描圖器與相對運動軌跡之造形方法

A Study on the Forming Method of the Shape Tracer and the Trajectory of Relative Motions

10.6381/JD.200403.0087

廖冠智(G. Z. Liao)；孫春望(C. W. Sun)

幾何 ； 造形 ； 相對運動 ； 軌跡 ； 描圖器 ； Geometric forms ； Shapes ； Relative motions ； Trajectory ； Shape tracer

設計學報

9卷1期（2004 / 03 / 01）

87 - 106

繁體中文

描圖器是一種常見的兒童繪圖玩具，本研究試圖以這種玩具為出發點，觀察各種不同的轉輪尺寸、洞口位置與大小等因素所產生的造形變化與特質；並探討其背後隱含之多層次相對運動概念。多層次相對運動的軌跡可以產生多樣性且具美感的幾何形態，可以提供設計或藝術工作者豐富的素材。本研究繼續深入解析多層次相對運動系統之組合程序與方法，期望能夠有系統的理解與掌握這種造形的新方法。 從研究結果得知軌跡造形的運動型式組合程序可簡化成三個概念層次的變因：「運動系統間關係的複雜程度」、「運動系統間的軌跡型式」與「軌跡形成的幾何敘述」。從這些變因可以推導出基本模式，選擇系統間的軌跡型式與幾何描述，以及調整相關參數與變化範圍，使電腦能夠解讀並描繪設計者所設定的運動型態。 本研究的延續重點是建立更多樣性的運動型式與其間的組合模式，並深入探討Depth-first Search與Breadth-first Search之概念與方法，更快速的建構更多的可能組合方案，透過藝術或設計工作者的篩選，產生獨特而具備視覺美感的新穎造形。

The shape tracer is a combination of both tool and toy. Children use shape tracers to draw many different but interesting patterns. The patterns generated with shape tracers are determined by the size and the location of the wheels and the holes. The concept behind shape tracers is very similar to multiple-level relative motion. Multiple-level relative motion can be used to create various geometric forms that are visually appealing. The purpose of this study is to analyze deeply into the mechanism of combining different motion systems, with the expectation to systematically understand and control this new methodology of form generation. Research finding suggest that the problem of combining different motions systems can be broken into three factors: the complexity of the relationship among motion systems, the pattern of trajectory among motion systems, and the geometric description of the trajectory. A basic model can be derived from these factors. With the selection of different motion, the setup of combination and manipulation of the values, artists or designers will be able to ask the computer to draw patterns they want. The result of this study calls for further exploration of more and new motions and different combinations of the motions. More efforts should be made to investigate the concepts and methods of ”Depth-First Search” and ”Breadth-First Search”, in order to accelerate the generation of patterns. After the screening of the artists or designer, the patterns will become unique and visually appealing.

1. Akin, O.,Akin, C.(1996).Expertise and Creativitiy in Architectural Design.Proceedings of the First International Symposium on Descriptive Models of Design,Turkey:
2. Anderson, J. R.(1995).Cognitive Psychology and its Implications.Freeman:
3. Berkowitz J.(1994).Fractal Cosmos-The Art of Mathematical Design.San Francisco:Amber Lotus.
4. Website: Recursion, Dept. of Computer Science
5. Liao, G. Z.(2001).Forms of Golden Section, Fibonacci Numbers and Recursive Multiple-level Relative Motions.第六屆設計學術研討會論文集,高雄:
6. Liao, G. Z.(2000).台北,臺灣科技大學設計研究所.
7. Liao, G. Z.(2001).Generating Geometric Forms by Manipulating the Angular Increments of Recursive Multiple-level Relative Motions.2001基礎造形學術研討會,台北:
8. Mitchell, W. J.(1990).The Logical of Architecture-Design, Computation, and Cognition.Cambridge:The MIT Press.
9. Newell, A.,Simon, H.(1972).Human Problem Solving.Englewood Cliffs, NJ:Prentice-Hall.
10. Website: Leaning by Design, Georgia Institute of Technology
11. Simon, H. A.(1996).The Sciences of the Artificial.Cambridge:The MIT Press.
12. Sun, C. W.(1999).Relative Motions and Complex Shapes.ISAMA.
13. 孫春望(1998)。相對運動軌跡構成之幾何造形研究。1998基礎造形學術研討會論文集，台北:
14. 朝昌直巳著、林品章譯(1990)。光構成。台北:藝術家出版社。

1. 廖冠智、孫春望(2005)。遞迴性多層次相對運動之幾何圖樣研究。設計學報，10(1)，89-106。