Design Tooling - Sketching by Computation

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Information

Introduction
Topology is a method of describing information based on relative rather than absolute positions. A topology is specified in terms of connectivity and adjacency between objects. The topologies of a tree, lattice, network are usually described by nodes and a connecting links whereas grids are described by adjacent/neighboring cells. Topologically the location of the Central Park in New York is between 5th and 8th Avenues and 59th and 110th Streets, the exact geographical position is irrelevant in this kind of description. Because of this features, topological descriptions are focusing on local conditions rather than global.

Tree Topology

  Network Topology

Grid Topology

Honeycomb Topology

Voxel-Grid Topology

Information

Topology and Mathematics
Mathematically, topology is relatively a new field related with the theories of groups, graphs etc. Topology is an abstraction/generalization of geometry; while objects are "rigid" in Euclidian geometry their topological counterparts are "flexible" (as long as they don't tear or break). A circle, a square and a triangle; a straight line and a curve, for example are topologically equivalent. Topology is also known as the geometry of the rubber sheet.

Circle

Convex Hull

Deformation

Square

Surface of Sweep & Surface with Trim

Information

Topology, Form and Growth
D'Arcy Thomson used topological transformation in describing the formal relationships between species. In the following images for instance, a human skull under a topological transformation comes close the the skull of a chimpanzee. The role of topology in this instance is one of an underlying structure that remains behind the phenomena, but establishes a continuity and relation between them.

Basis Grid

Human Skull

Transformed Grid

Chimpanzee Skull

Baboon Skull

Information

Topology and Computation
There are many computational applications based on the principles of topology. Cellular automata, which a model of computational theory, operates on a grid of cells. Texture mapping is also performed in topological (uv) coordinates for applying two dimensional pixel maps on three dimensional objects. NURBS curves and surfaces are based on parametric equations of topological coordinates. Configurational maps, which study behaviors of visibility, accessibility and so on, are also based on ideas of adjacency. Finite Element Analyses are also depended on topological transformations of meshes for improving the results of stress calculations etc.

Cellular Automata

  Texture Mapping

NURBS Surfaces

Configurational Maps

Finite Element Analyses

Information

Alexander Christopher (1964), "Notes on the Synthesis of Form", Cambridge, Harvard University Press

Eisenman Peter (1999), "Diagram Diaries", New York, Universe

Mitchell, William J. (1990), "The Logic of Architecture: Design, Computation & Cognition", Cambridge, MA, MIT Press

Topology and Architecture
The idea of a topology in architecture is not new because in one sense, diagrams and sketches describe directly or implicitly some sort of topological relationship between objects. Axes and grids, for instance, usually represent an underlying structure of spatial configuration. Diagrams of adjacency, bubble diagrams are also topological maps. I think the important lesson from the historical presidents is that topology was interpreted in more ways than merely form. 

Topology become once more relevant to design by providing the ability to access, think of, generate and manipulate "design information" in a manner which was impossible to employ a few years earlier. The topology provided by computation is continuous rather than discrete and that's the essential difference between its historical precedents. The ideas of continuity and discreteness are explained later on. It is fair to say that the design our time is trying to find, attach, understand and accumulate the meaning of this sort of new possibilities.

 There are many possible levels of engagement with these ideas both concrete (in the formal expression) and abstract (in the way of design thinking). The next section of interpretations illustrate only a small range of thoughts about design and topology.

Discrete Topologies

Frank Lloyd Wright

Life House, 1938

Jester House, 1938

Sundt House, 1941

Continuous Topologies

Peter Eisenman, Virtual House, 1997

Greg Lynn, Tea & Coffee Towers, 2003

dECOi, Aegis Hyposurface, 1999

Bernard Cache, Objectile, 1999

R & Sie, Snake art gallery, 2003

Interpretation

Topology as object
The most straight foreword approach in interacting with topology can be achieved through its visual expression, which is usually geometric. In this fashion the method maps immediately to its result. Forming NURBS surfaces is one example of this case; by manipulating the control points and/or curves of the surface the underlying topology is altered which in turns has an immediate visual feedback on the form.  In this kind of tight relationship there are a few chances to introduce computation without disturbing the implicit nature of the interaction. There are, though, many possibilities of making this process more intuitive than merely pushing and pulling control points in space. There are also some interesting aspects of design thinking that emerge by performing this kind of computational design.

Local & Global

By modifying a  NURBS curve or a surface there are two interesting things that happen simultaneously. Local changes of the controls affect the whole object. Furthermore, the changes are not homogeneous but have a rate of fall-off. In this respect the traditional idea or local change in contrast to global change in a design is shifted by this topological behavior. The boundary between what is considered global or local, plan or detail for instance,  still exists but its nature is rather different. This phenomenon is highly frequent so topology as a theme can be exploited in order to push it in the foreground.

Ranges

The difference is found in the nature of information definition which is now continuous instead of discrete. In other words, while previously there was a concrete point of distinction between two phases of a process, of two conditions, of two design elements etc, now there is a negotiatable range. What and how things happen in these continuous ranges is not a given-default decision but become subjects to design investigation. For instance, the way public space becomes private, external and internal environment blend are contexts on which an interpretation of the blending function is essential part of design. Blending between two conditions is generic though; how exactly it is performed is the design and computation is a medium that allows it to be defined in terms of continuities.

Thresholds

A threshold is a boundary conditioning mechanism in which a continuity is forced to break down in a discrete elements. In other words, a property such as "lightness" can vary infinitely between its domain, say absolute illumination and complete darkness. Breaking down is discrete components, high lights, mid tones and dark areas, is necessary for realistic reasons.  Initially, because people have a definite span of perception; we can distinguish typically "x" amount of tones of gray between black and white, "y" amount of concurrent streams of information, and so on. A threshold is a simple boundary value, a cutting point and eventually a connector between the ambience of computation and human perception.

Media

Practically the question of how to design under these circumstances becomes one of control. Roughly speaking, traditionally, plan and section are the means for applying design decisions in global and local scope, respectively. The validity of these representation media springs from the fact that their interconnections are tight. In other words, changes in a plan immediately affect the section completely, not a drawing but its representation target which are the local conditions, and vise versa. Now, this makes sense because in dealing with a design based on discrete boundaries there is no way that you can fall off. In the spatial definition/context of the continuous its a different story.

For these reasons, even though plans and sections are highly important means of design propagation, they fall short because of their limited scope. I think we should consider these media as generic samplers: like a thermometer, that you use to get a rough estimation of the global temperature conditions of an environment by measuring it in only one point in space (only one sample).

Computation can be thought of as a way of building personal conduits between design thinking and making.  In other words, computation may be considered as an expressive medium, like any other, with specific unique characteristics, advantages and constraints.

Examples

Physics

see also metric-based design methods

An interesting mechanism for operating on complex curved geometry is through physics. Principles of attraction and repulsion allow an abstract way of control over geometry. The point of using these mechanisms is because they are not affecting the design information partially/heterogeneously but rather globally/homogeneously. Even though the results of such principles are visually  interesting, because of the implicit nature of the manipulation which is performed in a distributed  but concurrent manner, it highly cumbersome to gain some sort of control over process because of the solid nature of complexity that is introduced in just one step. There are of course auxiliary techniques such as constraints, but still a generic system of forces is rather uncontrollable. Physics on the other hand are powerful because they produce an immediate procedural feedback that can be captured by animation for instance.

A system of physics can be more dense more meaningful if it wraps around a concept which has some sort of external reference (physics with some structural connotation, physics as a way to represent people's behavior in an urban context for instance) or when there is no direct or excusive manipulation of spatial geometry but rather its properties (light / shadow, materiality etc).

Stylianos Dritsas 2004

Boxes deformed by attraction field

Blending

Because of the continuous characteristics of computational geometry/topology (based on curves and surfaces) there are some special operations such as  interpolation. Interpolation is a process of blending between a number of boundary conditions. The most simple form of it, is linear interpolation between numbers (what is the middle/ a fractional value between min and max). In three dimensions interpolation is commonly known as morphing and it is certainly more complex operation. A NURBS curve is produced by interpolating through the control points using a rather complicated blending function (a.k.a. the polynomial basis function). A lofted surface is produced by interpolation between curves. The characteristics of the used function produces different results. The number of the intermediate positions of an interpolation is of course infinite.

As with the physics, it is generally difficult to handle direct geometric manipulations with these techniques without incorporating some external reference. The powerful idea behind interpolation is that it makes easy to pan through a space / range of designs. It is also helpful because it allows decisions between end conditions to be continuous and relational to each other rather than discrete and absolute.

Another pretty nice way to employ interpolation is in kinetic structures (or any other type of animated form) and interpret the morphing are a property of motion. This approach may be more interesting if the surface/curve/point is considered as scaffold of the actual object(s) which adapt on top of it (see the next section for this). In this fashion motion can be embedded in form not as a direct action of pushing and pulling it geometrically but rather in the more subtle way of topology.

Stylianos Dritsas 2004

Morphed surfaces creating volume

Source Code & Instructions

Blob & Antiblob

The blob is the result of a volumetric representation of space based on discrete volumetric elements also known as voxels. Voxels are living on a three dimensional grid of cells and their two-dimensional counterparts are the pixels of a bitmap. A blob (Blinn, 1982) is technically defined as an implicit surface; a surface produced by a special form of mathematical function f(x, y, z) = 0. In the case of commonly known blob form, the function actually represents a field of point forces. Other kinds of simulations of fields and phenomena can evolve in this space.

A blob is not a simple concept, even though it has been trivialized as being an architectural formal typology. An interesting aspect of it is that the representation used behind the liquid animated form is volumetric, which means that a blob describes actually spatial consistency (rather than a boundary, a surface). The surface rendered on screen, is just the result of a thresholding, a non-planar section inside the volume defined by the function. Imagine how much information is lost and how poor an image becomes by using thresholding to turn it in black and white, to get an idea of the relationship between the blob and its visualization.

Imagine now being able to design volumetrically, inscribing properties (that is more than colors or surfaces) in space. What paradigms, what metaphors can be employed in dealing with this sort of process. Can this model of spatial thinking be realized with out computation?

Stylianos Dritsas 2003

Download application

Implicit Surfaces Using Different Field Functions

  Interpretation

Topology as scaffolding/placeholder
Topology is employed mainly as a scaffolding or a placeholder of design information. The general idea is close to the mathematical definition of topology as an abstraction of geometry, a geometry commonly know as of the rubber sheet. In this case the computational processes evolves in the topologically defined space. The space may be continuous, such a surface, or discrete, such a grid of cells.

Regulatory

The nature of topology is rather regulatory: an abstraction forced upon an empirical information-space which behaves as an underlying inner-structure (though it doesn't have to remain there). The use of regulatory devices is not a novel idea; grids and axes, for instance, are commonly used in design. It is also important that regulatory devices are not neutral in any case. There are many historical examples that illustrate this point ranging from the ancient temple symmetries to the modern obsession with grids to our current fascination with non-Euclidian geometries. 

Adaptation

The generation of topologically adaptable geometry is probably the most common way of employing topology as a scaffolding. There multiple reasons, such as structural and/or decorative,  for employing this approach. The principle is straight foreword: instead of drawing two dimensional shapes on a rubber sheet and then deforming it, this approach suggests of modeling geometric (spatial) objects on a topological basis which are then mapped on its geometric expression. Drawing objects on top of NURBS surfaces and then changing the surface while the drawn geometry readapts is a good example. Creating a topological map (a tree structure, lattice etc), drawing parametric objects along its nodes and the instantiating geometric results based on input parameters is another very common example.

Relativity

Topological systems are relational, the position is subdominant to connectivity, which in turns means that it is not trivial to create easily measurable results. For instance, the distance on the globe is not calculated as the length of a linear segment connecting two end points. Therefore, the payback for having the ability to easily deform objects is that it becomes more difficult to figure out both their position and distances. Of course there are methods of performing all these calculations but it sometimes becomes non-intuitive. In that sense these properties of topology forces definitions of objects to be parametric in order to have some ability to pass along the process all this indeterminacy and eventually be able to propagate backwards the end decisions.

Example

Prototyping and Fabrication

Rapid prototyping was a project that played with the idea of using topology as a scaffolding  from a practical point of view. The idea was to create physical artifacts / prototypes / sketches from a digital representation. A script was written for this purpose, that produced a network of interlocking ribs on tops of NURBS surfaces. The ribs were then transformed from 3D to 2D by unrolling and each one was numbered and packed. Therefore the process was collapsed into only the laser-cutting and assembly parts (I wish robots were cheaper).

The example is very straight foreword, the surface was treated as a place holder of "structurally" flavored information. The process reproduced manually is feasible but never the less impractical because of the time needed for executing the volume of geometric manipulations. Furthermore, this kind of sketching has some more advantages such as it is stable (the computer is not going to miss any detail by mistake, only from some internal error), other properties such as curvature can be employed in order to produce more accurate results etc. Finally, the fact that you get a physical representation of an object is highly informative in many more ways that a its digital representation can provide.

 Stylianos Dritsas and Sameer Kashyap 2003

Original Surface

 Network of Interlocking Ribs

Prototyping elements

Laser-cut pieces

Assembled prototypes

Light Sculpture: Materialization of light information on surface

This project was an experimentation in using specific information of physical environment / objects as materials for designing new ones. Our intention was to create a walkway pavilion for a museum, using light information mined from the sculptures hosted inside the museum. The procedure involved sampling the luminosity of the sculptures using photometric instruments, transformed the data globally and microscopically. Finally using parametric and generative design systems produced a family of canopy - surfaces on which we mapped the information as an aperture control system.

Sawako Kaijima and Christiana Raber, 2003

 Process sequence of gathering, transforming and mapping information

Procedural Skins

Due to the bounding nature of surfaces a usual metaphor for their design is that of a skin. An architectural skin can be a facade, a spatial partition or any element that divides space into sub-spaces; a skin based on its physical metaphor: a layer that primarily separates and secondary functions as a filter that allows controlled  / selective transfer though it. A rather volumetric interpretation of a skin is that of a multilayered skin or one with thickness which behave spatially.

A skin is an element which even though it is material it is not inert; it behaves according to a procedural mechanism, to its environment, to its audience, to itself etc. Computation in this case operates as an experimentation platform in which these behaviors / processes can be evolved and refined. In relation to the previous interpretation of the topologic patterning, this one moves one step further from a pure geometric game by incorporating some external information.

Light Skin

see also metric-based design methods

Light-skin was a project of this conceptual basis. The goal was to rethink architectural light not as a static mechanism for delineating the volume/mass/form properties of space but as a time-sensitive device which can project its motion properties on the object/subject and allow the observer to pan through its properties being either static or mobile.

The inquiry for a non-static expression of light in design was implemented using topology as an underlying structure of a geometry that was evolving by taking simultaneously in consideration of the form and the encoded light conditions. The generated geometry had a compositional approach based on multiple elements that were adjusting their size and orientation along the underlying surface's direction and an external light path. Furthermore, the impact of light on the elements was locally deforming them according to another encoded behavior of protection-repulsion or attraction.

Stylianos Dritsas 2004

Play shadow animation

  The strips adapt both the local conditions of the surface and the external lighting conditions

Topology as info-space
Finally, topology can be interpreted as a design information space which has no direct relationship with a formal expression. For example, using some sort of topological mapping in order to represent, collect the data, reorganize, process and translate them into an object. Topological transformations are used in simulation because a grid for instance introduces a regularity which is computer-friendly but simultaneously it doesn't have a concrete phenomenal result. There has to be therefore a translation phase into geometry, and this translation does not have to be necessarily regular. Surfaces, for instance produce a curved geometry, even though they are based on a flat / planar topological representation.

On the other hand, computational regularity is not a prerequisite for human understanding. We can process visual information extremely efficient than computers. So, in this case, it doesn't make sense to be restricted by the computational ways. Create your own relational mappings which are based on personal understandings and then encode them in a computational manner, when applicable. That might be tough to do but it is a good way to avoid homogeneity and arbitrariness, which is a usual side effect of taking all the default options.

This way of thinking is powerful but it proves to be relatively difficult because there has to be a cut between what is observed (the object) and its internal representation (the topology). Furthermore, the translation mechanism has to be "unbiased" in terms of avoiding direct interpretation of the topology as object. The following examples present a. a way of producing custom topologies that don't have to be homogeneous and b. some basic idea of how they can be translated into objects (through behavior rules).

Example

Donkey's Path

(see also the design   metrics section)

A few years ago, actually even today in some villages,  the way to go about with planning routes in hilly sites around populated areas was by using donkeys as "path tracing devices". A dripping bucket of paint was attached to a donkey and it was "directed" to go down hill. The donkey based on its best experience in hill climbing went eventually down the hill. The road way was paved then over the path marked by the donkey. Now, this situation sounds unrealistic but it captures the idea of an agent-based mechanism for mapping a context and create a partial interpretation based on local conditions. What the donkey knows is that it has to go down the hill but on the same time it finds the way to go down in the most easy and safe way that it can perceive. The counter example of donkey-paving is the highway construction which runs through a landscape forcing the environment to adapt.

Encoding a behavior and simulating it provides some intuitions about a landscape. The results are always partial and biased towards a few parameters of importance. But that's on the other hand is the same results provided by producing sketches from a survey in the context itself.  The design information captured is not of the same nature but they can be both sophisticated and trivial depended on the sketching process. It is important though to say, that it is easy to over-estimate / over-interpret the information that a computational sketcher, based on a simple process, can provide.

Computation offers a way of extracting quantitative information which may have some perceptual qualitative value. Moreover, by scaling the experiment and  sending a large amount of agents to scan the landscape it is possible to get a global mapping of the tendencies rather than a single local result. These kind of information are impossible to be mapped and employed without computational means. The questions of how can these results can be possibly employed creatively, is of course a conceptual matter.

The following images illustrate a custom mapping process. The images in themselves can be both interpreted as objects (you might want to actually use the paths drawn on the surface) and as  custom topologies that another layer of processes can run on top of them and produce the final objects. Personally, I try to avoid making diagrams the final objects of a design or even just directly paving geometry over them. The translation may be procedural, rule-based, preferably driven by external to computation and geometrical paradigms. 

Stylianos Dritsas 2004

- Red: fastest path downhill (elevation), Blue: least sloppy path (curvature).

- Path traced using both elevation and sloppiness principles.

- Overlay of the path, the landscape contour lines and the curvature analysis.

- A map of motion tendencies / vectors on the landscape.

- A map showing the prominent routes formed by repetitive sampling.

Landscape Filtering for University Campus Design Project

This experimental scriptlet was a part of a studio project for the design of an Asian University for Women in Bangladesh. The purpose of it was not to employ it as means of form-finding, even though it significantly affected the formal expression of the design, eventually. On the contrary, this project,  was able to demonstrate how computation can help creative design processes at the conceptual level and how representation can help the designers by attaching meaning to geometries.

The studio started with a visit to the site. The site was located on a landscape with many small, complex hills (90% of the site are hills), where as of this moment, nothing has been built. There, I noticed that there were two senses of community. A community that is formed through visual connection; when one stands in the landscape and remotely interacts with other people. The other sense of community is created by the accessibility and the proximity of ones topographical location to another.

In order to experiment with these concepts, I used the topographical map of the site to regenerate a landscape model on the computer and then wrote a script that created visual boundaries from any point on the site. The task was to make an overall site plan for this university. Initially I went through series of random point analyses  in order to understand its visual boundary characteristics. Eventually, I was able to find places with interesting visual properties for specific program functions. The task of developing a building-complex configuration was also assisted by this procedural analysis tool. The built space itself was designed around wide openings reflecting the intention of making vivid visual communities. The initial script was more of a guideline to understand the site and to organize the intention.

Sawako Kaijima 2004

Generative Planning based on visibility and accessibility criteria.

Genera House

The Genera House project strived in capturing the complex relationship between a surrounding light-environment and human visual perception in a design artifact. The basic conceptual design elements were structured in the form of algorithms, based on the mechanisms of the eye functions. These algorithms were used to find desirable light conditions within a given three-dimensional environment. The idea was to design an architectural form that would correspond and interact with its complex surrounding.

The procedure involved sampling light information from a series of photographic material, populating with light data a three-dimensional volumetric representation of space based on voxels, processing this data-space through visual filters and thresholding the information cloud into discrete areas of interest. Eventually, a formal result emerged out of both the interpretation of given conditions and iterative refining design process.

Sawako Kaijima 2003

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