饕餮摺紙積木分類方法之研究

A Method to Categorize Taotie Origamic Building Blocks

陳美汎(mei-fan chen)

指導教授 ： 呂克明

亞洲大學/資訊學院/資訊工程學系碩士班/碩士(2007年)

摘要

摺紙積木是創新、創意的一門學問，紙積木不但可以隨意的拆開重複使用，也可加以著色或做圖案設計，這是其他材質積木所不能取代的。這些模型可以應用在創作教材、遊戲、建築積木等，隨著組合數學理論的引進，也有更多元的發展。
將一張64個等腰直角三角形組成的正方形的平面密鋪圖形紙，利用積木立體觀念配合摺紙，將這種密舖理論將之轉為立體，並配合建構原則以及摺紙步驟摺出模型，創造了包括立方體六大型、貓眼、鯨魚、翅膀以及魟魚共十類饕餮紙積木基本模型，藉由模型皆有角、面、邊三個要件的特點，我們可以驗證多面體的歐拉特性數。針對各個基本模型的特徵做有系統的變化，發展出1180個變化的衍生型。在這些龐大數量的模型中，利用四步驟將龐大數量的模型做有系統的分類歸納整理。
步驟一是辨識，依照模型的型體做辨識來判別模型類別。步驟二是分類，將同一類別模型中固定做同一特徵變化的為一類。步驟三是命名，命名方式像網路IP地址一樣為四碼，分別代表模型類別、正面、反面及側面四個位置的變化特徵。步驟四製圖：利用階層座標圖方式呈現，直軸是將模型的正反面透視平面圖
分別畫出，用來表示模型正反面的改變特徵，正面以實線構圖，反面則以虛線構圖；而橫軸是表示模型側邊的改變特徵。
在創造過程中，我們採邏輯思考方式創造，因為饕餮紙積木是紙積木四大類裡分割最多的，變化性過大，因此無法確定是否為完整。未來可以發展利用電腦對饕餮模型可以摺出的模型做運算，驗證完整性，使之更加完整及有說服力，當往後發展更複雜的摺紙類型時，此問題也將迎刃而解。

關鍵字

平面密鋪 ； 歐拉特性數 ； 階層表示法

並列摘要

Origamic building block is a branch of innovative and novel knowledge. Reusability and capability of coloring and design patterns are two features that are irreplaceable by other than paper building blocks. These models come with the newly introduced combinatorial mathematics. They can be applied to the fields of creative teaching material, intelligence game, and building blocks.
By giving a piece of square paper that is made of 64- isosceles right triangles and by using the tessellation theorems to create the 10-types of the 3D tessellation models including the 6 types of cube models, cat eyes, whale, wing, and ray fish of the Taotie origamic building blocks models. Based on a number set of vertices, faces and edges of polyhedron, we can verify Euler characteristics. Having systematic changes to the characteristic of each basic model, we then developed the 1180-deriving types of models. Now we propose the 4-step to categorize the Taotie origamic building blocks that is listed as follows:
Step 1 is to identify and distinguish according to the type of the models. Step 2 is to classify throughout the same type of models. It needs to distinguish model characteristics in details. Step 3 is to denominate and give the name similar to an IP address 4-code. The code denotes class, top, bottom, and side in sequence for recording model’s characteristics. Step 4 is to draw the 2D graphs by using layer-based representation. The Y-axes denote two columns that each represents the top and bottom of the models, respectively. It shows the model’s characteristic changes. The wireframe of the top drawing is represented in a solid line while the wireframe of the bottom drawing in a dotted line. The X-axis denotes a row that each represents the side model. It shows the model’s characteristic changes.
Having derived in the way of logic thinking to create more models of Taotie origamic building blocks, we found that the Taotie’s is the most complicate one among the Triblock, Diamondback, Napoleon, and Taotie 4-class origamic building blocks. Unfortunately we are unable to confirm whether some models intact. In the future, we will be focused on the above problems or even the same problem of more complicate class of building blocks and will then resolve them by using computer calculation to verify and validate whether they are is intact or not.

並列關鍵字

plane tessellation ； Euler characteristics ； layer-based representation

參考文獻

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