Ko Joy - Geometric computation : foundations for design

FOUNDATIONS FOR DESIGN

Joy Ko and Kyle Steinfeld

First published 2018
by Routledge
2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN

and by Routledge
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Routledge is an imprint of the Taylor & Francis Group, an informa business

2018 Joy Ko and Kyle Steinfeld

The right of Joy Ko and Kyle Steinfeld to be identified as authors of this work has been asserted by them in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.

All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers.

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Publishers Note
This book has been prepared from camera-ready copy provided by the authors.

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library

Library of Congress Cataloging-in-Publication Data

Names: Ko, Joy, author. | Steinfeld, Kyle, author.
Title: Geometric computation : foundations for design / Joy Ko and Kyle
Steinfeld.
Description: Milton Park, Abingdon, Oxon : Routledge, 2018. | Includes
bibliographical references and index.
Identifiers: LCCN 2017004365| ISBN 9780415811965 (hb : alk. paper) | ISBN
9780415811972 (pb : alk. paper) | ISBN 9781315765983 (ebook)
Subjects: LCSH: Architecture--Mathematics. | Design--Mathematics.
Classification: LCC NA2750 .K58 2017 | DDC 720.1/51--dc23
LC record available at https://lccn.loc.gov/2017004365

ISBN: 978-0-415-81196-5 (hbk)
ISBN: 978-0-415-81197-2 (pbk)
ISBN: 978-1-315-76598-3 (ebk)

Typeset in Akzidenz Grotesk and Scala Sans
by Kyle Steinfeld

CHAPTER 1.01
ELEMENTS OF A COMPUTATION

CHAPTER 1.02
OBJECTS, TYPES, AND EXPRESSIONS

CHAPTER 1.03
VECTORS, POINTS, AND COORDINATE SYSTEMS

CHAPTER 1.04
COLLECTIONS AND CONTROL FLOW

CHAPTER 1.05
FUNCTIONS

CHAPTER 1.06
LINES AND PLANES

CHAPTER 1.07
TRANSFORMATIONS AND INTERSECTIONS

CHAPTER 1.08
BUREAUCRATIC TYPES

CHAPTER 1.09
CURVES

CHAPTER 1.10
SURFACES

CHAPTER 1.11
THE DESIGN OF OBJECTS

Geometric Objects

Computation is central to significant innovations that are shaping the way that design is practiced today. No longer the peripheral specialty it was even just a decade ago, design computation is now accepted as a necessary area of practice in many creative design disciplines, including architecture and industrial design. It is considered a distinct domain of academic inquiry, and has become an essential topic in design education.

The idea to write this book arose out of the challenge in finding a foundational text or curriculum that addressed computational design in a comprehensive way, one that moves beyond software and speaks to its core elements. The structure of this work reflects what we consider to be the foundational topics that will empower readers to understand the underpinnings of computational media in visual design. Our emphasis on foundations is deliberate. In our experience as design educators, while agility in software may be easily acquired and is often instantly gratifying, it retains little value once the software in question inevitably becomes obsolete. In our experience, while technical knowledge of software is fleeting, a grasp of the fundamentals persists.

The content of this work reflects our conviction that math and code are equal partners in computation. The treatment of the topics throughout this text represents an integration of these two partners, a union that required a resolution of their distinct concerns. As practitioners and instructors of design, we know that a purely mathematical approach often does not light the way to an implementation in code. However, we also have observed how the ability to sketch a routine in code can help to shed light on non-intuitive mathematical concepts, which in turn can lead to fruitful generalizations and insights. We hope that our readers will take away a specific set of knowledge and skills that underlie topics in computing, computational geometry and mathematics, and have structured this work accordingly. Our treatment is synthetic by necessity. By pairing topics in code and geometry, we present the two key faculties required by a designer interested in making a place for computation in creative practice: an understanding of the structure of code in object-oriented programing, and a proficiency in the vector-based geometric constructs that underlie much of computational media in visual design. To clearly communicate this material, a number of tools have been developed that support and extend beyond this text. These include:

> A visual vocabulary of diagrams and graphic devices developed for this text. These are used throughout this text in order to provide a useful shorthand for the reader, and are employed in related on-line materials.

> A stand-alone library of code developed as an accompaniment to this text. The Decod.es geometry library is open-source, freely available on-line, and will be described in detail as we progress.

> A set of practical examples informed by essential mathematics, but led by their useful implementation in code. Selected sections of code are presented in this text in support of our discussion, while full implementations are available on-line.

Learning to script with geometry, to compose in this medium that hews close to the heart of the structures that govern digital media, bears value beyond the tactical benefits of acquiring a new skill. A grasp of geometric computation can widen the reach of creative computation more generally, and can empower designers to better face the challenges of contemporary practice.