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Curved-folding origami design PDF

123 Pages·2019·29.92 MB·english
by  Mitani
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CURVED-FOLDING ORIGAMI DESIGN CURVED-FOLDING ORIGAMI DESIGN Jun Mitani CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2019 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper International Standard Book Number-13: 978-0-367-18027-0 (Hardback) 978-0-367-18025-6 (Paperback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Names: Mitani, Jun, 1975- author. Title: Curved-folding origami design / Jun Mitani Other titles: Curved folding origami design Description: Boca Raton, Florida : CRC Press, c2019. | Includes bibliographical references and index. Identifiers: LCCN 2018060524| ISBN 9780367180256 (pbk. : alk. paper) | ISBN 9780367180270 (hardback : alk. paper) | ISBN 9780429059179 (ebook : alk. paper) Subjects: | LCSH: Origami. | Folds (Form) | Paper work | Classification: LCC TT872.5 .M5644 2019 | DDC 736/.982--dc23 LC record available at https://lccn.loc.gov/2018060524 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface ........................................................VII 5. Folding Cones ........................................57 Prologue: Folding a Curve Means a Lot .....IX 5.1 Making a Cone without Cut .....57 Author ........................................................XIX 5.2 Making Conjoined Cones .............60 5.3 Making a Partial Cone ..................62 Appendix: Folding Back a Cone .........66 1. Fold a Curve ............................................1 1.1 Folding a Simple Curve ..................1 6. Folding Back at Straight Line ...............69 1.2 Folding a Winding Curve ...............4 1.3 Folding a Squiggle .........................6 6.1 Combining Straight and Curved-Fold Lines .........................69 6.2 Aligning Straight and Curved 2. Aligning Curves .....................................13 Lines Alternately ...........................71 2.1 Pleat-Folding Two Aligned 6.3 Aligning Line-and-Curve Pairs Curves ............................................13 Rotationally Symmetrically ..........72 2.2 Aligning Many Curves ..................16 2.3 Aligning Curve and Reversed 7. Other Techniques ..................................77 Curve .............................................20 7.1 Providing Projections and Hollows ..........................................77 3. Aligning Rotated Curves ......................35 7.2 Folding Cylinders ..........................77 3.1 Making Rotationally Symmetric 7.3 Laying Out Alternatingly.............80 Structures ......................................35 7.4 Folding Closed Curves .................83 3.2 Decentering ..................................38 Appendix: Example of Whipped 3.3 Aligning Whirls .............................38 Cream .........................................88 Appendix: Is Paper Really Inelastic? .....43 Afterword ....................................................97 4. Tucking ..................................................45 Index ............................................................99 4.1 Tucking One Line .........................45 4.2 Tucking Multiple Curves...............47 4.3 Repeating Tucking .......................48 V Contents Preface It hink most of you enjoyed origami when computer-based designing is a high hurdle you were kids. The most basic origami is to and not an easy method. Do we really need fold a sheet flat along a straight line, corner a computer to make shapes by folding paper to corner or side to side. If you were to “fold along curves? I am a computer science this paper as you like,” you would start with researcher, but I gave it a try with computer- folding it flat. It is widely considered that paper free curved-fold origami. Paper can be folded should be tightly folded. However, paper along curves relatively freely, but not that freely. is bendable. The paper can also be folded Most randomly drawn curves do not fold well. along a curve by adding a fold on its bended, To obtain beautifully designed modelings, we curved surface. This “curved folding” has not at least need knowledge about how fold lines drawn much attention. However, the surface are laid out. This book presents shapes that are of the paper created from curved folding formed by curve-folding paper, together with produces geometric, elegant shading. I have fold line patterns. Its contents are a record of created a number of geometric solid objects fun experiments from my own real experience through computer-calculated designing of with sheets of paper. You will be able to create shapes obtained from folding curves. Those a variety of shapes by combining the fold techniques are organized in the book titled line patterns in this book. I hope to share the 3D Origami Art (CRC Press, 2016). Fortunately, beauty of curved surfaces created by paper that book inspired many people to know with as many people as possible. the world of curved-fold origami. At the same time, it made me recognize again that Jun Mitani VII Preface Prologue: Folding a Curve Means a Lot P.1 Shapes from Bending and tangent surfaces. These are called “devel- opable surfaces”. A developable surface is Paper a shape consisting of lines. Each shape in Figure P.2 is also an assembly of lines, though First, let’s be clear about the difference they are not visible. So, a ruler tightly fits on between “bending” and “folding” a sheet of its surface. Figure P.3 illustrates the consisting paper. Bending is to change the entire paper lines of the three types of developable sur- into a smooth shape without creating edges, faces. By actually bending a sheet and closely as in Figure P.1. observing its surface, you can roughly estimate This produces a smoothly curved surface. how the lines are arranged. And, thinking the However, the bent shape quickly opens back direction of these lines are very important in flat if it is not held or taped due to paper’s creating a curved surface out of a sheet. ability to return to its original state. The end There are only three types of developable result is the shape balanced between this surfaces. However, you can make shapes with property of the paper and the fixed point. A different types of developable surfaces, as somewhat thick sheet produces a beautifully seen in Figure P.4, by smoothly connecting a curved, tense surface with no deflection. curved surface with another curved one or a Paper is inelastic and does not deform curved surface with a plane. The left is esti- freely like a rubber sheet. There are only three mated to be a shape that combines a cylinder known curved surfaces that can be made from bending a sheet of paper—cone, cylinder, Figure P.1 Bent paper. Figure P.2 Paper bent into a cone and a cylinder. IX Prologue: Folding a Curve Means a Lot

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