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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/56581完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 尤春風 | |
| dc.contributor.author | Te-Chi Liu | en |
| dc.contributor.author | 劉得祺 | zh_TW |
| dc.date.accessioned | 2021-06-16T05:36:01Z | - |
| dc.date.available | 2015-08-17 | |
| dc.date.copyright | 2014-08-17 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-08-12 | |
| dc.identifier.citation | [1] Bajaj C.L., Hoffmann C.M., & Hopcroft J.E., “Tracing surface intersections,” Computer Aided Geometric Design, vol 5, pp. 285-307, 1988.
[2] Farouki, R.T. , “Direct surface section evaluation,” Geometric Modeling: Algorithms and New Trends (G. Farin, ed.), SIAM, pp. 319-334, 1987. [3] Goldman, R.N., “Two approaches to computer model for quadric surfaces,” IEEE Computer Graphics and Applications, pp. 21-24, 1983. [4] Grandine, Klein, “A new approach to the surface intersection problem,” Computer Aided Geometric Design, vol. 14, pp. 111-134, 1997. [5] Hartmann, E., “Numerical implicitization for intersection and Gn-continuous blending of surfaces,” Computer Aided Geometric Design, vol. 15, pp. 377-397, 1998. [6] Kim, K.J. & Kim, M.S., “Computing all conic sections in torus and natural quadric intersections,” Proc. of Israel-Korea Bi-National Conference on New Themes in Computerized Geometric Modeling, pp. 11-20, 1998. [7] Levin, J.Z., “Mathematical models for determining the intersections of quadric surfaces,” Computer Graphics and Image Processing, vol. 11, pp.73-87, 1979. [8] Liu, X.M., Liu, C.Y., Yong, J.H. & Paul, J.C., “Torus/torus intersection,” Computer-Aided Design and Applications, vol. 8, pp. 1-12, 2011. [9] Maekawa & Patrikalakis, “Shape interrogation for computer aided design and manufacturing,” Springer, pp. 139-140, 2001. [10] MathWorld, “Torus,” http://mathworld.wolfram.com/Torus.html [11] McKain, D., “Jacomax,” https://www.wiki.ed.ac.uk/display/Physics/Jacomax [12] Miller, J.R., “Geometric approaches to nonplanar quadric surface intersection curves,” ACM Transactions on Graphics, vol. 6, no. 4, pp. 274-307, 1987. [13] Piegl, L., “Geometric method of intersecting natural quadrics represented in trimmed surface form,” Computer-Aided Design, vol. 21, no. 4, pp. 201-212, 1989. [14] O’Connor, M.A., “Natural quadrics: projections and intersections,” IBM journal of Research and Development, vol. 33, no. 4, pp. 417-446, 1989. [15] Qiang L., Sanyuan Z. & Xiuzi Ye, “Algebraic algorithms for computing intersections between torus and natural quadrics,” Computer-Aided Design, vol. 1 , no. 1-4, pp. 459-467, 2004. [16] “Rational polynomial functions,” http://www.math.dartmouth.edu/opencalc2/cole/lecture19.pdf [17] Xiahong J., Changhe T. & Wenping W., “Topological classification of non-degenerate intersections of two ring tori,” Computer Aided Geometric Design, vol. 30, pp. 181-198, 2013. [18] 尤春風, Spring Solid System實體模型系統，國立臺灣大學實體模型系統實驗室。 [19] 高晨峻, “應用Dupin Cyclide 求解環形曲面和自然二次曲面間相交區線的探討”,國立臺灣大學機械工程研究所碩士論文, 頁30-51, 1998. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/56581 | - |
| dc.description.abstract | 計算曲面交線是電腦輔助設計系統不可或缺的核心功能，例如布林運算牽涉曲面相交計算來表示分割後的區域。計算的效率和正確性，是曲面交線研究中重要的指標。
本研究探討兩環形曲面之相交曲線之演算法則，以及相交曲線之拓樸結構。提出的演算法也會經由一些較為極端的範例測試其強健性。此法則牽涉搜尋相交曲線的關鍵點，並根據不同情形加以分類，進而求得拓特徵。 本研究實作的平台是利用CAD系統（Spring Solid System），搭配開放原始碼的電腦代數系統（Maxima）作為外部函式庫處理代數式之化簡，展開等操作。 最後，本文測試數種相交範例，以驗證本方法的可行性和分析誤差。 | zh_TW |
| dc.description.abstract | Computing intersection is a core function of CAD systems; for instance, a Boolean operation involves calculating surface intersections to determine divided region. Efficiency and correctness are the key issues of surface intersection fields.
This thesis is focusing on the algorithm of computation between two toroidal surfaces and the topological structure of intersection. Extreme cases will be tested for examining its robustness of the proposed algorithms. These algorithms involve searching the characteristic points and applying the classification to determine topological features. The thesis is implemented on a CAD platform (Spring Solid System) and an open source computer algebra system (Maxima) for processing algebraic symbols. Finally, the thesis takes several intersection samples for measuring the feasibility and errors. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T05:36:01Z (GMT). No. of bitstreams: 1 ntu-103-R01522602-1.pdf: 6369909 bytes, checksum: 4ebc3968aaaa46e27d36a1d77c37967c (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 致謝 i
摘要 ii Abstract iii 目錄 iv 圖目錄 vii 表目錄 xi 符號表 xii 第一章 緒論 1 1.1 前言 1 1.2 研究動機 3 1.3 文獻回顧 5 1.4 研究內容 8 1.5 開發環境 9 1.6 論文架構 10 第二章 自然二次曲面相交曲線 11 2.1 曲面相交分類 11 2.2 曲面方程式類型 12 2.3 有理參數多項式曲面與隱含代數式曲面之相交曲線 13 2.3.1 方程式 13 2.3.2 追蹤法（tracing method） 13 2.3.3 特徵點 14 2.3.4 歧異點分析 16 2.4 有理參數多項式曲面之相交曲線 18 2.4.1 方程式 18 2.4.2 網格法 18 2.4.3 分割法（subdivision method） 19 2.4.4 marching method 20 2.5 隱含代數式曲面之相交曲線 21 2.5.1 數值隱含法 21 第三章 環形曲面與環形曲面相交曲線 23 3.1 曲面相交類型 23 3.2 方程式 24 3.3 特徵點與交線線段 26 3.4 特徵點之拓樸特徵與分類法則 28 3.4.1 前言 28 3.4.2 邊界點 28 3.4.3 轉折點 29 3.4.4 分支點 30 3.4.5 孤立點 31 3.5 複合特徵點 33 3.6 垂直交線線段 38 3.7 演算法則 41 3.7.1 演算法流程 41 3.7.2 特徵點搜尋 42 3.7.3 離散相交點分群法則 44 3.7.4 資料結構 48 3.7.5 代數運算系統程式應用介面 50 第四章 案例驗證與探討 51 4.1 測試資料 51 4.1.1 測試資料分類 51 4.1.2 正確性參考標準 53 4.2 測試結果 53 4.3 討論分析 75 4.3.1 誤差討論 75 4.3.2 分割精度與正確性 75 4.3.3 計算時間討論 76 第五章 結論與未來展望 79 5.1 結論 79 5.2 未來展望 80 參考文獻 81 作者簡歷 84 | |
| dc.language.iso | zh-TW | |
| dc.subject | 相交曲線 | zh_TW |
| dc.subject | 環形曲面 | zh_TW |
| dc.subject | 二次曲面 | zh_TW |
| dc.subject | 特徵點 | zh_TW |
| dc.subject | 演算法 | zh_TW |
| dc.subject | 環形曲面 | zh_TW |
| dc.subject | 二次曲面 | zh_TW |
| dc.subject | 相交曲線 | zh_TW |
| dc.subject | 特徵點 | zh_TW |
| dc.subject | 演算法 | zh_TW |
| dc.subject | algorithm | en |
| dc.subject | characteristic points | en |
| dc.subject | intersection curves | en |
| dc.subject | torus | en |
| dc.subject | natural quadrics | en |
| dc.title | 環形曲面與環形曲面之相交曲線與拓樸分析 | zh_TW |
| dc.title | Topological Analysis of Torus/Torus Intersection | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳俊銘,鍾添東 | |
| dc.subject.keyword | 環形曲面,二次曲面,相交曲線,特徵點,演算法, | zh_TW |
| dc.subject.keyword | torus,natural quadrics,intersection curves,characteristic points,algorithm, | en |
| dc.relation.page | 84 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-08-13 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 機械工程學研究所 | zh_TW |
| 顯示於系所單位： | 機械工程學系 | |
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