近年來，3D 列印技術越來越接近消費者階級，因此擁有個人3D 印表機的使用者也
隨之上升，然而其限制卻也很多，細狀結構就是其中一個限制。在列印細狀結構的時候，一般都會產生過多且複雜的支撐材料，難以拆除。但由於細狀結構的特性，使得使用者很難在其結構上設計卡榫或是使用黏膠，因此一些利用切割以及旋轉的方式來規避支架列印的演算法在實際組裝的時候便會遇到困難，而難以組裝的的特性也讓大型的細狀結構列印無法實現。再者，細狀結構在尚未完全成型的時候可能會有穩固性不足的狀況發生，使得列印的過程中很可能會因為機台的搖晃而倒塌，且沉積式印表機的列印方向一致性則會導致細狀結構的部分截面形狀過於極端，造成部分部位的品質不甚理想。
為了解決這個問題，本研究利用了翻模的技巧來實行反向製造的概念，也就是利用3D 列印製造細狀結構的外模，再將可硬化的液體材料灌入，待硬化之後拆除外模，以獲得細狀結構的製造結果。以翻模作為製造手段已行之有年，其相關知識及技巧也不少，對使用者來說相對易上手且有趣。細狀結構不僅對列印機來說是一大難題，對翻模來說也是一項較難人工設計的物件，所以本研究對不僅是解決細狀結構之於列表機的問題，也等於是探討了細狀結構翻模的作法。翻模不僅能夠解決一般列表機製造細狀結構的問題，亦具有可快速複製的優點，所以本研究雖然以消費者階級的列表機為目標設計演算法，但也可套用至各種翻模工序甚至於工業開模。

In recent years, 3D printer is getting more and more available. However, there still exist many limitations, which the problem of thin structure is included in. Precisely speaking, much support material is being generated as printing thin structure, and these
parts are difficult to be removed. Due to the property of thin structure, it is not easy to design bolt or to use glue on it. Therefore, some sort of algorithm rely on segmentation and rotation to avoid generating support material is not practical upon assembly process. The difficulty of assemably also make the fabrication of big thin structure not possiable. Also, sometimes it could be not so stable before totally formed, resulting in collapse with chance while the machine is shaking. Even more, we know that an FDM printer has to deposit material to form the object in a certain fixed direction. A thin structure usually contain extreme cross-section shape so a bit worse quality is expected.
To deal with above problem, we apply molding technique to implement the concept of negetive fabrication, which means we print the cast of the object and inject molding liquid. Then we wait until hardening to get the result of the object. Molding technique is accepted for a long time, plenty of skills are derived to improved it. We can even see it in a student craft class, so it is fair to command it as approachable and interesting for normal user. Objects with thin structure is not only a problem for printing, but for designing their molding cast manually. Hence, our work solve the printing problem as well as benefit to molding field. On the other hand, molding has the advantage of rappid reproducing. Consequently, our method is not only suit for consumer class 3d printer, but also other type of molding system, even at the industrial level.

中文􁄔要i
Abstract ii
目錄iii
圖目錄v
1 􁆣論1
2 相關研究5
3 系統概觀7
4 模具生成9
4.1 體素和超體素. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.1.1 切面. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.1.2 格線. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.1.3 簡化分群. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1.4 移動限制. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2 合併. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2.1 優先列隊. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2.2 順序性. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.3 組裝與拆裝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 輸出. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5 前置優化21
5.1 格線. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2 切面. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.3 旋轉. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6 成果與比較26
6.1 鑄模. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.2 數值比較. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6.3 實際結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
7 結論33
7.1 總結. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.2 限制與未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
A Proof 35
B Discussion 40
C Other Details 45
Bibliography 46

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