“Transformation on Parametric Design Models” is an academic paper written by Carlos Barrios to present a research in progress in the development of parametric models for generation of complex shapes using parametric design, and introduces a methodology for exploration of possible designs generated from a single model. It also provides a case study on the designs of the Spanish architect Antonio Gaudi and examines the fundamental rules of form generation of the lateral nave columns of the Sagrada Familia temple in Barcelona. “A parameterization is presented as a fundamental tool for design exploration, which allows the reproduction of the original shapes designed by Gaudi, and the generation of a large set of new designs.”[1]
Barrios introduces the Parametric Modelling CAD systems as initially intended for the aeronautical industry, but later “making their way into the architectural domain since they provide a powerful framework for conception of design, allowing the description of multiple instances ad possible designs from a single modelling schema.”[2] Barrios further explains the breakthroughs posed by the introduction of parametric modelling system, as it overshadows the traditional CAD systems in terms of expanding the design process beyond current limitations, hence Experimental Modelling.
He states the principal advantage of a parametric model is the level of flexibility it provides to perform transformations that would result in different modifications and configurations from using one single geometrical components, creating an instance of a parametric model. It is important to note that parametric modelling creates an instance for each of the modified geometry component, thus allowing the designer to perform alterations and reconfigurations of the geometry without erasing and redrawing.
Barrios further explains the scope of design instances that a parametric model can generate, will be dependable on a balance between the parameters, the constraints of the geometry and the freedom or choices provided by the parameters. “The parameterization schema will determine which are the attribute subject to parametric transformations, in other words which components of the model will vary ad which components of the mode will be fixed.”[3] The range of the parameters can vary is determined by the step value of the parameters, along with its constraints.
Barrios moves onto discussing the parametric model for the columns of the Sagrada Familia. He observed Gaudi’s design rule are regulated by his architects’ intuition and interpretation of natural forms, as oppose to scientific knowledge of mathematics and geometry. Even though there are four initial shapes, the parametric model does not determine what kinds of shapes are valid. In terms of potential result and modification, the parameterized possibilities are infinite, as long as the shape is closed. He explains parametric combinations by stating “the number of design instances will not only depend on the number of shapes, but the possible combinations among them.”[4]
Barrios reinforces that the generation of a parametric model requires a level of design and planning deeper than just the presentation of an idea, but resulting a very powerful and versatile framework for design exploration. In the context of architecture, “most cases have used applications of parametric models in the context of design development, where most of the design decisions have been made”[5]. He then evaluates the purpose of parametric design and concluded that a well defined parametric model can serve as the means of creating designs in a particular purpose, while discarding other than do not fit the criteria.
Barrios finishes off with speculate how many possible designs a parametric model can generate, since all of the designs are obtained through altering and changing the initial shapes of the parametric model. “Design space (DS) of the parametric model equals to the sum of number of parameterized entities (PE) , and the step value of the parameters (SV), multiplied by the number and types of constraints (CN) which determines the degrees of freedom. “[6] He concluded that the number of designs generated by the parametric model is directly proportional to the number of parametric entities. “If we were to consider that design representations, such as plans, elevations, and 3D models, are geometrical models in an explicit representation, we must conclude that they are subject to parameterization. This proves that there is a great potential for applications in architectural design that has yet to be explored.”[7]
[1] Carlos Barrios, Transformations on Parametric Design Models: A Case Study on the Sagrada Familia Columns (2006) Department of Architecture, Massachusetts Institute of Technology, USA p.1
[2] Carlos Barrios, Transformations on Parametric Design Models p.1
[3] Carlos Barrios, Transformations on Parametric Design Models p.2
[4] Carlos Barrios, Transformations on Parametric Design Models p.7
[5] Carlos Barrios, Transformations on Parametric Design Models p.7
[6] Carlos Barrios, Transformations on Parametric Design Models p.8
[7] Carlos Barrios, Transformations on Parametric Design Models p.8
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