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Foundations of Design : Representation, SEM2, 2018 M3 JOURNAL - PATTERN vs SURFACE Sophie Rhodes

998175 Colby Vexler + Studio 14


WEEK 6 READING: SURFACES THAT CAN BE BUILT FROM PAPER IN ARCHITECTURAL GEOMETRY Question 1: What are the three elementary types of developable surfaces? Provide a brief description. Developable surfaces simplify structural work through geometric mapping of three dimensional objects onto a flat surface. Three elementary types of developable surfaces are cones, cylinders and tangent surface of space curves. With zero Gaussian curvature, they can be mapped inexpensively onto flat surfaces, allowing the use of freeform curved envelopes with single curved surfaces using any flat material such as metal, card or paper. Cones and cylinders are elementary developable surfaces that can be obtained by bending a flat sheet of material. The lines of a cone extend from a profile curve base and taper to a point at the apex. The cylinder works with parallel straight lines moving to intersect profile curves. The tangent surface of space curves is the plane that becomes developable due to the union of lines to the curve.

Question 2: Why is the understanding of developable surface critical in the understanding of architectural geometry? Choose one precedent... In today’s built environment Vitruvian geometry occurs in every proportion of a structure. The very planar nature of the developmental surface means it can be tested and measured employing the geometrically straight lines that simplify their construction. The developmental surface shape can be unfolded to the plane without deforming, creating many easily manufactured sheets. The design of complex and organic shapes can initially be tested which allows architects to understand the geometric structure and its nature. Developmental surface shapes become the foundation of the construction design. Huyghe and Le Corbuisers Puppet theatre – Using rigid diamond panels the curved surface, implying movement, was possible using single interlocked panels of triangles to create an organic shape. The use of geometry in developmental surfaces has allowed the creation of this beautiful structure.



2d Panelling, Pattern: Triangular - A developable surface

3D Panelling, Pyramid 1 - Offsetting points to create a bounding box for the 3D panels.

3D Panelling, Pyramid 1 - Using an attractor point located outside of the surface to offset points.


VARIABLE 3D PATTERN Initial concept involving a progression of four pronged triangles opening up. Attractor points were used to manipulate the surface.

Experimenting with attractor curves rather than attrator points. Triangles with one and two apexes were used to simplify the surface.

Refining the use of attractor curves, utilising the ‘away’ and ‘towards’ options to altar the height and placement of shapes. This arrangement eventually engendered the final design.



Unrolled surface used to produce two prototypes. The net was generated in

Prototype of the two predominant triangular pyraminds employed in the design. Con-

rhino, while the line weight and colour was editied in Adobe Illustrator.

structed out of ivory card which has been cut, scored, folded and then glued in place with pva.



Question 1: What is digital fabrication and how does it change the understanding of two dimensional representation? Digital fabrication is the use of machinery to cut or build a design, using computerized information. This allows the generation of intricate geometry, eliminating some of the intermediate design steps. This may provide a new overview of the structure. It can create similar results as drawing may (without the use of digitization), but can also save time for the designer and offer precision and accuracy. It allows the designer to move easily between the original drafts and the element’s final construction making adjustments as required. Digital fabrication has created a less formal manner of design and changes the understanding of two dimensional representation by closing the passage of time (and therefore cost) on the birth of the concept and the model.

Question 2: Suggest two reasons why folding is used extensively in the formal expression of building design? Folding allows the integrity of a material’s original characteristics to remain intact. It creates new spaces from planar materials and provides the illusion of fluidity. The dimensional concept transforms from two to three, allowing it to be visualised as a whole or smaller pieces. This is very useful in building design and easy/economical to manufacture. Folding also provides an inherent structural stiffness, stronger than its original planar shape. This allows a form to become self-supporting and maintain its shape in multiple scales.



Five individual modules have been used throughout the terrain. However, bounding boxes were utilised to further manipulate the heights and progressions of shapes on the surface.

Final digital model, displayed as an isometric view and in the shaded display. Variable custom modules have been paneled into an undulating landscape, using bounding boxes and attractor curves.



Combined, a total of 34 unrolled surfaces printed on seven A1 pieces of ivory card formed the final 3D paneled terrain. Each net has been labeled, and every cut or fold line has been numbered. After generation in Rhino, the unrolled surfaces were imported into Adobe Illustrator where line weight and colour was adjusted to ensure the ink on the backface was not visible in the final product. Five was the maximum number of one and two apex pyramids capable of being unrolled at once, to ensure they remained developable. However, the pyramids with four apexes had to be divided in two before unrolling, otherwise the surface was non-developable.



Plan view of final paneled landscape

Close up of paneled landscape




Manipulating attractor curves to replicate the undulation of the terrain and vary height.

Five variable modules used in final landscape.

Final landscape divided into net sections.

Using scalpel and metal ruler to cut out unrolled surfaces.

Glueing together the pyramids with four apexes with pva glue and bulldog clips.

The unrolled surfaces before editing in Adobe Illustrator.

Laying out each constructed panel according to their labels before connecting them together

Connecting the individual panels together.


Module 3 - Pattern vs Surface  
Module 3 - Pattern vs Surface