Beyond Prototype is an advanced digital fabrication seminar developed at Columbia University Graduate School of Architecture Planning and Preservation by Jason Ivaliotis and Nicholas Kothari. This course focuses on the development of hybridized, folded meshes that simultaneously serve as both structure and building envelope. Students develop parametrically controlled tessellations and transform them into building component systems that can be built using conventional sheet stock materials. These tessellated systems are extracted from the digital realm and built at full scale.
The relationship between the components of structure and the components of enclosure is conventionally considered to be mutually exclusive. However, in an environment where material efficiency and speed of fabrication is becoming more important, there exists an opportunity for the architect to intervene within the fabrication process to assimilate both structure and envelope into one hybridized system. Beyond Prototype students study the complexities of transforming non-uniform NURBS geometry with superimposed surface tessellation into a three dimensional network. This generative process is employed as a strategy for developing new architectural component systems that are composed of folded elements. Students use Rhino and Grasshopper to devise automated design and fabrication processes. Instruction focuses on using Grasshopper to create parametric and environmentally responsive cellular networks and prepare this digital geometry for fabrication.
Beyond Prototype enables students to use digital software as a generative, parametric tool and the laser cutter, CNC Mill, plastic bender and welder as a means to bring virtual systems into the physical realm. Students use these machines to extract forms from conventional, acrylic or aluminum sheet stock that can be transformed using cutting, bending and fold manipulation to create a topological network of elements: a homogenous, self-supporting mesh. In this manner, complex systems are formed from simple surfaces and building structure is obtained from non-structural materials. Specific emphasis is placed on the use of multiple systems of geometry within the same cellular network in order to discern elements of surface and elements of connection. As a result, students are able to explore and design a complex, homogenous mesh of a single material that performs efficiently as both structure and enclosure.
The research objectives of this course encourage students to devise functional design applications, establish contextual relevance for their component systems and propose realistic, fabrication scenarios based on quantifiable material and mechanical constraints. Components are extracted from the digital realm; built at full scale; tested and reevaluated, effectively taking us Beyond Prototype.
Phase I - Analogue Modeling
The first component of Beyond Prototype focuses on the generation of a tessellated surface by employing analogue modeling techniques. Each design team creates a two dimensional grid of polygonal patterns to organize their cellular network. The base grid is printed on a single sheet of paper and through experimentation with techniques of cutting and folding, they formulate a strategy for bending this single surface into a rigid three dimensional mesh.
Phase II - Parametric Modeling
Using Rhino as a generative platform, each design team creates a NURBS surface or object that will serve as the overall form for the final project. Students are required to propose a practical application for this surface which will help drive its form, such as a pavilion design, shell system or building façade. Using Solid Works each team performs a finite element analysis on the surface to analyze structural deficiencies within the overall form to ascertain where cellular variation will be needed for rigidity. The folded cell developed within the analogue models is recreated within the digital environment. Using the parametric tools of Grasshopper, each team formulates a strategy for superimposing their 2D base grid onto the 3D surface model and creating a parametric component system by mapping the folded cell onto the overall surface. The objective is to create a skin/structural hybrid where the cellular surface is able to achieve structural rigidity through tessellation, a variable network of rigid folds and a three dimensional system of connections.
Phase III - Prototyping and Fabrication
Each team identifies a significant formal or structural moment within their cellular network. Using the laser cutter, CNC mill, welder and plastic bender to extract the cells from the virtual realm, students construct a full scale, physical counterpart in folded acrylic or metal to physically demonstrate the underlying design principles of the system.
Beyond Prototype has been developed with an extensive library of digital modeling and fabrication tutorials, which are taught concurrently with the process of building physical prototypes. In addition to lectures, students participate in tutorial sessions where they are able to follow along with live faculty software demonstrations on individual computers in the digital laboratory. Fabrication tutorials in CNC milling, plastic bending and welding are offered in the Digital Fabrication and Metals Laboratories. In addition, Beyond Prototype is supported by its own library of instructional videos which cover parametric modeling in Grasshopper, complex detailing, and preparing digital models for fabrication on the CNC mill. Digital Fabrication tutorials are also available in PDF format, serving as a detailed instruction manual to supplement the course.
Beyond Prototype Tutorials:
Lesson 1: Form Generation in Rhino
Lesson 2: Introduction to Grasshopper and Parametric Modeling
Lesson 3: Finite Element Analysis in Solidworks
Lesson 4 : Component Mapping in Grasshopper
Lesson 5 : Component Join in Grasshopper
Lesson 6: Component Fabrication: Unrolling Complex Geometry in Rhino and Designing Hardware Connections
Lesson 7: Drawing for the Machine: Toolpathing in MasterCam for CNC Milling
Lesson 8: Drawing for the Fabricator: Creating Assembly Diagrams for Fabrication
Lesson 9: Digital Rendering and Techniques of Representation
Week 1: Form Generation: Case Studies in Surface Generation and Component Systems / Periodic Surfaces / Layered Meshes / Rhino Surface & Tessellation Modeling / UV Division
Week 2: Parametric Network Creation: Joinery Techniques / Connective Geometry / Component based Grasshopper Modeling / Flattening / Unfolding
Week 3: Material Simulation: Solid Works Modeling and Element Analysis
Week 4: Automated Fabrication: Drawing for the Machine/ using Grasshopper and Rhino tools for unrolling 3D Geometry and Machine File Preparation/ Tool Pathing/ Hardware Selection and Modeling
Week 5: Fabrication Techniques: Metal Fabrication / CNC Milling / Plastic Bending / Adjustable Jigs/ Welding / Finishing/ Thermoforming Plastic
Week 6: Presentation & Assembly Methods: Prototyping / Drawing for the Fabricator / Component Assembly Diagrams/ Photorealistic Rendering Techniques/ Full Scale Fabrication and Physical Assembly Process
1. Pentagonal Bubble Wall
Columbia University GSAPP, Spring 2007
Jason Ivaliotis and Nicholas Kothari
Maintaining coplanar geometry in non-triangulated surfaces is one of the many challenges when modeling a fabrication-ready system that is built around a double curvature. Triangulating the geometry is a common solution to achieving co-planarity, however this limits the patterns and forms that can be developed. The major innovation in this project is the subdivision of giant triangular planes into three pentagons. Each pentagonal cell has a unique bent flap detail which allows for easy and adjustable edge-to-edge connections. Connection details are based on the initial study of primary and secondary geometric components where one cell type remains static while the other dynamically adjusts its angles to form a flexible connective geometry.
The overall form of the mesh system is determined by the triangular base grid. Points are strategically pushed and pulled to create an S-shaped base and a curved section which promotes structural stability and proper balance of the system. The triangles are subdivided and transformed into pentagonal cells for rigidity.
The prototype consists of eighteen pentagonal cells, each folded from a single sheet of acrylic. The outer pockets that form the connective geometry between cells were bent using a plastic strip heat bender and an adjustable triangle to calibrate the computer generated angles. The primary geometry, consisting of pentagonal pyramids, was bent around a static jig composed of the flat pentagonal face unique to each cell. The bend joints of each cellular pyramid were folded in sequence and bolted together on one face. This fastening technique minimized the need for hardware connections and allowed the final prototype to be as seamless as possible. A second iteration of the system features a double skin condition where each cell was mirrored about its flat face. This configuration produced a deeper, more rigid mesh which transformed the flat pentagonal faces into gusset plates and the connective geometry between cells into closed pockets. A three cell prototype was constructed to test this design strategy.
2. Aquatic Research Platform
Columbia University GSAPP, Spring 2012
Students: Andrew Maier, Ping Pai, Mark Pothier and Alejandro Stein
The Aquatic Research Platform is a floating observatory that controls human interaction with marine life. The cellular mesh forms a porous surface where aperture size controls engagement with the water. The areas that rise above the surface of the water contain larger apertures that allow users to pass through the net-like platform and engage with marine life. The submerged areas of the platform contain smaller apertures to provide a smoother walking surface and a protective barrier between human inhabitants and the more dangerous aquatic life forms. To provide for a smooth walking and climbing surface that is appropriate to this type of marine application, the folded panels conceal all hardware connections within the interior of the connective geometry between cells.
The initial analogue studies focused on the generation of a cellular network formed from minimal cutting and folding. The base geometry was created with triangular cells formed from three simple panels. Each panel contains only three folds and fastens to adjacent panels to form a triangular cell with a central aperture. The geometry of the folded mesh is generated by several parametric definitions in Grasshopper where the opening and closing of the triangular aperture responds to the degree of submersion into the water. Distance based attractors are employed to control the opening and closing of the apertures as well as the overall depth of the cellular construct.
3. Urban Carpet
Columbia University GSAPP, Spring 2012
Students: Aisha Alsager, Wes Bassett, Matthew Celmer and Jason Hill
The Urban Carpet is envisioned as a multifaceted system that is able to gracefully transition between shelter and walking surface. The lower portion provides a smooth surface tessellation for sitting or climbing while the upper portion becomes a wall and a sheltering canopy with apertures of variable size and depth. These apertures provide a container for organic plant life that can emerge from within the wall and cover the outer surface by using the cellular mesh as an armature. Each unit within this system is fabricated from two panels of 1/8” aluminum sheet stock that form a rigid structure from the intricate, triangulated folds of the connective geometry between cells.
The initial analogue studies focused on the creation of a rigid three dimensional cell formed from a single sheet of paper. The folded mesh is generated by several parametric definitions in Grasshopper to map the rigid cellular geometry onto any free form surface. Each cell is composed of two folded panels that are mirrored about their center axis and joined by gusset plates. These components act as folded bricks which each contain a parametrically controlled aperture that is surrounded by a triangulated mesh used to connect with adjacent cells.
4. GYNA Pavilion
Columbia University GSAPP, Spring 2012
Students: Belen Gandara, Giovanni Fruttaldo, Katerina Petrou, Mary Adams, Zakiya Franklin
The GYNA Pavilion was designed as an interactive component system. The primary geometry is composed of bent aluminum panels with triangulated folds that form an aperture at the center. These apertures vary in size based upon their proximity to the ground. Apertures within the canopy remain open to allow natural light to permeate into the center of the pavilion, while apertures closer to the ground plane are smaller to provide for structural stability. Each aperture receives a prismic insert composed of frosted acrylic. These inserts form the interactive component of the mesh as they can be removed and repositioned as seating elements underneath the canopy. The prisms are parametrically controlled through Grasshopper. They vary in size along with their parent aperture, thereby providing seating for a wide range of inhabitants: from small children to adults. The folded cells are instantiated onto the curved surface and Grasshopper is used to rationalize and flatten the geometry for CNC fabrication.
5. AMO Pavilion
Columbia University GSAPP, Spring 2011
Students: Omar Morales-Armstrong, Adam Gerber and Mark Paz
The AMO Pavilion is envisioned as a multifaceted system where the lower portion provides a smooth surface tessellation for seating while the upper portion spreads out into a sheltering canopy with translucent apertures of variable size and depth to allow for light transmission. This system is based on a pattern of triangulated forms where the fluid geometry produces a series of pockets and apertures of variable size and closure.
The folded mesh was generated by several parametric definitions in Grasshopper where the opening and closing of the star shaped apertures responds to both formal and environmental conditions, such as surface stress or solar orientation. Distance based attractors are employed in grasshopper to control the opening and closing of the apertures as well as the overall depth of the cellular construct. The entire system can be parametrically mapped to any freeform surface allowing apertures to vary in size and the mesh to increase its depth to provide for greater rigidity in areas with higher stress. After the CNC contouring process, a parametrically generated frit pattern was etched onto each acrylic cell to give the folded surface a second layer of aesthetic complexity.
6. Aperture Canopy
Columbia University GSAPP, Spring 2011
Students: Michael Gonzales, Bo Liu, Lalima McMillan and Kim Nguyen
The Aperture Canopy was conceived as a flexible system of modular components that are able to alter their parameters in order to perform as different tectonic elements. The folded geometry forms a series of diamond shaped pyramids that are fastened to a secondary substrate in an alternating pattern. This configuration allows the mesh to obtain thickness by growing outward from the center in both directions. All of the pockets are CNC milled from acrylic sheets that vary in texture and transparency.
The cellular units were digitally recreated in Rhino using the parametric components of Grasshopper. The entire system can be parametrically mapped to any freeform surface allowing the pyramids to vary in size and the mesh to increase its depth to provide for greater rigidity in areas with higher stress. Through the use of distance based attractors, the parametric grasshopper definition allows the folded pyramidal cells to either grow into columnar structures that form an integrated support system at the base of the pavilion, or collapse to provide a thinner surface as the mesh expands into a sheltering canopy at the upper levels.
7. Fabric Tessellation
Columbia University GSAPP, Spring 2010
Students: Timothy Bell, Tong Hao, Shaun Salisbury and Andrew Teng
Generated from a pattern of offset nestled triangles, this component system mimics the fluid and flexible geometric forms of collapsible fabric structures or pleated shades. The initial analogue studies focused on the creation of a flexible cellular network formed from cutting and folding one sheet of paper. A collapsible, triangulated mesh emerged and was modified to include wedges and gusset plates for rigidity. Through a folded plate system of triangulated ribs and diamond shaped apertures fitted with transparent acrylic, this project achieves a state of total enclosure, where structural components provide a means of shelter. The mesh is divided into four-sided cells whose edge flaps fold up and join with triangulated gusset plates to provide axial and lateral support. The cellular units are digitally recreated in Rhino using the parametric components of Grasshopper to create tessellated surfaces with a double curvature. The entire system can be mapped onto any free form surface allowing the transparent sections to vary in size and the mesh to increase its depth to provide for greater structural rigidity. Fabric Tessellation was presented at ACADIA 2010: Life inFormation.
8. Nature Cultivator
Columbia University GSAPP, Spring 2010
Students: Trevor Hollyn Taub, Ethan Taylor & George Valdes
This pocket wall system proposes a unique type of modular construction where folded volumetric components would act as a new type of three dimensional building block. Each unit contains two apertures, mirrored about a center line to form a deep interconnected mesh. The components are tessellated in a running bond pattern, strategically employing a system of bent aluminum gussets and folded sheets of acrylic for transparency. The apertures provide deep pockets for lighting and/or coconut husk green wall systems to be inserted into the mesh. The initial analogue studies focused on the creation of a two sided pocket system which would attain rigidity through mirroring the individual cells to form a deep mesh. As a result, the cells became deep, folded brick units. These cellular components were digitally recreated in Rhino using the parametric components of Grasshopper to map the cells onto variable surface forms and control the size of the central pockets. The adjustable depth of each modular component allows the folded mesh to either collapse into a thin building envelope or expand to become deeper when needed for structural rigidity.
9. Pocket Pavilion System
Columbia University GSAPP, Spring 2009
Students: Gonzalo Casis, Elia Karachaliou, Masaki Morinobu, Natalia Roumelioti, ShengWei Shih
The geometry for this cellular system was generated from a square grid that was divided into triangles with diamonds inset at the center. This two dimensional base grid was transformed into a series of 8 point cells, each containing four triangulated pyramids. Each set of pyramids can expand and contract to increase and decrease the porosity of the overall form. Four of the outer segments of each cell form a faceted connection with the adjacent cells, while the remaining four segments radiate out from the center to meet at a common point. The expandable pyramids and multifaceted connections enable the system to adapt to changes in required structural depth, curvature and porosity. The overall form of the cell is determined by a quadrilateral grid. The two dimensional pattern of triangles and diamonds is superimposed onto the overall surface of the pavilion. Points are pushed and pulled to create a series of triangulated pyramids and perforations which vary in scale.
10. Pod Shell System
Columbia University GSAPP, Fall 2008
Students: Rajiv Fernandez, Eunki Kang and Sungab Kim
This cellular system is organized by a base grid of triangulated diamonds that fit inside of each other. The initial analogue models for this project are produced from a single sheet of paper with a series of cuts. Three dimensional forms are achieved from a single sheet by cutting along the center line of each diamond and pulling the sheet apart. However, the fabrication process for transforming the cells into a rigid acrylic mesh requires that the system be divided into several components. By dividing the cells into pyramids connected by triangular wedges, a new organization of cells is revealed and a higher level of complexity is achieved. The entire system is produced from triangular faces which allow almost any form to be produced using this cellular kit of parts. In this particular case study, the final form is a structurally rigid pod.
11. Operable Rosettes
Columbia University GSAPP, Fall 2008
Students: Jorge Barragan, Sina Mesdaghi, Saskia Maria Nagel
This cellular mesh is composed of an aggregation of two cells that fit inside one another to attain rigidity. The outer cell adopts a triangular form and bifurcates into triangular folds at the corners to allow for fastening to adjacent cells. Each triangular cell contains a central rosette which forms an inner ring of tight rigid folds. This rosette can be configured to produce a series of open and closed apertures. When the rosette is closed, the surface is completely sealed. Each rosette is composed of folded translucent acrylic, creating a rigid structure at the center of each cell that acts like a ring truss. The initial analogue models produced a rigid set of six cells that formed a polyhedron shape. The base geometry was then reduced to a set of three cells which allowed the system added flexibility to adapt to surfaces of variable curvature.
12. Pavilion System 01
Columbia University GSAPP, Spring 2008
Students: Ingrid Campo Ruiz and Jose Luis Perez-Griffo
This rigid skin is composed of panels which are tiled consecutively by mirroring each cell about the x and y-axis in order to produce a seemingly random array of components. The primary cells are generated from 2 rotated squares which twist in opposing directions, forming a vortex shaped cell with triangulated faces. This configuration allows these primary cells to be read as a complex overlapping pattern rather than a simple tiling of square units.
The final prototype consists of two cell types: (1) the vortex shaped quadrant with center aperture formed from four triangles that are twisted around a square center quadrant and (2) a diamond shaped connection plate spanning between the vortexes. The primary cells are static and remain the same size while the diamond connection plates vary in size to allow the system to bend and conform to any curved surface. The folded cells are applied to a non-structural scaffold which acts as a formwork that can be removed after the fabrication is complete or remain in place to mount lights and equipment.
The research and course material for Beyond Prototype is developed and managed by Jason Ivaliotis and Nicholas Kothari. For more information on current projects and lectures, visit the Research section at www.versa-design.com.
Jason Ivaliotis is a founding partner of Versa and serves as the director of design for the New York office. He began his professional journey as a designer and educator at Miami University in 1999. Over the last decade he has gained a wealth of experience as a project designer and team leader ...