樂高立體書的自動生成系統

Abstract

紙摺立體書利用紙張堆疊與交互作用來產生複雜立體結構，其精巧的摺疊設計能讓各年齡層的人皆感到有趣味。而樂高(LEGO)從1940年代發展至今，成為了在建構立體模型的領域中家喻戶曉的一種工具。在2016年，Lego公司的Lego ideas平台出現了將紙摺立體書與樂高積木結合的樂高立體書結構，激發了我們想要設計可以自動化生成樂高立體書之電腦輔助系統的動機。\n雖然在先前有針對紙摺立體書與樂高建構的各種研究，但並沒有將兩者結合的相關研究，故本研究在樂高立體書的觀察與分析下，提出了三個樂高立體書的機制，透過公式化來分析樂高磚間如何彼此排列形成合理的樂高立體書結構。接著我們設計一個系統，將輸入的二維影像透過使用者選定的機制與相關參數來生成初始結構，接著透過我們提出的優化目標函式與優化流程，在無窮的三維結構設計複雜度與可行的時間中，來生成同時具有穩定性與複雜度，且合理的樂高立體書結構。在研究結果中，我們輸入多種不同類型的影像與參數產生結果，來驗證我們系統可用於各種輸入影像的可行性。

Paper pop-ups demonstrate complex three-dimensional structures by the arrangement of paper. The delicate design of paper pop-ups fascinates people of all ages. Since the 1940s, Lego becomes a well-known tool in the field of constructing three-dimensional models. In 2016, a V-fold type Lego pop-up book was published on the Lego ideas platform. This amazing work has led to our computer-assisted tools for designing Lego pop-ups.\nAlthough there have been various studies on paper pop-up books and Lego construction, there is no related research that combines the two. Therefore, based on the observation and analysis of Lego pop-ups, we propose three Lego pop-ups mechanisms. We analyze how to arrange the Lego bricks to form a reasonable Lego pop-up structure through general formulation. Based on the proposed mechanisms, we design a system to generate an initial layout design from the input of two-dimensional images and user-specified mechanisms and parameters. Then, through the proposed optimization model, we compute a stable structure that is easy to assemble in a feasible time even the complexity of the three-dimensional is infinite. We verify the feasibility of the proposed method by various kinds of input images of our system.