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DIGITAL DESIGN + FABRICATION SM1, 2016 M1 JOURNAL - Hyperbolic Paraboloid

Teddy Cham660341

Timothy Cameraon / Tutorial 3

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Measured Drawings

The hyperbolic paraboloid is flattened out and measured in a 2D plane to fully understand its net. The nature of a folding object makes measuring precise angle of folds impossible and thus will be ignored as the overall shape in general is very flexible.

The object is photographed in a flat plane and then traced over in rhino in preparations for the 3d modeling process. Replicating a net allows direct understanding of the object as a flat surface before manipulation.

Measuring Methodology

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Using a rhino model it is significantly more accurate to measure the dimensions of the hyperbolic paraboloid as a 3d object.

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Analysis

A hyperbolic parabolic is a surface with infinite 3 dimensional points. Unlike a normal paraboloid it has hyperbolic and parabolic cross sections thus giving it a swirly 2 curved surface.

In spatial structures, they are a surface system that specialises with double curvature. Using a defined equation a series of straight lines (or in this case panels) can be arranged to form a double curvature.

Defined mathematic equation: z = x^2 - y^2

The Hyperbolic Paraboloid Curvature

The object uses folding sequences to match the double curvature nature. As shown, a double curved surface is impossible to create with paper as it only has 2 planes.

By folding inwards and outwards according to the net it is possible to reproduce such properties

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Shadow and Light

In addition to creating a double curved surface using panels and folds allows the creation of additional shadow and lighting on the surface. This can be used to manipulate moods or create different spatial senses depending on the intensity of the fold thus the depth of the shadows.

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Digital Model

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Digital Model Process

1. Lofting 2 edge surfaces to create general shape

2. Reproducing the net of the item on top

3. Projecting the lines of the net onto the hyperboloid 4. Removing the lofted surface to clean up 5. Manually adjusting the height of each line/fold

6. Using the created points to generate a surface panel by panel

7. Repeat for all sides

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Sketch Model

Taking the concept of double curvatures generated from fold-ing patterns. The geometry and symmetry is kept because it creates a spatial sense of comfort, ideal for a sleeping pod.

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Sketch Model Progress

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How does this respond to your personal space?

Curve / Dome / Tent

Sketch Design #1

The open top allows lighting in that is emphasised by the panel and folding to create a relaxed spatial emotion once inside. The combination of enclosure and exposure creates a medium at the middle point of privacy and comfort can be achieved.

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How does this respond to your personal space?

Enclosure / Privacy / Security

Sketch Design #2

Total enclosure. Gives a sense of extreme privacy and at some point caustrophobia. The jagged panel and fold edges creates a rough and bold expression to convey this feeling to anyone looking from the outside.

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Sketch Design #3

Frisby / Swirls / Spiral

How does this respond to your personal space?

Another approach is to try to curve the panels themselves, and then folding it afterwards. A sense of elegancy is created within the spatial environment. The curved panels themselves create a more natural lighting gradient that does not seem forced whilst still obeying the panel and fold system.

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