Computational Crumpling Draft #1

computational

crumpling

tales of paramorphic gestures written_edited by joanna sotiriou university of thessaly department of architecture

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COMPUTATIONAL CRUMPLING tales of paramorphic gestures written_edited by joanna sotiriou professor: sophia vyzoviti university of thessaly department of architecture

computational crumpling Paper is a material known to everybody. It has a network structure consisting of wood fibres that can be mimicked by cooking a portion of spaghetti and pouring it on a plate, to form a planar assembly of fibres that lie roughly horizontal. Real paper also contains other constituents added for technical purposes. This review has two main lines of thought. First, in the introductory part, we consider the physics that one encounters when ‘using’ paper, an everyday material that exhibits the presence of disorder. Questions arise, for instance, as to why some papers are opaque and others translucent, some are sturdy and others sloppy, some readily absorb drops of liquid while others resist the penetration of water.

-Mikko Alava and Kaarlo Niskanen, “The Physics of Paper”, 2006.

When one googles “origami”, the first link that comes up is the site www.origami-instructions.com. This is probably the best way to highlight the most basic element of this technique: instructions. Origami acknowledges a piece of paper as a map with strict coordinates that one has to follow in order to produce a predetermined result.

A professional is able to just look at a model and then visualize the “paths” carved on the paper that led to the specific final form. It is a one way road: each model has its own set of rules and vice versa.

Crumpling was introduced by Paul Jackson and later on developed as a philosophy and art in origami world by Vincent Floderer. By definition, crumpling indicates a more random action resulting to a wrinkled or creased deformation of an object (usually paper). However, in Vincent Floderer’s artwork, tiling is a strong element which again, leads to the production of regular forms.

Denying the presence of any kind of rule in the structure of an object is, at least, utopic. Even the most visually abstract form’s structure in nature is based on a fixed set of rules which most of the times is not perceptible due to the random of its image. When manually crumpling a paper, one does indeed act impromptu on the material. However, the creased result can be analyzed and furtherly deconstructed to a set of rules explaining the deformation.

Rahul Narain, Tobias Pfaff and James F. O’Brien from University of Berkeley, California observed the elegance of what we call “abstract” in a crumpled paper and a wrinkled t-shirt. They described extensions to the adaptive remeshing scheme that accommodate crumpling and folding behaviors in sheets formed of stiff materials. Reversing the procedure of crumpling revealed a total of mathematical equations that could potentially regulate this casual action.

Crumpled paper provides an example of plastic deformation that is particularly challenging to simulate, as its high in-plane stiffness causes deformation to be concentrated along narrow creases and at point singularities.

-Mikko Alava and Kaarlo Niskanen, “The Physics of Paper”, 2006.

What if the ridges, the valleys and the points consisting a crumple could be categorized in functional units so that we could draw a random-looking crumple from scratch? This paper is an attempt to understand the logic based on which Freeform Origami works, a software developed by Tomohiro Tachi “that allows users to interact with origami forms while altering the crease pattern of the model”. More specifically, it is being attempted to analyze the way this software reads the graphic representation of a ridge and a valley so that one can directly design a feasible crumple.

computational crumpling A commonly cited example (of topology in mathematics) is the London Underground map. This will not reliably tell you how far it is from Kings Cross to Picadilly or even the compass direction from one to the other; but it will tell you how the lines connect up between them. In other words, it gives topological rather than geometric information … We do not ask: how big is it? But rather: does it have any holes in it? Is it all connected together, or can it be separated into parts?

- Neil Strickland What most interests architects who theorize about the logic of curvilinearity and pliancy is the meaning of ‘event’, ‘evolution’ and ‘process’, that is, of the dynamism that is innate in the fluid and flexible configurations of what is now called topological architecture. Architectural topology means the dynamic variation of form facilitated by computer-based technologies, computer-assisted design and animation software.

-Giuseppa Di Cristina Since it is not allowed to tear up the paper but instead alter the links connecting the nodes on its surface in order to deform it, we could assume this research has its deepest roots in the concept of topology. In the research presented in this book, we travel among homeomorphic shapes and therefore spaces, studying (partly instinctively) the algorithms based on which any alteration will result to a foldable and thus constractable shape (given that our material is plain paper).

However, the architecture community has not been quite clear about the specific use of the term “topology”. The contradiction between the flexibility of a topological digital form and the absolute shape of an actual piece of paper that could not be overlooked during the specific design process leaves one doubtful as whether the term “topology” applies accurately in this case. Nevertheless, introduced by Mark Burry, another term may describe this paper in a much more clear and conceivable way: Paramorphs.

Paramorphs are forms that have consistent topology but unstable topography.

-Mark Burry

The original mineral forms, but conditions then cause it to be unstable, so it transforms into the other mineral with the same chemical structure while retaining the original crystal shape.

-from “Paramorph” The Mineral and Gemstone Kingdom Throughout the procedure introduced in this book, links and relations change according to a varied set of parameters while, as stated before, the structure stays the same. In this case, the parameter of the biggest importance was the fixed materiality given. This fact blurres the lines between the computational and the actual design of the desirable final form. Additionally, since the whole project started with an absolute lack of any kind of knowhow for this matter, experimentation played the biggest role in creating the parameters that would create the nodes’ relations of the final, foldable structure.

Sources: On Topology by Reza Esmaeeli / http://topology.rz-a.com Paramorphism on Wikipedia / http://en.wikipedia.org/wiki/Paramorphism “The New Mathematics of Architecture” by Jane Burry and Mark Burry, Thames & Hudson 2010 ISBN: 978-0-500-34264-0

why projection mapping?

INTRODUCTION

METHOD FOLLOWED The first step was to note how points should be designed so the software will move them either upwards or downwards (forming ridges and valleys accordingly). I designed units, studying the various graphical representations that form a ridge or a valley. Simultaneously, I experimented with tiling these units to understand the way freeform origami reads multiple units in a single paper and the connections that needed to be created in order to achieve a functional folding between the same units.

Gathering the rules that resulted from the Units and their tiling, I started again from scratch, only this time there was no room for multiplication whatsoever. In “Trials” section, I tried to discover the general rules that exist behind a functional total of ridges and valleys, based on the previous results. Initially, I tried to see how one can design a “basic ridge” which would serve the purpose of the framework core. Also, there was some investigation on the folding of the plane edges and how the design can fully control its move. This brought up some controversial issues like whether a polygon or a triangle influences more the folding in the software. Using voronoi patterns, I designed planes that would work exclusively on polygons and planes on which polygons would work as basic ridges and triangles would work as a back up. Nevertheless, the most controversial issue was the dipole between complexity and functionality. Naturally, the less complicated designs (most of them were consisted only of voronoi patterns) would give a simple polyhedral 3D model which was stable but without valleys while the designs that were consisted of densified triangulations would fail to be folded under numerous bugs.

30 trials, 70% of them being completely dysfunctional and 20% being semi functional with little bugs resulted to a set of observations and rules that were successfully applied to models that would combine a certain level of complexity and functionality. Still, I did not have full power on it as its final form was 80% predicted and intentionally designed while the remaining 20% was unpredicted via the ways the software folded it that I had not spotted till that time.

INTRODUCTION

At that point, there was a big realisation: the functional forms had one thing in common. There was a coherency in the relationships between the nodes, less like in a pattern type of way and closer to a certain visual recurrency of a law/parameter.

Based on this observation, I started designing again, from scratch. Even though the relationship between the final parametric computational design on the plane and the materiality of the paper was not clarified and established, it was deeply approached in such a level that the final form was 100% functional, stable, design-wise satisfactory and most of all, controllable.

INTRODUCTION

SOFTWARE USED

HOW TO READ THE PAPER

Interactive Voronoi Diagram Generator with WebGL by Alex Beutel (open software http://alexbeutel. com/webgl/voronoi.html) AutoCad 2013 by Autodesk Freeform Origami by Tomochiro Tachi (open software http://www.tsg.ne.jp/TT/software/) Blender 2.63 (open software http://www.blender. org/download/) Pepakura

In most of the units and trials, there is a “RULES APPLIED/STEPS FOLLOWED” and a “COMMENTS” section. Technically, the latter is a total of observations recorded when each trial wes being carried out meaning that some of them are false. The observations proven were general rules are marked in bold. However, one should not oversee the false ones since they were the base on which I could really grasp the idea behind Freeform Origami.

Trials and Units are marked as DYSFUNCTIONAL, SEMI FUNCTIONAL and FUNCTIONAL. DYSFUNCTIONAL indicates that the design caused such a number of bugs that a model was not able to be produced at all. SEMI FUNCTIONAL indicates a design that caused a certain number of bugs that would make it unstable yet foldable with a need for further manual editing in Freeform Origami. Last, FUNCTIONAL indicates that the design was stable and foldable. However, some designs were declined because they would not combine the desirable equilibrium between functionality and complexity.

un its

UNITs

#1

FUNCTIONAL

UNITs

COMMENTS: 1. By pressing only space in FreeForm Origami, the program responds only to the second unit (in the same way it responded before the tiling). The upper unit is reversed and the lowest unit does not respond at all.

2. By hitting “B” (command for “unfold”) the program seems to be “reading” the units as they are seperate forms. By hitting “B” and space multiple times (for this example, they were pressed 4 times), the program finally reacted in the expected way.

SEMI FUNCTIONAL

SEMI FUNCTIONAL COMMENTS: 1. By pressing only space in FreeForm Origami, the program responds only to the left part of the tiling. The right part is not folded at all.

2. Following the previous step (pressing B and space repeatedly) the program finally folds both parts. However, this time calls for manual edit on the vertices (left click on the vertex you want to lift or press downwards).

UNITs

#2

FUNCTIONAL COMMENTS: 1. As expected, FreeForm Origami reacts accordingly. The vertex is pushed downwards.

2. Tiling unit #2 followed the same pattern of procedure with tiling unit #1.

3. The color of the line connected to the corners of the paper indicates the move of the point they are refering to.

UNITs

#3

DYSFUNCTIONAL COMMENTS: 1. Unit #3 seems to be completely dysfunctional. The program does not correspond to the folding command and the edges tend to be torn apart.

#4

SEMI FUNCTIONAL

COMMENTS: 1. Giving a more simple geometry compared to #3 UNIT seems to facilitate the software reaction.

UNITs

UNITs

#5

SEMI FUNCTIONAL COMMENTS: 1. The program seems to be recognizing the small and more densified geometries more easily (the first folding occurs at the smallest red and blue lines as shown in the image above). By pressing B and space repeatedly, the program shows a bug.

2. The previous observation leads us to the assumption that folding is a relative procedure for the program (paper materiality).

#6

UNITs

SEMI FUNCTIONAL RULES APPLIED / STEPS FOLLOWED: 1. Draw a ringe and a valley from one paper edge to the other.

2. Connect red lines to exterior angles and blue to interior ones.

COMMENTS: 1. The program recognizes the pattern but the folding is not stable.

2. Not foreordaining the fold of the corner of the paper seems to be working, Freeform Origami folds it based on the ridges and the valleys created inside the area.

UNITs

#7

FUNCTIONAL

COMMENTS: 1. The program fills the missing triangles.

#8

UNITs

FUNCTIONAL

RULES APPLIED / STEPS FOLLOWED: 1. Create a voronoi diagram.

2. Trace the voronoi pattern with a red line, creating multiple ringes.

COMMENTS: 1. Although simplified to the core, the exclusively ridged voronoi pattern seems to be working. The program creates a stable fold.

However, since there are no valleys drawn, the form is simplified with its edges being folded to the extreme compared to the empty polygons which tend to remain flat.

UNITs

voronoi pattern used

TRI ALS

#1

TRIALS

RULES APPLIED / STEPS FOLLOWED: 1. Draw the basic ridge between vertices A and C (not as a straight line).

2.Connect the ridge to the rest of the vertices of the perimeter (B and D).

3. Create triangulations. _Each blue line should meet each perimetrical edge once and only one time (vertices excluded). _Create all the possible paths between the blue and red vertices. In the end, there should be only triangulations formed.

DYSFUNCTIONAL COMMENTS: 1. Red lines connected to an edge on the perimetre (A, B, C or D) tend to lift up the edge of the “paper�.

2. When a red line and a blue line are connected to an edge on the perimetre as well, the lift up seems to be more intense.

TRIALS

#2

RULES APPLIED / STEPS FOLLOWED: 1. Create a random polygon in the center of the rectangular perimeter.

2. Devide the polygon into triangles, keeping them to the possible minimum (one left rectangular).

3. In each triangle, create inner triangulations connecting each vertice to a random put standar point of your choice (it is neither an orthocenter nor a centroid).

4. Connect the exterior angles of the polygon to the vertices A,B,C and D with blue lines.

5. Create extra polygons connecting two exterior angles of the basic polygon and inserting a new vertex.

6. If there is an interior angle of the basic polygon used in a new polygon, connect it with the new vertex (red line).

DYSFUNCTIONAL

COMMENTS: 1. The area of each of the triangulations and the folding complexity are inversely proportional elements.

#3 RULES APPLIED / STEPS FOLLOWED: 1. Track the voronoi pattern creating polygons. (red line) 2. Create inner triangulations using the voronoi points as convergence points for the blue lines (blue line).

SEMI FUNCTIONAL

COMMENTS: 1. The voronoi pattern is working. However, the triangulations confuse the program.

TRIALS

TRIALS

#4

RULES APPLIED / STEPS FOLLOWED: 1. Create a voronoi pattern with 10 serial points in the center and 4 near the edges of the perimeter.

2. Track the voronoi pattern.

3. Create the minimum possible amount of triangulations by connecting each angle of the inner polygons to the perimeter using blue lines.

4. Divide each of the inner polygons in two triangles.

FUNCTIONAL COMMENTS: 1. Having a voronoi pattern as a base for the design simplifies the folding of the .dxf. However, the result tends to look more like a simple polyhedron and less than a random 3D form.

2. The nodes tend to move according to the “color majority�. When the number of blue and red lines is equal, red overrides. (Examples on the next pages)

TRIALS

tends to move upwards red = blue

tends to move downwards red <blue

TRIALS

tends to move upwards red > blue

#5

TRIALS

RULES APPLIED / STEPS FOLLOWED: 1. Create a voronoi pattern with 6 points.

2. Trace the voronoi pattern.

DYSFUNCTIONAL COMMENTS: 1. Red lines close to the perimetrical corners (A,B,C,D) confuse FreeForm Origami creating bugs. The “paper” does not fold correctly and edges overlap each other easily.

TRIALS

#5.1

RULES APPLIED / STEPS FOLLOWED: 1. Use the trace from trial #5.

2. Connect the red traces to the the perimetrical corners via a blue line.

3. Leave a polygon empty and “fill” the rest with a blue line (you do not have to connect all the vertices).

SEMI FUNCTIONAL COMMENTS: 1. The empty polygon acts like an apex for the folded form.

2. Large areas tend to follow up the movement of the smaller ones.

#5.2 RULES APPLIED / STEPS FOLLOWED: 1. Use the trace from trial #5.

2. Add another empty polygon.

3. Connect each corner with two blue lines.

FUNCTIONAL COMMENTS: 1. The ridge is corregated by the two empty polygons acting like apexes.

2. Two blue lines connected to the peripheral corners move the paper downwards in a smooth way.

TRIALS

TRIALS

#6 RULES APPLIED / STEPS FOLLOWED: 1. Experiment with a different peripheral geometry.

2. Draw a ringe from edge AD to BC. 3. Reinforce it with polygons.

4. Connect the resulted exterior angles to edges AB and DC.

SEMI FUNCTIONAL COMMENTS: 1. Software reacts perfectly to a simplified .dxf consisted exclusively on red polygons.

2. When two red lines seem to converge on the peripheral edges, software creates a bug.

3. The further a red line is drawn from a peripheral corner, the better the software manages the corner-folding.

#6.1 RULES APPLIED / STEPS FOLLOWED: 1. Experiment with a different peripheral geometry.

2. Draw a ringe from edge AD to BC. 3. Reinforce it with polygons.

4. Connect the resulted exterior angles to edges AB and DC.

FUNCTIONAL

TRIALS

TRIALS

#7 RULES APPLIED / STEPS FOLLOWED: 1. Repeat all the steps from trial #6.

2. Add a second ringe.

3. Create a valley (a “blue ringe”) in between the two ringes.

4. Connect the blue vertices with the inner angles of the ringe (there is a mistake in the image shown) with a blue line.

5. Connect the exterior angles with a red line.

DYSFUNCTIONAL COMMENTS: 1. The start and end point of a blue line should only be connected to either the peripheral edges or an interior red angle.

2. The exterior red angles should only be connect to red lines.

3. There is a bug on the A corner.

TRIALS

TRIALS

#7.1 RULES APPLIED / STEPS FOLLOWED: 1. Fix the bug mentioned in the trial #7_1 by applying the comment #2 from trial #4 (red<blue result to the downward movement of the vertex).

FUNCTIONAL COMMENTS: 1. The lack of connectivity between certain vertices does not seem to create a bug in the software. It rather simplified the folding procedure.

TRIALS

PEPAKURA SOFTWARE By importing the .obj model in pepakura, we notice that the developable model of our folded object is divided in two parts.

TRIALS

#8

FUNCTIONAL

TRIALS

TRIALS

LING CRUMP

#1

CRUMPLING

CRUMPLING

CRUMPLING

CRUMPLING

#2

CRUMPLING

CRUMPLING

#3

CRUMPLING

CRUMPLING

planar projection

triangulations edges

edgesâ&#x20AC;&#x2122; coordinates

draft model 1:10