II
08.8 FABRICATION METHOD
Despite the normal limitations of classic 3D printing technologies, in recent years there have been a lot of examples coming from academia in which a number of people have translated FDM-like printing processes to robots. Gramazio and Kohler’s Mesh Mould Research Project at ETH Zurich (2012-2014) creates a lattice like structure as a reinforcement for a load bearing wall by spatially extruding molten plastic. Filametrics, a project completed at Bartlett, UCL by the RC4 design cluster directed by Giles Retsin and Manuel Jimenez Garcia (2), is a 3-meter 3D printed space-frame like structure. Other examples include Dirk Van Der Kooijs Endless Chair, AI Build(1).
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Robots offer the advantage of scale and they allow the designer to investigate design methods without needing to develop a custom machine for the 3D printing. Typical 3d printing processes are characterized by layered approach which attracts a variety of constraints like stability of material, overhangs or self-intersections. Spatial extrusion is a process where a robot arm extrudes plastic in the air rather than in horizontal layers. The most obvious advantage of this strategy is speed of printing. Nevertheless, it does not come without constraints, but they are used as drivers in the design process.
3. 3D printing test 4. Detail, 3D printing test 5. Nozzle 6. IO System for Nozzle
During the year, the fabrication approach has been changed and modified in relation with the design process. The benefit of Emergent Subdivision in terms of fabrication, are different. By employing a bottom up approach as growth instead of manipulation, we achieve a heterogeneous distribution of material in a matrix field that is oriented according to the directionality of a vector field. During the growth process, the algorithms containing the constrains from the fabrication should be programmed to ensure that the design result will be printable by robotic spatial printing. The geometry design of the heterogeneous voxel should be adapted to spatial printing to make the tool path continues and be collision free. Thus, we simplify the geometry of voxel by decreasing the connections of struts and the common structs of voxels.
and limits from articulated singularities and articulated robot joint angles. Therefore, I made a matrix of different tool paths to printing the same geometry and checked which would be the best parameter for the general printing. After that, a loop is created in Grasshopper to check any possible collision and robot singularities, then modify defective position. The loop will end when the whole structure can be printed without any collision. The thermal control and the optimized speed settings of robot will accelerate the printing process. The temperature and speed of robot are crucial for the quality of the printed result. The statistic from preview printing help me to get the functions for temperature changing. Basing on this function, is possibile to achievethe minimum printing time for each voxels.
The nozzle design is needful for avoiding collision with existing obstacles and selfcollision during the fabrication. The previews references point out the robot end effector should be as small as possible to reduce its impact for the existing structure. So, we increase the nozzle’s length and decrease the radius to minimalize effective influence of the nozzle. We need the algorithms for controlling the performance of melted material. Meanwhile, the algorithms are requisite to avoid collisions with existing obstacles
Fabrication Process
DISTRIBUTED DIRECTIONALITY AD Research Cluster 1 The Bartlett
Bartlett • AD • RC1 Madalin Gheorghe Arianna Di Pasquale Zhihao Li Huaibo Han