DZ Bank Study

1.2 Building and Atrium: Isolated Axonometric

University of Southern California School of Architecture Fall 2017

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2.1 Geometric Principle: Elements _ 2.1 DZ Bank Building Date: 2000 Location: Berlin, Germany Architect: Frank Gehry Stzuctural EngineerΊ : Hans Schober of Schlaich Bergermann & Partner.

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_ 2.1 Facts

1. Diagrid Glazing allows light to reach the spaces below and acts as a view portal to the horse head within.

2. The occupiable horse head is both a conference room & acts as the center piece of the atrium space. Its double curved panelized surface is a defining feature of the building itself.

3. Triple height atrium acts as the membrane between the interior and the exterior of the building. It also serves as the division between the residential apartments and the commercial bank programs.

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4. The open floor plan expresses the gravity the horse head has over the entire building. The circulation swirls around it and the office spaces and windows are all facing the horse head.

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Horse Head Roof Glazing Atrium Enclosure Atrium Floor Plan

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Building Floor Plan

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2.2.1 Geometric Principle: Relationships / Axonometric _ 2.2.1 Curvature Analysis

Curvature Analysis is a method of determining the concavity or convexity of a curve at any given point. This is a step-by-step computation of the normal vector on the contour curves extracted from a doubly curved surface.

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extract a contour line from a given surface

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divide the curve into points with a high resolution and determine the curvature vector at each of the division points

3 4 5 6 7

perpendicular to the contor

By drawing a line with a start point, vector and length it can be easily determined the exact point at which conditions of “concave” and “convex.”

Split the contour at these points.

Find the “implied centroid” of the contour

a

Attach a point [a] to each of the divided contour points to act as an “anchor point”

a

b

Attach a point [b] to a circle drawn about the “implied centroid” and draw a line from the “anchor point” to the

b

linear action that will perform an geometric inversion of each instance of concavity to convexity and vice versa.

repeat the above steps for each subsequent contour line and create a lofted surface from the resultant deformed lines

line _5’

line _4’

line _5

line _4

line _1

line _2

line _3

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2.2.2 Geometric Principle: Relationships / Parallel

Curvature Diameter

Type A [ 10 Contours ]

er t e

re

tu a rv

am i D

Cu

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2.2.3.0 Geometric Principle: Variables

_ 2.2.3.1

0% Inversion / Origin Condition

_ 2.2.3.2

50% Inversion / Mid Condition

_ 2.2.3.3

100% Inversion / Full Condition

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Degree of Inversion -

None. Each “bend” for the contoured rib is shown here at the origin condition.

_ 2.2.3.1 0% Inversion / Origin Condition This geometric variation consists of the lofted surface created from the initial curvature study contour lines before any major inversion transformation has been applied. The “origin condition”.

_ 2.2.3.1 Advantages -This geometry produces the largest overall volume, allowing for a wider range of programatic options -This geometry is closest to the initial “horse head” geometry, thus producing a recognizable form -The manipulation of the elements is at its most natural state -Each contoured rib is a similar length and overall shape

_ 2.2.3.1 Disadvantages -Formally the least diverse option as compared to the initial condition

0.00’

Degree of Inversion _ 2.2.3.2 50% Inversion / Neutral Condition This geometric variation consists of the lofted surface created from the half inversion of the initial curvature study contour lines. Where extreme concave bend been morphed to center. The “Neutral condition”.

Half. Each “bend” for the contoured rib is shown here at the most neutral condition. This curve is measured against the origin condition.

vv

3.36’

_ 2.2.3.2 Advantages

-This geometry produces the largest overall volume, while maintaining the least amount of double curvature, thus creating the simplest panelization system.

-The manipulation of the elements is at its most universal state.

-Each contoured rib is a similar length and overall shape.

-The surface is fundamentally simpler to understand creating a wide range of reading among viewers.

_ 2.2.3.2 Disadvantages -Formally the least diverse in spatial conditions

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Degree of Inversion _ 2.2.3.1 100% Inversion / Extreme Condition This geometric variation consists of the lofted surface created from the fully inverted contour lines, where each concave bend has been morphed to convex and vice versa. The extreme condition.

Full. Each “bend” for the contoured rib is shown here fully inverted, from concave to convex. This curve is measured against the origin condition.

6.72’

_ 2.2.3.1 Advantages -Formally, this is the most interesting and complex shape produced by the inversion process, with extreme double curvature throughout.

-This geometry consists of two “compartments” at the front and the back, with an implied passage between.

-Smaller overall interior volume produces opportunity for more intimate space.

-Radical, expressive surface.

_ 2.2.3.1 Disadvantages -Discretization of such radical double curvature could prove costly/inefficient

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3.3 Building and Atrium: Isolated Axonometric

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