Morphing: A Guide to Mathematical Transformations for Architects and Designers

By Joseph Choma

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  • Hardback
  • 886 illustrations
  • 232 pages
  • 8¾ x 8¾ ins
  • ISBN 9781780674131
  • Published January 2015

Cylinders, spheres and cubes are a small handful of shapes that can be defined by a single word. However, most shapes cannot be found in a dictionary. They belong to an alternative plastic world defined by trigonometry: a mathematical world where all shapes can be described under one systematic language and where any shape can transform into another.

This visually striking guidebook clearly and systematically lays out the basic foundation for using these mathematical transformations as design tools. It is intended for architects, designers, and anyone with the curiosity to understand the link between shapes and the equations behind them.

There is also an accompanying site that allows you to try out your own morphing designs: www.morphingbook.com

About the Author

Joseph Choma is the founder of the Design Topology Lab, an interdisciplinary design research practice. He completed his graduate studies in design and computation at the Massachusetts Institute of Technology. Currently, Joseph teaches within the School of Architecture at Clemson University.

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CONTENTS

 

Introduction

 

Transformations

Translating

Cutting

Rotating

Reflecting

Scaling

Modulating

Ascending

Spiralling

Texturing

Bending

Pinching

Flattening

Thickening

 

Combining Transformations

Cutting and Spiralling

Scaling and Spiralling

Modulating and Spiralling

Spiralling and Ascending

Texturing and Spiralling

Bending and Spiralling

Spiralling and Bending

Pinching and Spiralling

Flattening and Spiralling

Spiralling and Flattening

Spiralling and Thickening

 

Combining Shapes

A Mound

A Meandering Mound

A Leaning Mound

A Steeper Mound

A Creased Mound

A Creased and Pinched Mound

A Wedge

A Ridge and Trench

Two Ridges

Another Ridge and Trench

A Valley

Moguls

 

Analyzing

Japan Pavilion – Shigeru Ban Architects

UK Pavilion – Heatherwick Studio

Mur Island – Acconci Studio

Son-O-House – NOX/Lars Spuybroek

Ark Nova  – Arata Isozaki and Anish Kapoor

Looptecture F – Endo Shuhei Architect Institute

Mercedes-Benz Museum – UNStudio

 

Developable Surfaces

Plane to Cylinder

Cylinder with Ascending

Cylinder with Texturing and Ascending

Cylinder with Flattening, Texturing and Ascending

Cylinder with Modulating, Flattening and  Texturing

Plane to Cone

Cone with Spiralling

Cone with Spiralling and Texturing

Cone with Spiralling, Texturing and Modulating

Cone with Spiralling, Texturing and More Modulating

 

Assumptions

 

Bibliography

 

Acknowledgements