Parametric Transformation

Irina Shaklova — Sat, 23 Nov 2013 20:55:25 +0000

Image credit: Diana Quintero de Saul, Parametric studies for a responsive surface, source http://www.dianaqsaul.net/2011/09/25/parametric-studies-for-a-responsive-surface-system/

D’Arcy Wentworth Thompson ”On the Theory of Transformations” (“On Growth and Form” , 1917)

D’Arcy Wentworth Thompson was among the first to cross the frontier between mathematics and the biological world and as such became the first true biomathematician. His main work is the book “On Growth and Form” (published in 1917, expanded version published in 1942).

In the last chapter “On the Theory of Transformations , or the Comparison of Related Forms”, the author shows how differences between organisms can be presented geometrically. He saw form as a mathematical problem and growth as a physical problem.

Thompson was inspired by Albrecht Dürer’s works who used grid systems in his studies of human proportion. (Geometry, Treatise on Proportion). These works influenced Thompson’s theory of coordinates, which stated that the process of evolution as well as development could be comprehended mathematically by applying certain topological transformations.

An important topic discussed is how he regarded the mathematical transformation. He believed that all mathematical points that comprised a line drawing respected the principle that biological homology pertained to structures, but not necessarily individual point locations on structures. Rather, it was how the mathematical points were represented as a whole. His diagrammatic representation consisted of a superimposed grid that he used to to judge whether he had developed a reasonable formula for a specific form transformation. Clearly the only purpose of the mathematical grid was to demonstrate the whole geometry of the transformation as a deformed coordinate system.

In his “Theory of Transformations” he describes several ways of deforming the Cartesian grid of coordinates:

1. Linear variations along XY axis (fish eye resembles human eye after that kind of transformation)

2. Non-linear transformation which is based on logarythmic definitions

3. Shear concept – usage of various angles to transform

4. Radial transformation – in which one set of lines are represented as radiating from a focal point, while the other set is transformed into circular arcs cutting the radii orthogonally.

In his transformational grids he used the principle of plot points where each point corresponded to another and are defined in the space which is the basis of parametric design. This book is still relevant nowadays to understand the process and evolution of transformation. What should be considered here is that the transformation is not random but due to a certain mathematical logic.

Doubts

1. What if something is already deformed – how can you explain it mathematically?

2. Thompson only analyzed parts of organisms as opposed to creating a thorough analysis on the whole thing.

3. Thompson doesn’t explain relation to function but explains the jump in progress of forms while the evolution explains functionality.

Thompson viewed organic form as a ‘diagram of forces’ from which we can infer that the nature of the forces that act upon it now can be the same forces that have acted upon it in the past. With the help of this force metaphor, He saw how these different forces changed during both ontogenetic and evolutionary history. He concluded this through the mathematical comparison of forms.

Personal Research

Currently the technology that we us to produce architecture is evolving at a rapid pace, therefore I am interested in how the current technology responds to nature. There have been many examples of how architecture mimics the natural environment. With the aid of parametric technology, forms can be manipulated and transformed to resemble almost anything. I propose to research how we can manipulate parametric forms that can adapt to a certain environment as nature adapts to its particular environment.

Bernhard Rudofsky – ‘The Conditioned Outdoor Room’

Irina Shaklova — Sat, 09 Nov 2013 21:47:59 +0000

the source of the picture http://blog.bolandbol.com/2013/01/26/applying-the-pattern-language-inviting-entry/

Throughout history, humans have attempted many times to control climate but is it really controllable? After analyzing the reading, clearly the central themes are climate control, the human relationship to outdoor spaces, and how the importance of a garden inside of a dwelling has changed throughout history. The relationship between these main ideas are the central argument of this essay and how all of them are connected to climate.

To understand the present one must understand the past. History has shown us that humans adapt to the place that they live or grew up in and most importantly to the air that they breathe. An interesting example from reading is the journey of the English settlers to North America. As said in the reading they were not the most advanced house builders and knew very little of more advanced building technology therefore the transition from England to New England was a hard one. Their attempt to manipulate the climate of North America was successful in the sense that they were able to control the indoor spaces but unsuccessful with showing no importance to exterior aspects to a dwelling. This building tradition has been used for generations and most surprisingly is still being used today. Houses today manipulate the temperature of the interior space to keep out the external climate conditions, but is this really how it should be?

These current living conditions separate humans from our natural climate and the habitat that we are meant to live in.

The reading also talks about how the garden was historically an important part of a dwelling, but throughout the years that has since changed, being pushed outside of the program of the dwelling.This idea has created an imbalance between humans and nature. The human should consider himself as a part of nature and not as a conqueror. The way the reading talks about gardens is an example that shows the link between nature and humanity to be lost. The idea of the garden as described in the reading should be like an additional room with no ceiling, providing natural ventilation, vegetation, scent, and liveliness to a dwelling. In terms of modern society, one of the reasons why the garden has disappeared from the dwelling is the lack of land. This makes it impossible to create a livable outdoor space for everybody. That’s why humanity has to change it’s perception of nature and reintegrate gardens into the program. The way I view this topic is going back to the roots to recreate the link between humans and nature as long as humans are equal to it rather than being its conqueror. It is essential to return to this historic principle to maintain a balanced relationship between nature and humanity.

Personal Research:

For my future personal research I would like to focus on the idea of integrating nature in habitable spaces. The idea of enclosed spaces or “boxes” is becoming irrelevant nowadays because of growth in population, therefore we need to find the solution in which we can create habitable spaces for everybody.

Advanced Architecture Concepts » Irina Shaklova

Parametric Transformation

D’Arcy Wentworth Thompson ”On the Theory of Transformations” (“On Growth and Form” , 1917)

Bernhard Rudofsky – ‘The Conditioned Outdoor Room’