aurelVR

aurelVR.com This book is primarily an archive of projects that is gradually expanding through teaching and practice. In analogy to the periodic table this archive can hold, but also predict, elements before their actual discovery or realization in design. Within this framework the projects resist a reductive chronological or typological classification, common to many architectural portfolios. The juxtaposition of environmental scale and geometrical structure furthermore extrapolates the social and political dimensions of the project.

Teilchen - Nanostructures Particle Geometry: Points / Dots / Circles / Spheres / Raeume - Agorastructures Spatial Geometry: Lines / Folds / Surfaces / Fractals / Denkweisen / Felder - Megastructures Political Geometry: Houses / Cities / Landscapes / Metabolism / Umwelten – Ecostructures (oikos / house) Ecological Geometry: Environments / Climates / Futures / Borrowing from Andre Malraux’ musee imaginaire this archive is meant to expand like an archive imaginaire; an archive perpetually fertilizing and propagating new designs.

Hence, the projects are not “sorted” in any specific order but grouped as described above and indexed with their periodic value. An interactive version is available at www.aurelVR.com

Structures and Geometry

Subway Sorter NYC

Brooklyn Smart Dots

New Bouwkunde TUD

Nouvelle Comedie Geneve

Spluegen Rest Stop

Zurich Beach

Rotterdam Transportation Museum

Dubai Tensegrity Tower

Re-For-Mat

Zurich Elephant Park

Berlin Einheits Denkmal

Urban Village Shenzhen

Tetra

Euro Marseille

Continous Parametrics

VB Logic

Introduction

Manifesto 6 Structures and Geometry

9

Archive Imaginaire Description of Projects Teilchen - Nanostructures

Particle Geometry: Points / Dots / Circles / Spheres /

Brooklyn Smart Dots Subway Sorter NYC New Bouwkunde TUD Zurich Elephant Park

16 22

28 38

Raeume - Agorastructures

Spatial Geometry: Lines / Folds / Surfaces / Fractals /

Euro Marseille 48 Berlin Einheits Denkmal Dubai Tensegrity Tower

56 62

Denkweisen / Felder - Megastructures

Political Geometry: Houses / Cities / Landscapes / Metabolism /

Zurich Beach 72 Re-For-Mat 78 Tetra 90 Nouvelle Comedie Geneve

98

Umwelten – Ecostructures (oikos / house) Ecological Geometry: Environments / Climates / Futures /

Rotterdam Transportation Museum Urban Village Shenzhen 114 Spluegen Rest Stop 122

106

Post-Script Teaching / Continous Parametrics Bio Aurel von Richthofen

134 148

Manifesto /

Design

During my studies at ETH and Princeton, as a teacher at OSU and as a practicing architect I have researched formal strategies of design first through a set of procedural approaches then by applying parametrics on various scales - yielding unprecedented geometrical results - challenging the standard practice of architecture.

Instead of selecting a range of “suitable” forms to pursue the design, thereby post-rationalizing geometries as architecture, I understand parametrics as architectural design in advance of form. Design decisions necessarily take place at the moment the algorithm is written, yet the formal result cannot be anticipated, unless computed. Parametrics design unfold a series of geometric results at the moment constraining environmental parameters are applied to it. Combined with the computational power of standard computers, large numbers of results can be generated, compared and evaluated. This is where I see an intriguing design research tool that I gradually apply to a broader range of architectural objects, re-evaluating the design process and opening a potential new design discourse.

Manifesto / Algorithm

My research process invests into the generative potential of architectural design through the use of computation tools, especially scripting languages and information processing. It is a well-established currency that the wide usage of computation tools have unearthed and redefined not only the objects of architectural production, but also architectural creativity, as a procedural evolutionary phenomenon; an open-source practice. With new creative tools of expression, design agency may now be shaped at a stage prior to the precision of formal intent, in a relocation of focus from object-orientated design to procedural design. However, it is my intent in my teaching pedagogy and academic research to introduce in this conversation the cultural legacies of this fundamental disciplinary shift and explore theoretical ideas in parallel to technologies and digital tools. It is my intention to understand scripting processes next to the vision and the imaginary cities of the Metabolists that advocated the propagation of single units in space; we may conceive of capsules as binary units. While witnessing the affect of slight numerical information changes to the emerging forms of a script in Rhinoceros, to think of Reyner Banham’s “controlled environments” and the production by numerical data as in varying temperature thresholds.

Manifesto /

Teaching

Manifesto /

Practice

During the last two years, I have had the privilege to consolidate such ideas as a pedagogical experiment, specifically in four design studios and three design seminars at the Ohio State University. Generally speaking, the aim in my courses has been to translate information to material systems and conceptualize databases as generators for design creativity. In all courses, prior to formal articulations, students wrote “scripts” in a 3D software environment, parallel to writing a scenario or programme in words. In conjunction with seminars in advanced digital fabrication, students became editors of scripts and parameters, orchestrating geometries and, ultimately, working towards a non-standard understanding of design. The aim was not only to bridge across the boundaries of architectural theory and computational design, but also to reinstate the ideal of the architect as universal thinker engaging on all levels of the discourse, bridging technology and culture. As result, both undergraduate and graduate students responded overwhelmingly with emergent and unprecedented research projects. The work of students in my seminars has become the material for a “work in progress” exhibition – Option Explicit - in the main gallery of the Knowlton School of Architecture at Ohio State University.

In parallel to my academic work, I am the principal of aurelVR, architecture and design firm based in New York City and founded in 2007. aurelVR is engaged in experimental projects, - architectural design competitions, experimental form prototypes, and design research - as well as architectural and construction projects -residential renovations, furniture design, exhibition installations and retail design. Currently, aurelVR is engaged with the interior design of a 3,500 sq.f apartment on Park Avenue, NYC, the design of an exhibition installation at Columbia University, a design-research grant to create a pedagogical web tool, an open source database of material experiments, as well as an international design competitions. Operating on various scales and contexts, practice and teaching become necessarily intertwined.

Aurel von Richthofen, July 2009

6/7

Introduction -

structures and geometry

This book is primarily an archive of projects that is gradually expanding through teaching and practice. An archive, in this context, is understood as the dynamic framework for the emergence of architectural expressions and not design statement per se. In analogy to the periodic table this archive can hold, but also predict, elements before their actual discovery or realization in design. Within this framework the projects resist a reductive chronological or typological classification, common to many architectural portfolios. The juxtaposition of environmental scale and geometrical structure furthermore extrapolates the social and political dimensions of the project. The periodic table structures elements according to atomic weight and electron orbit. The present archive organizes architectural projects in geometrical structures and environmental scales.

Geometry is understood threefold: As mathematicalconceptual tool for the imagination and generation of complex forms. As material manifestation of architectural thought within the design process. As spatial articulation of underlying social, political and utopian forces within complex dynamic systems such as cities and environments. At the sub-human scale particles and nanostructures aggregate in molecular fashion, gravity is momentarily suspended, and the attractive forces behind elementary particles unfold their play to form new and unexpected materials. At the immediate human scale geometry delineates spaces and temporal sequences. Similar to a cinematographic ellipse, elements like lines, folds and fractals appear, relating the design project back to a larger ensemble. At the scale of enhanced human interaction megastructural geometry orchestrates landscapes and cities. Perceived as registration of a living process these geometries negotiate and describe political spaces. In a constant dialogue these geometries necessarily adapt and evolve, expanding the concept of Metabolism in architecture. At a global scale geometry has encompassed all aspects of architecture and is synonymous with environment.

Environments synonymous with eco-structures, again, differ from space by engaging explicitly into dynamic relationships of its constituent parts. Environment do not need to be literally alive. For example the interaction of sunrays on a body of water and rocks would form such eco-structural systems. Rather than an abstractum (space), environments are characterized by multiple recursive interactions in non-hierarchical form.

Teilchen - Nanostructures Particle Geometry: Points / Dots / Circles / Spheres /

The first chapter on Nanostructures describes the behavior of geometry at microscopic scale of particles; the environment is the weightless space of atomic interaction. Different economies of forces relate time and space as described by the uncertainty principle. Applied to information, these forces translate to the larger scale of urbanism. Brooklyn Smart Dots anticipate traffic in dynamic patters. Flow of pedestrians and vehicles is constantly registered and updated by classes of dots and vehicular agents. Constrained by external parameters patterns emerge on a meta-scale of street-scapes.

Subway Sorter rethinks geographic networks as time-based entities. Projected onto the New York Metropolitan Transportation system, the subway map re-organizes dynamically and portrays a new view on the city of New York itself. Applied to matter, the forces mentioned above manifest in primordial organizational types such as cellular clusters of Zurich Elephant Park and selforganizing maps of New Bouwkunde.

Raeume - Agorastructures Spatial Geometry: Lines /

Folds / Surfaces / Fractals /

The second chapter samples geometries at the scale of buidlings. In this category architecture engages in catalytic ways with its adjacent space and larger urban context.

Resonating beyond the boundaries of the object, the projects re-grouped as Agorastructures start to interact with a larger public space. EuroMarseille reconfigures a cathedral in Marseille by wrapping tubular vectors around it, thereby radically altering the church itself, the immediate neighborhood and its status

as a monument in the city. In a similar fashion Berlin Einheits Denkmal – a monument for the re-unification in the center of Berlin - points at various historical monuments in the vicinity, usurpating them and forming an indexical object. While the first project was changing the context by changing the signifier, the later, in a reverse strategy, becomes the sign of a monument by referencing the immediate context. Dubai Tensegrity Tower, finally, becomes a structure devoid of program, a display of its structural ingenuity. By virtue of tensegrity – a structural system that reduces tensile members to a minimum – the very structure of the tower is heightened, resulting in a tense accentuation of the space activated.

Denkweisen / Felder - Megastructures Political

Geometry: Houses / Cities / Landscapes / Metabolism /

The third chapter on Megastructures lists projects that deploy strategies discovered in Agorastructures and literally multiplies them. Projects resemble urban scale webs or mats. The larger fabric constitutes more than the sum of its parts, although local changes do not affect the overall system globally. Megastructures necessarily transition between Agorastructures and Ecostructures (see below).

Having reached a degree of saturation Megastructures are the captives of their scale and size. Zurich Beach literally multiplies the shoreline of Lake Zurich applying planar design strategies in section again. The linear character allows for the exploration of divergent ideas within the single structure. Re-For-Mat distills strategies implied in the “mat-typology”, transposes them into an inner urban setting and exponentially super-charges a layered landscape structure. Tetra takes the idea of exponential multiplication radically further. Conceived as a recursive fractal structure, this scheme for a house repeats itself endlessly in scale. Same originating diagram becomes a house, becomes a city, becomes a world.

Umwelten – Ecostructures (oikos / house) Eco-

logical Geometry: Environments / Climates / Futures /

Ecostructures re-group projects using geometry at larger scale. Instead of enacting a process of urban transformation through the alteration of local space Ecostructures re-collects projects hat aim at creating global spaces. Two fundamental differences distinguish Ecostructures from Agorastructures and Megastructures. In contrast to the previous categories space and geometry coincide in Ecostructures. While Agorastructures require a system of signifiers to change or create space quasi as a side-product, Ecostructures engulf the environment created. As described above, environments differ radically from space. The non-hierarchical feedback loop between constituent parts ultimately creates complex dynamic systems. The projects listed here orchestrate this play.

Varying in size from the interstitial space of a membrane to the exteriority of artificial landscapes, Ecostructures like Nouvelle Comedie Geneve and Rotterdam Transportation Museum investigate shallow depth of membranes as environments of their own right. Ecostructures like Urban Village Shenzhen and Spluegen Rest Stop re-configure existing landscapes (Alpine and urban) with intricate geometrical transformations.

Archive Imaginaire

Borrowing from Andre Malraux’ musee imaginaire – a global collection of arts in a virtual (?) museum without walls – this archive is meant to expand like an archive imaginaire; an archive perpetually fertilizing and propagating new designs. Hence, the projects are not “sorted” in any specific order but grouped as described above and indexed with their periodic value.

Its interactive version is located at: www.aurelVR.com

12 / 13

Teilchen - Nanostructures Particle Geometry: Points / Dots / Circles / Spheres /

BSD

Nanostructures: Brooklyn Smart Dots

Brooklyn Smart Dots

/ Competition entry for sustainable traffic solutions in Brooklyn, NY, 2008 / Aurel von Richthofen, Lydia Kallipoliti, Mitchel Joachim, programming Kaustuv Debiswas

Brooklyn Smart Dots originates in the radical re-conception of street traffic and proposes an intelligent surface of communicating luminous dots. With the advent of mechanical transportation came the necessity to mediate traffic flows based on the voluntary acceptance of rules and regulations by each traffic participant. Exceeding speed limits or disregarding traffic signals, for instance, could have deadly consequences. Because there was no immanent feedback mechanism, each traffic participant had to account for one’s own possible failures and of those of the others and the system. The confidence in the traffic participant’s ability to compensate system failure was a compromise in lack of a better technological solution. The set of rigid traffic rules stood in sharp contrast to the highly dynamic nature of traffic. // Smart dots aims to re-introduce swarm-intelligence into the shared space of pedestrian, mechanized and motorized traffic.// A field of Smart Dots registers vehicular and pedestrian motion, computes possible trajectories and collisions, projects traffic patterns, and communicates anticipatory solutions back to the participants in form of color coded visual information. Pedestrian and bikers will react to a bright visual signal, while automotive machines will be equipped with visual sensors. As a result traffic is visualized as a dynamic system and displayed as a forecast within the very space it is happening.

Implemented in a Java scripting language (Processing), vehicular classes and smart dots constantly update their states based on the dynamic information of the system. The system requires simple rules such as the avoidance of collision, maximum speed regulations, priority of right-over-left to escape chaos. Even if the system runs from random starting parameters, smart dots will asymptotically approach a harmonic traffic pattern, the optimized traffic solution. The resulting traffic patterns exhibit striking symmetries similar to “Tone Figures” discovered by Ernst Florens Friedrich Chladni in 1802. Smart Dots can be constrained even further by casting the system onto existing street-scapes.

In return, Smart Dot patterns are used compute urban traffic 16 / 17 design, leading to an emergent urban design.

Right: From hard street to Smart Dots Top: Smart Dots Rendering Bottom: Dot Bots / Next pages: Dot Environment

18 / 19

SUB

Nanostructures: Subway Sorter NYC

Subway Sorter

/ study project / New York City, 2008 / Aurel von Richthofen, based of a Java program written by David Rutten

The design research leading to Subway Sorter is rooted in an ongoing interest in the representation of traffic – here in the form of public underground transportation – as a means of psycho-geography of the city. ` The congested surface of Manhattan Island forces its inhabitants to use the antiquated underground system. A short historical survey shows that the present underground system is the result of projects by several competing private transport companies. In good capitalist manner each of these companies served specific boroughs with the financial and commercial center in the early 20th century.

Thus the system radiates linearly from downtown and midtown Manhattan to Upper East- and Westsides, Brooklyn, Queens and the Bronx without many connections. The linear transportation proved highly efficient and lead to a New York specialty of local and express trains sharing the same lines. As a means to connect boroughs and center, this system was a marvel. With the transformation of neighborhoods and relocation of financial and commercial activities, the system is on the verge of collapse. //Or is it?//

When these companies merged to the current Metropolitan Transport Administration in the 1960ies little was done to overcome the separation of the systems. In a demonstrative move the first map shows a unified and color-coded subway network mapped on the super-terrestrian geography of the city. As a result New Yorkers and visitor alike regularly experience the frustrations of a subway system that is almost un-intelligible. The 1972 map was an attempt to overcome geographic fidelity in favor of radical graphic abstraction. The 72 map shows lines running orthogonally and in 45* angles.

Central Park had shrunk to a green square and the red 1,2,3 lines meeting at Columbus circle had been placed west of the B,C,D,E lines instead of east for the sake of graphic consistency.

No wonder this graphically pleasing map found little recognition with Manhattanites using it and was replaced a few years later with the previous map. What made the New York subway system incomprehensible was the representation as a single geographic entity. Neglecting its legacy the map was neither usable above nor underground.

Subway Sorter is based on the idea that most essential information to the user is time. A subway user entering the system will know that approximately where to surface. What he or she does not care about is what intricate the turns the trains will take underground, leaving it to speculation whether to change in one station or the other. Ultimately one wants to know when the excruciating trip will reach its destination and one would like to know what the most efficient connections are. Subway Sorter inputs the New York subway system and re-organizes each segment on a time based scale. As the geography distorts a new map appears: Connection nodes between lines tie the system together, local stops in a line bulk out while the space between express stops shrinks, the linear shape of Manhattan inflates and wedges around the radiating satellites of Brooklyn, Queens and the Bronx.

Implemented as an iPhone application in alpha stage Subway Sorter feeds on live mta data. Localization through GPS and antenna triangulation tracks the users position. The map re-adjusts and computes time and connections in a single dynamic map.

22 / 23

225 St

207 St

168 St

161St

149 St

148 St 145 St 125 St

96 St

86St

59 St

42 St 34 St

Lex 59 Lex 53

47St 34St

Grand Central

Union Sq

14 St

W4 St Broadway

Chambers

Canal Fulton Wall

Bowling

Top: Subway mapping in equitemporal space

225 St 207 St

161St

149 St 125 St 148 St

168 St

145 St 86St

125 St 96 St

59 St Lex 59 47St

72 St

Lex 53

42 St

42 St

34 St

Grand Central

34St 14 St

Union Sq

14 St W4 St Broadway

Chambers Canal

Chambers

Canal Fulton Wall Bowling

24 / 25

Top: Subway Sorter Beta / iPhone App Right: Dynamic nodal diagram NYC

26 / 27

TUD

Nanostructures: New Bouwkunde TUD

New Bouwkunde

/ competition entry to rebuild the architecture school at TU Delft, the Netherlands, 2008 / Aurel von Richthofen with Kaveh Arbab, Rushabh Parekh, Mohammed Nazmy

New Bouwkunde is a radical design for a new school of architecture at TU Delft in the Netherlands.

Study, project and research within a school of architecture are normally shaped by an intimate relationship of scholars and students within a tight educational community. Not at Delft where the sheer number of more than 5000 students of architecture outgrow any sense of personal scale. The school is in fact a campus within a campus, a system of complex programmatic requirements and nested spatial hierarchies. The previous school avoided the dilemma of size vs education by creating a machine for learning, absorbing students and teachers alike, dwarfing the individuals against its multistory labyrinth and forcing them into pre-described patterns of thinking. Ironically the original concrete building collapsed after a short circuit in a coffee maker set fire.

Resisting the idea of a single machine, New Bouwkunde is a cluster of cellular bubbles. Cells come in different types responding to programmatic requirements. The cells re-combine according to temporal and local specificities of the university environment. Studio cells, office cells, auditoriums and labs form micro clusters. Larger programmatic cells, such as libraries and restaurants attract those clusters again.

Each cell constantly negotiates its position within the cluster and within the overall field. A shift in programmatic use will result in a new constellation. Each cell is equipped with a semi-translucent membrane. This membrane contains and protects the learning environment (Banham). The membrane acts as projection screen from the inside and communication device from the outside. The visual information of each cell reinforces the system. Thus the design achieves local specificity within a large cluster, bridging size and locale.

28 / 29

2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 13.8198 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 7.5694 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 15.1388 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 6.1804 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 13.8198 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 7.5694 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 13.8198 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 6.1804 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 10.7047 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 13.8198 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 17.8412 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 10.7047 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 6.1804 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 25.2313

2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 6.1804 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 6.1804 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 6.1804 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 7.5694 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 7.5694 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 10.7047 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 10.7047 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 15.1388 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 13.8198, 13.8198, 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157, 12.6157, 12.6157, 12.6157, 12.6157, 12.6157, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 13.8198, 13.8198 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 17.8412 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 25.2313

25.2313, , 17.8412, 12.6157, 12.6157, 12.6157, 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 13.8198, 13.8198 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157, 12.6157, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 17.8412 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 13.8198, 13.8198 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 , 4.3702, 4.3702, 4.3702, 6.1804, 6.1804, 6.1804, 7.5694, 7.5694, 10.7047, 10.7047, 15.1388

4.3702 , 4.3702, 4.3702, 4.3702, 6.1804, 6.1804, 6.1804, 7.5694, 7.5694, 10.7047, 10.7047, 15.1388, 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 4.3702 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 13.8198, 13.8198 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 12.6157, 12.6157, 12.6157 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 17.8412 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 13.8198, 13.8198 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 5.6419 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894 2.8602 , 2.8602 , 2.8602 , 2.8602 , 2.8602, 3.9894 , 3.9894, 25.2313, , 17.8412, 12.6157, 12.6157, 12.6157

Left: Programmatic Circle Packing / algorythm and model Top: Opacity transitions Bottom: Cluster and Campus / Next pages: Programmatic diversification

30 / 31

Faculty Lab Number of Spaces : 4 Area : 500 Radius: 12.6

Restaurant Number of Spaces : 1 Area : 2000 Radius: 25.213

Studio Number of Spaces : 350 Area : 25.7 Radius: 2.86

Restaurant Number of Spaces : 1 Area : 2000 Radius: 25.23

Educ Num

Auditorium 1 Number of Spaces : 5 Area : 60 Radius: 4.37

Office Number of Spaces : 162 Area : 50 Radius: 3.984

cational Facilities mber of Spaces : 5 Area : 600 Radius: 13.813

Public Facility small Number of Spaces : 3 Area : 500 Radius: 12.6

Auditorium 2 Number of Spaces : 3 Area : 120 Radius: 6.18

Public Facility Number of Spaces : 1 Area : 1000 Radius: 17.84

Studio Number of Spaces : 1 Area : 720 Radius: 15.138

32 / 33

Top: Axonometric section Bottom: Cluster on Campus Next pages: Sprawling mat

34 / 35BK2008-3205

ublic Facility of Spaces : 1 Area : 1000 adius: 17.84

Y1

ELE

Nanostructures: Zurich Elephant Park

Zurich Elephant Park

/ competition entry for the expansion of the Zurich zoo, Zurich, Switzerland, 2008 / Aurel von Richthofen with Rushabh Parekh, Scott Kittle, Josh Lawrence, Anthony Prousi, Matt Canterna

Zurich Elephant Park is an extension to the zoo in Zurich and a completion of its campus-like disposition. The Elephant Park negotiates a series of programmatic constraints based on the nature of designing for elephants and humans alike, moving away from the classic separation of exhibit and observer. Conceived as an environment the Park exploits human-elephant contacts in a maximum of ways. A diagram of the “Vitruvian Elephant� in analogy to Leonardo da Vinci’s famous drawing examines the range and reach of animals to derive a set of key proportions. Translated into a parametric model this diagram is applied to all zones of overlap between human and elephant spaces. In order to maximize these overlaps all spaces follow a loose organic geometry. As a result, visitors can observe the animals from closest possible distances and from all angles, without visual barriers. Far from being a simple extrusion in plan, the scheme gently drapes down the hillside. Visitors stroll over the grass roof landscaped as savannah to peek through termite mound-shaped light funnels.

Pathways encompass all exterior elephant ranges and reconnect to lead visitors inside where the same diagram regulates the experience. Linking two different scalar economies (human / elephant) the system constantly adapts to differentiate moments of architectural specificity.

38 / 39

Top: Boundary condition Elephants/Humans Left: Close-ups 40 / 41

Hauptweg Entdeckungsweg Seitenweg Anfahrt

Aussengehege Innengehege Besucher

Top: Internal/External Program Left: Circulation Diagram

Intern

42 / 43

Besucherweg Afrikanisches Gebirge

A2 Anlage für Bullen (800 m2)

A4 Huftiere und Schweine (250 m2) A3 Anlage für Bullen und Kühe (1'000 m2) B6 Lodge 2 (200 m2) B9 Toiletten (100 m2)

B3 Lodge 1 (200 m2)

B7 Terrasse (140 m2)

B4 Terrasse (140 m2)

B1 Edukation (400 m2) A1 Aussenanlage für Bullen, Kühe und Kälber (3'000 m2) B2 Arena (75 m2)

Grundriss 1/200

A3 Anlage für Bullen und Kühe (1'000 m2)

B8 VIP-Lager B6 Lodge 2 B5 Lager

B9 Toiletten B3 Lodge 1

B1 Edukation

B2 Arena

A1 Aussenanlage für Bullen, Kühe und Kälber (3'000 m2)

Grundriss 1/500

E6 Werk- und E9 Fahrzeuge Technik E2 Heu- und StrohC6 Quarantäne E7 Betrieblager E8 Dungraum E3 Futterküche C5 Arbeits- und Abtrennboxen für Bullen C3 Anlage für Bullen

C2 Innenstall für Kühe, Kälber D1 Huftiere und Schweine E4 Pflegerraum

C1 Innenanlage für Bullen, Kühe und Kälber

Wasserbecken E5 Filteranlage E1 Pfleger

Innenstall für Giraffen, Zebras

Raeume - Agorastructures Spatial Geometry: Lines /

Folds / Surfaces / Fractals /

EMR

Agorastructures: Euro Marseille

Lines

Mathematically lines and vectors form direct, one-dimensional relationships between points in space.

In the Modernist project linear structures reconcile the Utopian with the Monumental. In this function, lines and vectors work towards a new understanding of monumental and sacral spaces.

See EuroMarseille and Berlin Einheits Denkmal.

EuroMarseille

France, 2002 / Aurel von Richthofen

/ entry for an urban ideas competition,

The present cathedral of Marseille is an icon malgre-lui. Of no particular historical relevance it was built in the 1930ies as prominent sign overlooking the harbor, dwarfing its surroundings. In order to re-frame and re-direct this sacral building, EuroMarseille utilizes an ancient concept of axial shifting. When a basilica became too small its central axis was simply shifted by 90 degrees around the choir. The old central apsis became the new choir and a larger apsis was added to the structure. As a result the direction of the church shifted by 90 degrees, in some cases several times, as a succession of churches grew one on top of each other.

EuroMarseille transposes this planar strategy into three dimensions. Tubes extend out of the existing cathedral and wrap around the building and into the adjacent space. Dramatic cantilevers frame an identical external volume by delimiting its edges. Formally and structurally distinct form cathedral the extension nevertheless forces a new conception of sacral buildings itself, a structural tour de force bracketing the sacral space and while dismantling the dominating monumental character of the church.

48 / 49

Left: Manifesto Image Right: Sketch to Model

50 / 51

52 / 53

BED

Agorastructures: Berlin Einheits Denkmal

Berlin Einheits Denkmal

/ competition entry for a monument to the German re-unification, Berlin Germany, 2009 / Aurel von Richthofen

In search for a monument commemorating the 20th anniversary of the crumbling of the Berlin Wall and the German reunification the German parliament launched an international competition. Located at the center of the city the monument was to educate and commemorate at the same time.

This entry was recommended for continuation albeit the competition got cancelled for political reasons.

Berlin Einheits Denkmal differs from traditional monuments as it avoids metaphorical statements. It also critiques a younger phenomenon in monument design that seeks intellectual asylum in formal abstraction and fields. Instead, Berlin Einheits Denkmal aims to integrate its historical (and monumental) environment by registering vectors transcending imaginary historical strata in a highly dense urban setting.

These vectors form a vortex of lines, a dynamic node in space and point to reveal historical connections. The monument is intended to be used and explored by literally walking through it. The monument invites the public to stroll amidst its glass branches and climb its stairs to gain particular look-outs. By this literal appropriation the structure the public becomes a part of the monument and contributes to an idea of production of culture and history. A similar effect has been described in the introverted balcony of the Altes Museum by Schinkel within sight of the projected monument. Berlin Einheits Denkmal aims to integrate and update this idea, expanding the production of public space through the monument from a bourgeois to a democratic audience.

56 / 57

AUSBLICKE

INTERAKTIVE INFO RAHMEN

GESCHICHTS-FENSTER

SICHT LINIEN

PODEST

STRUKTUR

SITUATIONSPLAN M: 1/500

top: site relationships and vistas left: silhouette of structure

58 / 59

+23 M

BEGEHBARE RAUMSTRUKTUR

+16 M

+5 M EINGANGS-NIVEAU STADT NIVEAU

WASSERSTAND

GEWOELBE

top: section right:perspectives “Schlossbruecke”, “Bauakademie” & “Kupfergraben”

100578

PERSPEKTIVE SCHLOSS BRUECKE

PERSPEKTIVE BAUAKADEMIE

PERSPEKTIVE KUPFERGRABEN

DTT

Agorastructures: Dubai Tensegrity Tower

Dubai Tensegrity Tower

/ Competition entry for Thyssen Krupp award, Dubai, 2009 / Aurel von Richthofen

Dubai Tensegrity Tower is the pure exhibition of structure. Calling for an iconic tower devoid of program the elevator company sponsored competition merely indicated a desired height of 170 meters. Under economic constraints skyscrapers are normally used to multiply the footprint in the endless stacking of floor plates. Not in this tower without specifications on program, floor area ratio nor skin. By design, Dubai Tensegrity Tower is poised to become Dubai’s next Eiffel Tower: A tensegrity system heightening the ingenuity of its own structure.

The static principles behind tensegrity systems were discovered and exhibited by Russian Constructivist Karl Ioganson in 1921, but were not received in the West at the time. Ioganson called his invention spatial construction emphasizing the novel spatial capacities of the system. His art was meant to forecast engineering developments in buildings, bridges and machines. Re-discovered by Kenneth Snelson – a student of Buckminster Fuller – in the 1950ies in Syracuse, United States, and coined by the later as tensional-integrity, the system reduces all tensile members of the static system to a minimum thickness, where they can only act in tension. The remaining compression members are arranged such that they never touch each other, giving the impression of a structure magically suspended in the air. //Paris – Moscow – North Carolina – Dubai mark the utopian journey of this project.//

62 / 63

top: entrance perspective left: structural & programmatic diagrams bottom: tensegrity system

64 / 65

top: close-up on model left: elevations of 170m tower next pages: lobby and observation deck / tensegrity model

66 / 67

Denkweisen / Felder - Megastructures Political

Geometry: Houses / Cities / Landscapes / Metabolism /

ZB

Megastructures: Zurich Beach

Expanded Surfaces

/ Membranes and Mats. While projects like Rotterdam Transportation Museum explore the thickness of façade and membrane systems and Nouvelle Comedie Geneve aims to create depth and dematerialization in flat envelopes, two explorations of expanded surfaces operate on a larger urban scale: Zurich Beach, 2005 and Re-For-Mat Berlin, 2007 operate on and critique the urbanism of “mat” typologies. Moving up in scale, the expanded surface registers the space of predominant horizontal movement and inhabitation.

Zurich Beach

/ Urban development on the shore of Lake Zurich, Switzerland. Thesis project ETH Zurich, 2004 / Aurel von Richthofen

The city of Zurich developed out of the changing relationship to its bodies of water. The medieval city was arranged on both sides of the river. The industrial city gradually opened towards the lake shore. This urban re-orientation towards the city’s prominent water front happened relatively late in comparison to cities like Geneva or Lucerne, thus a beaux-art water front was never completed. Modernist approaches in landscaping the shore remained fragmented.

In contrast, Zurich Beach is radically embraces the lake. The project literally multiplies the shore line: Horizontally - in redesigning a meandering coast line of twice the original length; Vertically - in doubling the shore with a continuous line of cantilevering buildings. This strategy allows for a woven design, both in plan and in section, that accommodates various public programmatic entities: A conference center, theater, hotel, rowing facilities and a sailing center. The lake side promenade on the expanded shore line is totally public, ultimately linking city and lake.

72 / 73

Top: Cantilevering model over shoreline Left: Programmatic uses

74 / 75

Top: View of shoreline Bottom: Urban Strategy

76 / 77

MAT

Megastructures: Re-For-Mat

Re-For-MAT

/ Re-Formatting Berlin’s Free University, Berlin Germany. Thesis project Princeton University, 2007 / Aurel von Richthofen

Re-For-MAT is a critique of Berlin’s Free University designed by Georges Candilis, Alexis Josic and Shadrach Woods in 1965. Next to the ordinary means of architectural representation - such as diagrams, plans and sections - Candilis, Josic & Woods used a manual as a generative device for design. This manual, structured around a set of 13 synthetic rules and limitations, contained all the necessary information for the implementation of the architectural design of the Free University in Berlin. The Free University manual was an internal design and communication tool, originally composed by the architects in order to clearly communicate construction principles and establish a common groundwork for the different agents that would bring the project to its realization. At the same time, the manual was open to interpretation and criticism that reflected underlying cultural tendencies.

Re-For-MAT reuses the manual as an open source generative mechanism for this thesis project tracking step by step each principle and its potential redefinition. In analogy to the Free University manual Re-For-MAT follows two parallel strands of investigation: A theoretical research departing from the original manual leading through translation, interpretation and diagrammatic abstraction on one hand, and, a design research testing the urban, volumetric, structural and topographic aspects of the transformed ‘mat-typology’ on the other.

By re-inserting the mat into the very center of the city the project provokes a series of architectural and urbanistic reactions that the Free University could not have triggered due to its peripheral location. Transposed from Berlin’s south western suburbs to the nexus of historical, political and cultural activity in Berlin Alexanderplatz, the mat accommodates, adjusts and reorganizes its internal structure, intending to fulfill the urbanistic aspirations of the former project. The new mat reacts to this context in section, façade and elevation in addition to its stratified plan. As consequence the new mat lifts up from the ground, liberating a landscape at street-level and doubling it on the roof. The new mat inflates giving way to the emergence of local discrete elements within the global system.

The mat is a strategy for design as well as a design result. Equally the manual is a condition to, and a product of, the design process. Re-For-MAT liberates the creative potential of the original scheme and offers a critical comment to the current discussion on historicist reconstructions in Berlin. Eventually, my proposal renders a rule-based system that mediates between the contextual framework of the cultural and geographic limitations of my site in Berlin and the internal structure of the manual.

78 / 79

Top: Tomographic Axonometry Right: Apercus de Berlin

+21m Zoom-in

80 / 81

Multiple Landscapes

React to the urban context

Develop the Manual Design Research Intuitive Mutations vs Rigid Interpretation

Speed me up

The mat as stratified system

Inflate the mat

Introduce sectional development

82 / 83

Cut-Out Sections - Massing Diagram 84 / 85

86 / 87

Top: Topological Transformation of the Mat Right: Urban Implementation

TET

Megastructures: Tetra

Tetra

– ideal city, ideal house

/ conceptual project 2009 / Aurel von Richthofen with the graphic seminar sophomore class of 2008 & 2009 at OSU.

//The city is a tetra is a tetra is a house.// The house of the future is a tetrahedron.

In fact, it is a set of tetra- shaped rooms forming a little city of tetra-spaces that form a tetra-shaped house. Fractal in geometry, the ideal house can be applied as ideal city on a different scale. Recursive in time, a partial realization anticipates the future expansion.

Mathematically, the tetrahedron is the simplest platonic body next to the sphere. It yields a maximum of volume per envelope. It is made of four regular triangles, the simples planar geometries next to circles containing the maximum surface per outline. The tetrahedron has four point symmetries, three linear symmetries, two rotational symmetries.

My architectural obsession with tetrahedrons is more than a play on descriptive geometry. Tetra is the search for a new iconic diagram, an update of Le Corbusier’s Maison Dom-in-o. Corbu’s proposition was barely a project for a building (maison). It exhibited three floors slabs cast in reinforced concrete, held in space by and array of square columns. Naked steps indicated the possibility of a vertical movement. Remarkably, his propagandistic five points to architecture directly derived from this diagram: The continous landscaped ground, the free floor plan, the pilotis, the elongated window façade & the roof garden. Dom-in-o was the cast for all of Corbu’s later projects.

Tetra is tipped over its center of gravity so that it rests on one corner. This minimizes the footprint and all structure cantilevers from there. At the same time the internal floor planes level. The four faces of Tetra are never perpendicular to each other. Instead, two faces form an angle and brace space in horizontal or vertical direction. Tetra neither stratifies space horizontally (free plan) nor vertically (free section) alone, but in all three dimensions at the same time. The structure is plan and piloti in one. The result is free space.

90 / 91

Top: Cluster of Tetras Left: Colonies in the Air 92 / 93

94 / 95

96 / 97

NCG

Megastructures: Nouvelle Comedie Geneve

Nouvelle Comedie Geneve

/ competition entry for a new theater and opera house in Geneva, Switzerland, 2009 / Aurel von Richthofen with Rushabh Parekh

Designed as classic and contemporary theater and opera house, Nouvelle Comedie Geneve is a hybrid. For the sake of programmatic flexibility all main spaces are organized on one horizontal plane. Acoustic requirements on stage and seating given, constrained by the site, the resulting form is a simple massing diagram. Thus the section resembles Antoine de St. Exuperie’s hat-turned-elephant-eating-snake drawing from the Little Prince. The architectural exploration is bound to the thin layer of the façade. The skin necessarily becomes the mediating surface of this project.

Nouvelle Comedie Geneve explores a sophisticated fractal triangulation system. Applied on the surface in creases and corners of the volume an effect of dematerialization is achieved. The scalar congruence of the fractal breaks down the solid geometry derived by the inner program into ever smaller facets. These facets project in and out, creating a bi-fold illusion of increased depth and scale within less than half a meter of façade thickness. The recursive nature of fractalization controls depth by “generations” of fractals. Generations increase locally on the skin depending on the desired effect of dematerialization.

The folded nature of fractalization places Nouvelle Comedie Geneve within a series of surface/façade projects that aim to re-write complex surfaces with simple parametric rules. See Spluegen / Triangulation, Rotterdam / Skin.

98 / 99

100 / 101

loges restaurant

hall d'accueil

foyer locaux techniques

coupe transversale à l’échelle 1/500

loges salle et scène frontale locaux techniques

ateliers de montage stockage

coupe transversale à l’échelle 1/500

façades à l’échelle 1/500

foyer et loges

répétition

salle modulable

salle et scène frontale accès des décors et livraison stockage

locaux techniques

Top: Sections thorugh Auditorium Right: Entrance View

coupe longitudinale à l’échelle 1/500

foyer et loges

répétition salle et scène frontale

salle modulable

répétition locaux techniques

stockage

coupe longitudinale à l’échelle 1/500

102 / 103

Umwelten – Ecostructures (oikos / house) Eco-

logical Geometry: Environments / Climates / Futures /

RTM

Ecostructures: Rotterdam Transportation Museum

Transportation Museum

/ study project, Rotterdam, The Netherlands, 2002 -2003 / Aurel von Richthofen, Sander Troost

Rotterdam Transportation Museum is a linear structure occupying abandoned tracks next to the railroad station in Rotterdam. Its design resembles an illusive creature with metallic scales reflecting the surroundings. Its body is changing in width along a main linear direction of the tracks. Meant to be read en passant, from a moving train or in rushing to the station, the surface mediates between opacity and translucency, thickness and flatness, materiality and immateriality.

Conceptually, the project explores the space immediately adjacent to the human body, the few inches of space between skin and clothes. We carefully register this space every day, thereby constructing our individual identity. This space is of architectural interest insofar as it stands in between the body, traditionally seen as private, and the space in which the body exists, necessarily other, thereby public. As a third category of spaces neither private nor public, the in-between extends the body into the public realm, creating a membrane of permeable space.

The originating diagram describes a series of double-eight curves, serving as regulating sections. The resultant self-intersecting surface encapsulates various spaces similar to an inflated membrane. A second logic of scales is applied to the project, giving Rotterdam Transportation Museum both structural rigidity and revealing its inherent aesthetic logic.

The scale folding angle and the scale height correspond to the distance from the central spine. As the membrane inflates, the scales rotate vertical and overlap. As the membrane flattens, the scales relax, allowing light to pass through.

To test the geometric qualities the original algorithm was programmed in Autocad Lisp in 2002. The model was laser cut in stainless steel at the physics department of material sciences at ETH Zurich. The assemblage of the model relies on purely mechanical connections: Sections and floor-plates slide into each other, lateral scales fold up along dashed cut lines, creating a gentle pressure fit connection.

106 / 107

Top: Sectional development Right: Photographic Study: Skin-Space

108 / 109

Top: Plans and Elevation of Rotterdam Transportation Museum Left: Programmatic Sections

110 / 111

Top: Parametric Model implemented in Autocad LISP

Top: Steel-Cut Section

112 / 113

USZ

Ecostructures: Urban Village Shenzhen

Urban Village, Shenzhen

Study on interstitial urbanism in Shenzhen, China, 2005 / Aurel von Richthofen

Having grown to several million inhabitants in less than a decade the special economic zone of Shenzhen experiments on urbanism after urbanization. Urban Village, Shenzhen represents the reversal of the classic rural setting.

Following the expropriation of farmland the village is now surrounded by multi-story high-rise buildings and ten lane highway belts. In return, peasants were granted ownership of their tiny village lots. Following the official doctrine of “one country, two systems” Urban Village, Shenzhen explores fast forward capitalism in building up the lot of a small farm house to ten story apartment buildings.

Urban Village, Shenzhen proposes the radical re-organization of this congested space.

Instead of mushrooming buildings vertically on tiny lots, the project proposes to “slices” existing buildings horizontally, close vertical connector such as staircases and elevators (if any) and re-connect the spaces through lofty skywalks as needed. This new system webs the city and offers highest degrees of flexibility. Strategically breaking down spaces horizontally it can mitigate various scales and ultimately reconcile the village’s urban aspiration.

114 / 115

PUTIAN

ZHANGZHOU SHAOGUAN BEIJING

XIANMEN RONGSHENG

CENTRAL CITIES

SHANTOU

GUANGZHOU

SHENZHEN

SHENGZHEN MACAO

HONGKONG

YANGJIANG

BEIHAI

SHAOGUAN

MIANCHIANG

GUANGZHOU

ZHANJIANG

MACAO

WESTERN CITIES

EASTERN CITIES

HONGKONG ABROAD

ZHANJIANG ABROAD

HAIKOU

Scalar appropriation of Shenzhen

116 / 117

Top: Examining the Urban Village / Interstitial Spaces Right: Sections Next pages: Vertical connections in congested Urban space

118 / 119

?的感知和西方牛?和笛?儿 本的差?。它可以被描??是? 并可以在中国文化的各个方面找 最著名的就是中国?林，中国? 建筑。同?，也表?在大?的

的村落被深?包?着，并且?? ?去村落的尺度和周?城市中的 个?目??通??作?有机理 ??尺度和??的不同机制。 ?量多的基地本身的空??量而 分析：基地的?底?系的分析和 清除最旧/最破以及最新/最大的建 下的主要建筑?示了?去村落的肌 新的肌理交?的空?。南北和?西 示了基地??向量的肌理。?些 ?网?，?个网?将形成新

???策略?加在基地上。通? ?会和村落的肌理?生互?。 整个基地并整合了剩余的建筑， 的尺度。?个系?引入了一个 和村落，同?也?系了商?和居 建筑在与条状系?相交的部分被 插件），在非相交的部分?作? “屋?景”（ f ）成?

交通网格 ?底平面 ?存建筑 最近建筑 最老/最旧建筑 ?西街景 南北街景 策略：条 剩余肌理 ?形网格 剖面 平面 透? ?部 条 区?

_URBA

Interstit Shenzhe Urban V mation o ration of the town swallow This pro external global a gardens motion i After vis sity a sy re-evalu

AN VILLAGE

tial Urbanism en Villages form part of the rapid and un-planned urban transforof Shenzhen, across the border to Hong Kong. After the declaf Shenzhen’s special economic zone, within less than a decade, n grew to a population size of 4.5 million inhabitants, thereby ing neighboring villages. oject approaches Chinese culture from two standpoints. An l geographic mapping in scales of ten wants to expose intricate nd local redundancies. A cultural reading of traditional Chinese s and the abstraction of Chinese concepts of viewing and into a genetic code offer an internal approach. siting the site and working with local students of Tonji Univerystem of stripes is distilled and applied as urban strategy to uate and integrate further development into the Urban Village.

120 / 121

SPL

Ecostructures: Spluegen Rest Stop

Spluegen Rest Stop

study project, near Spluegen, Switzerland, 2002-2003 / Aurel von Richthtofen, Moritz Schoendorf, Lorenz Kocher

Spluegen is a landscape project located in the Upper Rhine Valley in Switzerland. The Upper Rhine Valley is characterized by its pristine alpine ecology, yet, contrasted with a mayor highway connecting Germany and Italy running through it. Articulating the impact of infrastructure on alpine landscape, Spluegen Rest Stop is an expanding field of “fins� running along the highway for about one kilometer.

The fins act as rhythm-keeper to passing vehicles, creating a cinematic effect of animation in landscape. In return the fins function as noise barrier to the settlement of Spluegen. Besides their interaction with the highway and the village, the fins engage the river Rhine as well. The river is directly feed from glacial waters and regularly peeks in spring and fall when melting snow and rain drain into the valley. Fluvial changes are dramatic, eroding large areas of arable land, threatening roads and settlements. The changes in water loads have spurred in recent years, as global climate change impacts the Alps. The fins of Spluegen Rest Stop act as piece de restistance, while the river becomes the motor for a gradual transformation of the landscape. Annual floods redirect into the field, sedimentation fills parts of the structure, while water slow down, relieving pressure on the river below. Sedimentation and erosion constantly change the appearance of the field of fins throughout time.

Man-made, yet partly reclaimed by nature Spluegen Rest Stop is an active landscape-infrastructure hybrid.

The design of Spluegen Rest Stop started with a parametrically controlled proto-fin. Designed in Maya and implemented in the coding language MEL in 2002, fins propagate by thousands, changing frequency, amplitude, direction and angle through a form-synthesizing feedback loop.

After fabricating a series of test models with cnc-technology, the original nurbs-curved shape was translated into a triangulated model of which a 1:1 prototype was fabricated on site.

The mock-up was then cast in concrete and placed in the Upper Rhine in early spring 2003. At our next visit a few weeks later the fin was gone.

122 / 123

Top: Rendering of Spluegen Right: Form-synthesizer progammer in MEL

124 / 125

126 / 127

Top: Sedimentation studies - Video stills

128 / 129

Top: 1:1 Mock-up on site Right: CNC-fabricated Model

130 / 131

Fingeruebungen (finger excercise on piano)

ongoing digital design research

FUB

Fingeruebungen: Continous Parametrics

Fingeruebungen

/ Continuous parametric design explorations, test and fabrication / Aurel von Richthofen

Aware of the limitations of cad software, these exercises in geometry constantly expand on non-standard methods of computation to give way to new geometries (or maybe new ways to generate familiar geometries).

Meant to train ones designing skills like daily piano hand exercises, Fingeruebungen are implemented in parts or in total and remain on the level of proto-projects and form a continuous design research. Exercises range from mathematical models (Danzer, Voronoi, Delauney), to artistic models (Hauer), to architectural models (Metabolism).

134 / 135

win(e)nvironments This studio will reconsider

Reyner Banham’s thesis on the “controlled environment” in order to document, comprehend and utilize climatic conditions as a space generating device. In The Architecture of the Well-Tempered Environment (1969), Banham articulated his view of “environmental power” distinct from a moralist ecological argumentation; rather, he presented the “well tempered environment” as a novel way to conceptualize space though immaterial elements - sound, light, electricity and moving images - and through numeric calculations: space as information.

The scope of this studio is to revisit Banham’s ideas on the ecologies of architecture in conjunction with recent experiments by Philippe Rahm on the (re-) creation of environments. Environments are understood twofold: As the immediate spatial ecologies of bodies, architecture and territories, as well as projected spaces of events in the transcendent meaning of the word. Subverting a techno-phenomenological approach traced earlier by Siegfried Giedion -modern chronist par excellence - environment will analyzed as a medium of emergency.. Site – Geneva, Switzerland [GPS coordinates: N46° 12’ 34.55’’ E6°09’ 00.07’’]

Foam Scape

In the context of this studio foam is an operative metaphor describing cultural processes of an inherently individualized society and a generative design model for an emergent architecture. In a first instance we will use foam as an analytical explication tool to research the intimate conditions of space production such as inhabitation, insulation and immunization.We will then analyze the adjacency of cells in a state of co-isolation and move on to complex cells clusters and stable foams.

The studio will thus derive foam prototypes and implement these as parametric modules. These modules will be scripted in Rhino using Rhinoscript.

Programmatically the studio will work on the redevelopment of the Berlin Tempelhof airport field. Berlin Tempelhof was the world’s first airport, the second largest building after the Pentagon, the umbilical cord linking West Berlin to West Germany during the Soviet blockade, yet became obsolete as inner city airport in the context of changing air travel. By introducing spectator sports we will test the thesis at the core of the studio: Can architecture find new ways to negotiate individual and collective spaces in a dynamic process without relying on pre-emptive notions of public and private, part and whole, object and landscape?

Metabolism Redux

Metabolism Redux will revisit Japanese architecture in the 1960ies, more precisely a Japanese avant-garde postulating an architecture of change, that they called Metabolism. Metabolism transpired into “common” architecture history and theory as a distinct phenomenon - both geographically remote and temporarily closed – an exclusive, yet failed utopia. While this Western perception adds another “-ism” to the collection of post war modern architecture, it falls short to capture the momentum that gave birth to an extraordinary wealth of ideas. What were the economic, social and political circumstances that triggered this explosion of projects? What were the pop-cultural forces mobilizing a whole country to propel itself into a sci-fi future? How are we to re-construct a Metabolist project that vanished just about 10 years after its first appearance on the international architectural scene?

Metabolism Redux will work with primary sources such as Japanese magazines, movies and advertising. Our focus will lie on the apparent advances in technology, an evolved visual language, an expressive use of biological, technical and cybernetical metaphors, and a general transformation of Japanese culture. In collecting and “reading” the visual legacy of Metabolism, we will derive a catalogue of Metabolist projects, eventually enabling us to recuperate Metabolism as a contemporary project. At the same time we will contrast Metabolism with cybernetic advances in pattern recognition, communication theory and computer technology.

The Metabolist Project is about production. The seminar will produce both a common catalogue and individual manifesto images. Catalogue: The seminar will produce a common catalogue of Metabolist projects by scanning, collecting and re-working Metabolist projects in their context of magazines, movies or advertisements. Manifesto Image: In good Modernist tradition, Metabolism exploited the power of imagery. Instead of re-designing a “complete” Metabolist project , we will produce poster size images of an updated project.

Deep Surface

Deep Surface is the first design studio exposure for sophomore students that decide to major in architecture. Within less than ten weeks, students learn basic digital and analog design techniques, familiarize themselves with the studio culture and develop a complex understanding of processes and concepts of architecture and resulting in a first indepe ndent project. Architecture is understood as open system of temporal and spatial relationships. Students manipulate surface understood as thick matter to produce a landscape proposal.

136 / 137

by Aurel von Richthofen, 2007

UNFOLD

DANZER TILE Method by Marc Fornes & Aurel von Richthofen, 2007

WIREFRAME MODEL -> <- RING CATALOGUE UNFOLDED SURFACES ->

NURBS CURVE THROUGH CORNER POINTS

LOFT CURVE 1-3 & 2-4

Top: Danzer Variation - Loops Right: 3D-printed model

BOOLEAN SUBSTRACTION LOFT 1-2

INTERLOCKING RINGS OF RULED SURFACES 1 & 2

138 / 139

Surface Evaluation

Non Planar transformation Top: Re-parametrizing Surface Right: Rule-based 3D network

140 / 141

142 / 143

144 / 145

Poem in script: VB Logic

Poem of the VB script: ‘The script is a code,

Dim script : script = code ‘The script is executable

Call main() ‘The script structure is linear,

End sub ‘The script is circular, elliptical

For i = 0 to Ubound() Next ‘The script creates variables to hold information

Dim arr : arr = array(x,y,z) ‘The script can take logical operators

If x > 1 then boolean = true ‘The script can write a poem

call poem(arr,i,boolean) function poem(arr,i, boolean)

if boolean = true then print arr(0)(i), arr(1)(i), arr(2)(i), end function ‘The script has an author outside the script

‘version 0.1 / copyright<author> 146 / 147

Aurel von Richthofen

(1978) is an architect, researcher and teacher invested in parametric design techniques challenging the standard practice of architecture. Aurel grew up in Berlin and Geneva speaking both German and French. He studied architecture at ETH Zurich, TU Delft and Princeton University. He graduated from the department of architecture of the ETH in January 2004 with honors. Aurel von Richthofen worked on a series of international competitions in a young Zurich architecture firm before continuing his education at Princeton University where he graduated with a post-professional Master degree in architecture in January 2007.

The same year Aurel von Richthofen founded aurelVR – a practice of design and research in architecture – in Brooklyn, NY. aurelVR operates on multiple scales and is currently invested in lofts in Manhattan, furniture design, exhibition design, as well as international competitions and research projects. aurelVR won numerous awards for its exhibition designs and has a growing base of clients for its cnc-fabricated installation pieces. aurelVR’s office is located in the Metropolitan Exchange Place (MEx) in Brooklyn and tabs into the collaborative spirit of upcoming design and research firms affiliated. During the last two academic years Aurel von Richthofen taught studios, seminars and workshops at the Knowlton School of Architecture at the Ohio State University as a Visiting Assistant Professor.

148 / 149

Structures and Geometry

Subway Sorter NYC

Brooklyn Smart Dots

New Bouwkunde TUD

Nouvelle Comedie Geneve

Spluegen Rest Stop

Zurich Beach

Rotterdam Transportation Museum

Dubai Tensegrity Tower

Re-For-Mat

Zurich Elephant Park

Berlin Einheits Denkmal

Urban Village Shenzhen

Tetra

Euro Marseille

Continous Parametrics

VB Logic

aurelVR.com This book is primarily an archive of projects that is gradually expanding through teaching and practice. In analogy to the periodic table this archive can hold, but also predict, elements before their actual discovery or realization in design. Within this framework the projects resist a reductive chronological or typological classification, common to many architectural portfolios. The juxtaposition of environmental scale and geometrical structure furthermore extrapolates the social and political dimensions of the project.

Teilchen - Nanostructures Particle Geometry: Points / Dots / Circles / Spheres / Raeume - Agorastructures Spatial Geometry: Lines / Folds / Surfaces / Fractals / Denkweisen / Felder - Megastructures Political Geometry: Houses / Cities / Landscapes / Metabolism / Umwelten – Ecostructures (oikos / house) Ecological Geometry: Environments / Climates / Futures / Borrowing from Andre Malraux’ musee imaginaire this archive is meant to expand like an archive imaginaire; an archive perpetually fertilizing and propagating new designs.

Hence, the projects are not “sorted” in any specific order but grouped as described above and indexed with their periodic value. An interactive version is available at www.aurelVR.com