自由曲面之摺紙演算

摺紙起源於發明紙張的中國，不過日本創造新的摺紙，將摺紙創新發揚光大。發展至今，摺紙已應用於許多科學領域。人們設計摺紙於2-D平面上，但摺疊過程會產生變形，因此，人們無法精確地預想摺疊後三維型態，然而在應用設計中，預先建構想像對於設計非常重要，此外，從古至今，人類追求幾何複雜之自由曲面，在當代，人們透過參數與數位化精準製造自由曲面，本研究企圖將摺紙與自由曲面結合，透過數位化精準預期摺疊型態。此研究之目標幫助設計師預期摺疊後型態之的自由型態摺紙演算，並有助於理解摺紙行為，本研究提出以物理引擎袋鼠(Kangaroo)來運算摺紙，同時在視覺化程式設計(Grasshopper)及犀牛(Rhino)上進行，便於參數化與建構模型，研究摺紙數學原理，並將數學規則，轉換為於物理運算之約束後並平衡建構之摺紙，並且建構出一套摺紙適應曲面之演算法，再進行實作測試，摺紙來檢驗確認此演算法之可行性。。本研究實際演算剛性鑲嵌三浦摺紙成功實測於數位與現實環境，但曲線摺實測效果有限。此研究幫助使用者設計摺紙於不同領域之設計，藉此幫助創作者對於設計摺紙之想像，並理解摺紙空間設計轉換於2-D與3-D之間，且探索摺紙的潛力於探索設計的可能性。

關鍵字

摺紙；演算法；自由曲面；剛性鑲嵌三浦摺紙；曲線摺

並列摘要

Origami is an art form and originated with the invention of paper in China, but was refined in Japan. Today, Origami has been used in various application fields. People design origami creases pattern on 2-D environment, but process of folding paper make origami transform . Consequently, they unable to precisely envision the 3-D folded shape. However, in the field of application design, having a anticipating structure of model is very important. In addition, From then until now, human pursue geometrically complex of freeform surface. In contemporary, freeform surfaces are precisely manufactured through parameterization and digitalization. In this study, we attempts to combine origami with freeform surfaces to accurately predict folded origami shape through digitalization The research goal is to set up an algorithm to help designer visualize a folded origami shape and perceive the origami behavior. We use physics engine, kangaroo, to calculate origami in Rhinocero and Grasshopper environment. By doing this, it can facilitate parameterization and construction of models, study the mathematical principles of origami, and convert the mathematical rules to physics constraints, then balance to origami and construct a set of origami to adapt to surfaces algorithms. Finally, the outcome is to be realize physically and fold them manually to confirm the feasibility of the algorithm. In this study, the actual simulation of rigid Miura-Ori tessellation was successfully measured in digital and real environments, but the curved-folding actual measurement effect is limited. The study help user to design origami in various field for application. Also, it help designer understand the mechanically transformation of origami between 2-D and 3-D space.　Furthermore, it benefits from exploring potential of origami and design possibilities.