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1 a Program for Origami Design Copyright ©1994–1998 by Robert J. Lang. All rights reserved. Portions (CFSQP) Copyright ©1993-1998 by Craig T. Lawrence, Jian L. Zhou, and Andre L. Tits. Use and distribution of this program is subject to restrictions described in the TreeMaker documentation. A Program for Origami Design Thanks for suggestions and algorithmic insight to: Alex Bateman, Toshiyuki Meguro, Tom Hull, Jun Maekawa, Fumiaki Kawahata, Erik Demaine, Barry Hayes, and Marshall Bern. Programmed with Metrowerks CodeWarrior ™ and Metrowerks PowerPlant™. Copyright ©1994–1998 by Robert J. Lang. All rights reserved. Portions (CFSQP) copyright @1993–1998 by Craig T. Lawrence, Jian L. Zhou, and Andre L. Tits. All Rights Reserved. Terms of License TreeMaker contains copyrighted code (CFSQP) that may only be used for non-profit purposes. TreeMaker may not be freely distributed. CFSQP's Conditions for External Use include the following 1. The CFSQP routines may not be distributed to third parties. Interested parties should contact the authors directly. 2. Due acknowledgment must be made of the use of the CFSQP routines in research reports or publications. Whenever such reports are released for public access, a copy should be forwarded to the authors of CFSQP. 3. The CFSQP routines may only be used for research and development, unless it has been agreed otherwise with the authors in writing. For more information on CFSQP, see http://www.isr.umd.edu/Labs/CACSE/FSQP/fsqp.html To obtain a copy of the TreeMaker executable, please provide the following information: Your name Your affiliation (must be a non-profit organization) Your e-mail address An affirmation that you will abide by CFSQP’s Conditions for External Use. An affirmation that you will only be using TreeMaker for non-profit purposes and will not redistribute the executable Confirmation that you are using a Macintosh™ computer (it won't run on anything else) sent to: [email protected] A copy of the executable will be emailed to you within a few weeks. If you like the program, drop me a line with your comments and attaboys. If you find bugs, drop me a line with a description and I’ll try to fix it in the next version. This software is provided as-is with no implied warranties of fitness or usability (but I hope you will find it to be be both fit and usable). 1 Table of Contents 1.0 Introduction ............................................................................................................. 4 1.1 Background ....................................................................................................... 4 1.2 Installing TreeMaker ......................................................................................... 6 1.3 Conventions ......................................................................................................6 2.0 Tutorials .................................................................................................................. 7 2.1 Tutorial 1: Designing a Base ............................................................................. 7 2.2 Tutorial 2: Imposing symmetry....................................................................... 15 2.3 Tutorial 3: Changing edge lengths .................................................................. 25 3.0 Tips and Techniques ............................................................................................. 34 3.1 Adding nodes .................................................................................................. 34 3.2 Making a plan view model ..............................................................................38 3.3 Forcing edge flaps ........................................................................................... 47 3.4 Fracturing polygons ........................................................................................ 52 3.5 Forcing symmetric angles ...............................................................................58 4.0 Reference ..............................................................................................................65 4.1 Introduction ..................................................................................................... 65 4.2 Main window .................................................................................................. 65 4.3 Creating a new Tree ........................................................................................ 69 4.4 Editing Parts .................................................................................................... 71 4.5 Menu commands ............................................................................................. 78 5.0 The Tree Method of Origami Design .................................................................. 112 6.0 TreeMaker Algorithms ........................................................................................ 143 6.1 Mathematical Model ..................................................................................... 143 6.2 Definitions and Notation ............................................................................... 144 2 6.3 Scale Optimization ........................................................................................ 144 6.4 Edge Optimization ........................................................................................ 144 6.5 Strain Optimization ....................................................................................... 145 6.6 Conditions ..................................................................................................... 146 6.7 Meguro Stubs ................................................................................................ 148 6.8 Universal Molecule ....................................................................................... 149 7.0 Software Model ...................................................................................................151 7.1 Overview ....................................................................................................... 151 7.2 Tree Classes: Details ..................................................................................... 160 8.0 Final Stuff ...........................................................................................................169 8.1 Comments and Caveats ....................................................................................... 169 8.2 Version History ................................................................................................... 170 8.3 Sources ................................................................................................................ 173 3 TreeMaker 4.0 Copyright ©1994–1998 by Robert J. Lang. All rights reserved. Portions (CFSQP) copyright @1993–1998 by Craig T. Lawrence, Jian L. Zhou, and Andre L. Tits. All Rights Reserved. Terms of License TreeMaker contains copyrighted code (CFSQP) that may only be used for non-profit purposes. TreeMaker may not be freely distributed. CFSQP's Conditions for External Use include the following 1. The CFSQP routines may not be distributed to third parties. Interested parties should contact the authors directly. 2. Due acknowledgment must be made of the use of the CFSQP routines in research reports or publications. Whenever such reports are released for public access, a copy should be forwarded to the authors of CFSQP. 3. The CFSQP routines may only be used for research and development, unless it has been agreed otherwise with the authors in writing. For more information on CFSQP, see http://www.isr.umd.edu/Labs/CACSE/FSQP/fsqp.html To obtain a copy of the TreeMaker executable, please provide the following information: Your name Your affiliation (must be a non-profit organization) Your e-mail address An affirmation that you will abide by CFSQP’s Conditions for External Use. An affirmation that you will only be using TreeMaker for non-profit purposes and will not redistribute the executable Confirmation that you are using a Macintosh™ computer (it won't run on anything else) sent to: [email protected] A copy of the executable will be emailed to you within a few weeks. If you like the program, drop me a line with your comments and attaboys. If you find bugs, drop me a line with a description and I’ll try to fix it in the next version. This software is provided as-is with no implied warranties of fitness or usability (but I hope you will find it to be be both fit and usable). 1.0 Introduction TreeMaker is a tool for origami design. Starting from a description of a desired origami model, TreeMaker computes a crease pattern for folding a base for the model from an uncut square of paper. This document describes TreeMaker, how you use it to design origami, and how it works. 1.1 Background Origami is the Japanese name for the art of paper-folding. The purest form of origami stipulates that you fold one sheet of paper, which must be square, and no cutting is allowed. These rules might seem restrictive, but over the hundreds of years that origami has been practiced, tens of thousands of origami designs have been developed for birds, flowers, animals, fish, cars, planes, and almost everything else under creation. Despite the age of the art, the vast majority of origami models have been designed within the last thirty years. This relatively late bloom of the art is due in part to a spread of the art worldwide and an increase in the number of its practitioners, but it is 4 due in large part to the development of a body of techniques for the design
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