Geometric Folding Algorithms: Linkages, Origami, Polyhedra

Erik D. Demaine, Joseph O'Rourke

  • 出版商: Cambridge
  • 出版日期: 2007-07-16
  • 售價: $7,150
  • 貴賓價: 9.5$6,793
  • 語言: 英文
  • 頁數: 488
  • 裝訂: Hardcover
  • ISBN: 0521857570
  • ISBN-13: 9780521857574
  • 相關分類: Algorithms-data-structures
  • 海外代購書籍(需單獨結帳)

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商品描述

Description

Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500s, but have only recently been studied in the mathematical literature. Over the past decade, there has been a surge of interest in these problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this intriguing treatment of the geometry of folding and unfolding presents hundreds of results and over 60 unsolved ‘open problems’ to spur further research. The authors cover one-dimensional objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from students to researchers.

• Fascinating, tangible, cutting-edge research with applications throughout science and engineering

• Full color throughout

• Erik Demaine won a MacArthur fellowship in 2003 for his work on the mathematics of origami

Table of Contents

Introduction;

Part I. Linkages:

1. Problem classification and examples;

2. Upper and lower bounds;

3. Planar linkage mechanisms;

4. Rigid frameworks;

5. Reconfiguration of chains;

6. Locked chains;

7. Interlocked chains;

8. Joint-constrained motion;

9. Protein folding;

Part II. Paper:

10. Introduction;

11. One-dimensional paper;

12. Two-dimensional paper and continuous foldability;

13. Single-vertex foldability;

14. Multi-vertex flat foldability;

15. 2D Map folding;

16. Silhouettes and gift wrapping;

17. Tree method;

18. One complete straight cut;

19. Flattening polyhedra;

20. Geometric constructibility;

21. Curved and curved-fold origami;

Part III. Polyhedra:

22. Introduction and overview;

23. Edge unfolding of polyhedra;

24. Reconstruction of polyhedra;

25. Shortest paths and geodesics;

26. Folding polygons to polyhedra;

27. Higher dimensions.

商品描述(中文翻譯)

描述

摺疊和展開問題自15世紀初的阿爾布雷希特·杜勒爾以來一直存在,但直到最近才在數學文獻中得到研究。在過去的十年中,對這些問題的興趣激增,應用範圍從機器人學到蛋白質摺疊。本書著重於算法或計算方面,介紹了數百個結果和60多個未解決的「開放問題」,以促進進一步的研究。作者涵蓋了一維物體(鏈接)、二維物體(紙張)和三維物體(多面體)。本書主要針對數學或計算機科學的高年級本科生和研究生,並以豐富的插圖吸引了從學生到研究人員的廣泛讀者。

• 迷人、切實可行、尖端的研究,應用於科學和工程領域
• 全彩色插圖
• Erik Demaine因其在摺紙數學方面的工作於2003年獲得麥克阿瑟獎學金

目錄

引言
第一部分 鏈接:
1. 問題分類和示例
2. 上下界
3. 平面鏈接機構
4. 剛性框架
5. 鏈的重構
6. 鎖定鏈
7. 交錯鏈
8. 關節受限運動
9. 蛋白質摺疊

第二部分 紙張:
10. 引言
11. 一維紙張
12. 二維紙張和連續可摺疊性
13. 單頂點可摺疊性
14. 多頂點平摺疊性
15. 二維地圖摺疊
16. 輪廓和禮品包裝
17. 樹方法
18. 完全直線