Math Objects An Origin of Architecture Daniel Baerlecken 1, Olaf Kobiella 2 1 Georgia Tech, College of Architecture, 2 TU Braunschweig, IGE 1 http://www.coa.gatech.edu, 2 http://www.ige.tu-bs.de/e 1 [email protected], 2 [email protected] Abstract. The paper discusses mathematical form generation as an academic 1 methodologyMath Objects to develop new approaches to architectural design. The academic designAn Origin studio of Architecture‘Math objects’ investigates the relationship between complex 3d-surfaces Danieland mathematicsBaerlecken 1, Olaf Kobiella in order 2 to expand the formal repertoire of architecture.1 GeorgiaIt claims Tech, thatCollege the of Architecture, process 2of TU form Braunschweig, generation IGE can be seen as an 1 2 autonomous entity,http://www.coa.gatech.edu, which is independent http://www.ige.tu-bs.de/e from an overall strategy or any a 1 [email protected], 2 [email protected] priori meaning. Architecture has always originated from a concept, eventually progressing Abstract.towards The a paper certain discusses form. mathematical This formmethodology generation as an has academic been reversed. The methodology to develop new approaches to architectural design. The academic paper discussesdesign twostudio studios “Math objects” undertaken investigates the in relationship the last between year, complex led by 3d- Daniel Baerlecken surfaces and mathematics in order to expand the formal repertoire of and Olaf Kobiellaarchitecture. at It the claims TU that Braunschweig, the process of form generation Germany. can be seen as an autonomous entity, which is independent from an overall strategy or any a priori meaning. Architecture has always originated from a concept, eventually Keywords: progressingGenerative towards design a certain; form.design This methodologymethodology: has been reversed.architectural The design paper discusses two studios undertaken in the last year, led by Daniel Baerlecken teaching; parametricand Olaf Kobiella form at the generation; TU Braunschweig, NURBS-modelling Germany. Keywords: Generative design; design methodology: architectural design teaching; parametric form generation; NURBS-modelling. Research Setup: Research Setup: Inputs Digital Techniques Subject and Educational Proceedings Architectural and Digital Theory Design Studio Manuals & Evaluations MA Students Architectural Projects Writings Outputs Math objects is generated out of a digital research framework as shown above. It ‘Math objects’ is generatedintegrates researchout of awork digital into theresearch students educationfeedback: curriculum Theoretical on the base and of atechnical digital results (part of design studio. This process can be seen as a program loop, with a continuous framework as shownfeedback: above. Theoretical It integrates and technical research results (partoutput) of output) of each of each iteration iteration directly inform the input work into the studentsinform education the input ofcurriculum the next de signon thestudio. Theof thedesign next studio design Math objectsstudio. has The been design studio ‘Math executed by two iterations of research and design work as presented below. base of a digital design studio. This process can be objects’ has been executed by two iterations of re- seen as a program loop, with a continuous search and design work as presented below. Section 17: Shape Studies - eCAADe 26 677 Mathematical Form: mathematical prototype by its deviates 3. Transference of the models and principles to the There has always been a deep connection be- context of a given project scenario (program and tween geometrical, mathematical principles and site). architecture – from the great pyramid of Giza, over 4. Exploration of interior spaces (massing) and sys- Brunelleschi, Palladio, to Le Corbusier up to today’s tems (structure and texture) in the scenario of architecture. Often these abstract and invisible, a model (ranging from large scale CNC-milled numeric machines have served as an architectural models over Z-CORP models to analogue mod- fountain of youth. ”Moreover, the perfection of math- els). ematical form is such (as Colin Maclaurin learned of This sequence of design techniques and com- the bee), that whatsoever is most beautiful and regu- puting skills fosters the student’s ability to question, lar is also found to be the most useful and excellent “. shape and interrogate space: The studio interrogates (On Growth and Form, D’Arcy Wentworth Thompson, the computer as an advanced design tool of form P.1097) generation and experimentation. The continuous Mathematical principles can inform architecture integration of analogue and digital modelling tech- in three different scales: massing, structure and tex- niques gives a substantial feedback to this design ture. This relationship has been explored in a series approach. of academic design studios and professional work In the following paragraphs the design works of the using a specific methodology, which is not just re- studio are presented, discussed and evaluated from search and also not just design, but both. The stu- four different perspectives: dios always focus on one or more of the three scales 1. Variables, formulas and geometries: An analysis (massing, structure or texture), although they are in- of specific mathematics and its ability to control terdependent and inform themselves vertically. The and shape complex form (Moebius-, Henneberg-, specific research ranges from mathematical form Klein-surfaces, etc.) structure and texture) to tessellation like Penrose Til- 2. Subjective choice and individual manipulation: ing, Danzer, Kite etc. (texture). an introduction and analysis of the rules, by Figure 1 form catalogue and form studies,Frauke Busdieker und Alke Malzahn In order to guide the students through the experi- which the mathematical shapes can be trans- mental design process, a gradual work flow has been formed to fit an architectural scenario (contex- developed. The elaboration of the mathematical tual alteration of variables, object scaling and model proceeds in four phases: morphing, non-parametric and manual inter- 1. Research on complex, mathematical forms. ventions (dirty-ism), integration of architectural 2. Creation of a form catalogue that explores the detail) 678 eCAADe 26 - Section 17: Shape Studies 3. Rapid prototyping and physical models: an anal- situations: grove, beach and sea. ysis and critique of the cross-media work flow, The design methodology aims at formal innova- with a focus on its ability to evaluate space and tion. This formal research is based on the assumption to inform the design process. that formally enriched architecture also has a higher 4. Design pedagogic: an evaluation of the Math- degree of functional complexity. In that sense formal objects studio as an approach to academic research is directly linked to programmatic research. teaching of architectural design. This aspect focuses on the transformative role of such digi- Project 01 - Julian Hartwig and Andre tal techniques for architecture - versus digital Stossun: techniques/ practices with a purely auxiliary ap- proach. Variables, formulas and geometries: Math Objects 01 - waterscape: The project from Julian Hartwig and Andre Stossun is based on the exploration of sine and cosine waves The design studio math objects 01 is based on mod- as deformative tools on a structural level. elling with Rhinoceros and the usage of the Math Starting with a stacked system of planar planes plug-in developed by Jess Maertterer which allows each plane deforms into a three-dimensional surface for the creation of complex geometry without time- creating grotto-like spaces with pockets of intersect- consuming rhino scripting. ing geometry. From this mathematical approach a Starting point of the process is an initial phase system of open and closed spatial configurations of abstract form generation using the Math plug-in emerges which has inherent structural properties. Figure 2 form catalogue, Julian Hartwig and Andre Stossun to create a catalogue of form variation. As a second Subjective choice and individual manipula- step the students are confronted with a building site tion: and a program and the resulting transformation of The transformation of the mathematical model fol- the prototype, which then has to be further devel- lows a multi-performative approach. By precise oped in the third phase by investigating the internal manipulation of the surface – using transitions with properties of the building and finalized in the last curvature continuity and clear defined moments of phase by creating a large-scale model. curvature discontinuity - the surfaces allow to be On a programmatic level the studio is deal- used as spatial division, as structure, as circulation, ing with the typology of a wellness spa – located as furniture, as technical equipment etc. in Heiligendamm, Germany in a decisive natural The mathematical model also informs the pro- environment. The side is marked by three different grammatic organisation of the building: By following Section 17: Shape Studies - eCAADe 26 679 the logic of a stacked and then deformed system between the different functional areas of the build- the building becomes vertically organized and ing. Other peaks provide structural support for the aims for a new type of a vertical spa in contrast to building. the traditionally dominating, horizontally organised typology. Rapid prototyping and physical models: Figure 3 design development, Julian Hartwig and Andre Stossun