geometry and topology 中文意思是什麼

geometry and topology 解釋
幾何與拓撲
  • geometry : n. 1. 幾何學。2. 幾何形狀。3. 幾何學著作。
  • and : n. 1. 附加條件。2. 〈常 pl. 〉附加細節。
  • topology : n. 地學志；【數學】拓撲學；拓撲（結構）；【解剖學】局部解剖學。adj. -ical
  1. As we all known, with the founding of euclidean geometry in ancient greece, with the development of analytic geometry and other kinds of geometries, with f. kline " s erlanger program in 1872 and the new developments of geometry in 20th century such as topology and so on, man has developed their understand of geometry. on the other hand, euclid formed geometry as a deductive system by using axiomatic theory for the first time. the content and method of geometry have dramatically changed, but the geometry curriculum has not changed correspondingly until the first strike from kline and perry " s appealing

    縱觀幾何學發展的歷史，可以稱得上波瀾壯闊：一方面，從古希臘時代的歐氏綜合幾何，到近代解析幾何等多種幾何的發展，以及用變換的方法處理幾何的埃爾朗根綱領，到20世紀拓撲學、高維空間理論等幾何學的新發展，這一切都在不斷豐富人們對幾何學的認識；另一方面，從歐幾里得第一次使用公理化方法把幾何學組織成一個邏輯演繹體系，到羅巴切夫斯基非歐幾何的發現，以及希爾伯特形式公理體系的建立，極大地發展了公理化思想方法，不管是幾何學的內容還是方法都發生了質的飛躍。
  2. An integrated information model of a product should include not only the information of the product ' s geometry and topology, but also its machining process information of manufacture oriented

    一個完整的產品信息模型，不僅應具備產品的幾何、拓撲信息，而且還應具備面向製造的加工和工藝信息。
  3. By this means, user can recover the model with arbitrary geometry and topology. during the interaction, the reconstructed results can be computed and displayed instantly because we use an optimization - tree based symbolic and numeric hybrid optimization - solving approach

    採用這種方法，系統在接受使用者的交互之後，可以實時地求解幾何參數與照相機投影矩陣，並即時地在一個三維窗口中顯示重建結果，做到真正的所見即所得。
  4. The key techniques for reverse engineering based on ct image are introduced. 3d reconstructed surface model does n ' t possess full geometry and topology information as solid geometry model. this dissertation presents an algorithm for rebuilding solid model from triangulated patch surface mod

    介紹了基於ct圖象反求的主要技術；針對重建三維表面模型不具備象實體幾何模型的數據那樣的完備信息的特點，提出一種基於ct圖象的反求技術的實體幾何造型方法，將重建模型轉換為邊界表示的實體模型，並將其作為本研究所開發的特徵造型系統3dmodeler中的一種反求工程實體造型手段。
  5. The design process of the proposed method is described as follows : the input of the method is the 3d sketch of a light steelwork, and the geometry and topology information of the members in a steelwork are established automatically. the steel types and function of the linked members are determined by means of interactive scheme according to the design requirements. and the arrangement of the steel members and their orientation are built according to the steel member ' s type, the function of the steel member, the knowledge of the steelwork and welding technology

    在該方法中，首先通過交互手段輸入輕型鋼結構的三維線框簡圖、自動確定結構的幾何和拓樸信息，根據設計要求輸入各桿件的型鋼類型和在結構中的功能；然後，根據型鋼類型、桿件功能、鋼結構設計知識以及焊接知識自動確定桿件的搭配關系、建立桿件的方位布置確定規則和節點板設計的規則；最後，利用這些規則來決定節點稈件連接關系、連接位置，確定節點板的類型、布置方位和位置，實現三維鋼結構的結構自動設計。
  6. The design process of the proposed method is described as follows : the user inputs the 3d sketch of a welded machine, and the geometry and topology information of the members in the welded machine are established automatically. the design information is acquired by the means of man - computer interaction. according to the knowledge of design and welding, the rules of bar orientation, joint processing and welding sequence are established

    用戶在autocad中輸入焊接機架的線框簡圖，提取出機架結構的幾何和拓撲信息，然後通過人機交互輸入設計信息，並根據機架的設計知識與焊接知識，建立機架的桿件方位布置規則、節點處理規則與焊接順序自動確定規則，最後在autocad中生成經過節點處理的機架三維實體，並提供一套合理的焊接順序。
  7. Professor chern was awarded the shaw prize in mathematical sciences 2004 for his initiation of the field of global differential geometry and his continued leadership of the field, resulting in beautiful developments that are at the centre of contemporary mathematics, with deep connections to topology, algebra and analysis, in short, to all major branches of mathematics of the last sixty years

    二零零四年邵逸夫數學科學獎授予陳省身教授，以表彰他開辟整體微分幾何學的成就。整體微分幾何學的精妙發展占著當代數學的核心，與拓樸學、代數學和分析學，簡而言之，與過去六十年數學的所有主要范疇都有密切關連。
  8. Abstract : a new data structure that one link - list was composed of polygon - surface table, edge table and vertex table was proposed to describe the geometry information and topology information of control polyhedron m in the rese arch of modeling with closed surface. compared with other structures which were a pplicable to the work, the structure was understandable, economize and conveniently to modify. after describing the detail of the geometry information, topology inf ormation included in the tables of polygon - surface, edge and vertex, and the poin t - link form of the adjacency multilist between the tables, a concise instance was given in clanguage array

    文摘:介紹了在閉曲面造型研究中，為描述控制多面體m的幾何信息和拓撲信息而設計使用的一種單鏈三表的數據結構.與其他適用與描述控制多面體的數據結構相比，該結構在結合了鄰接多重表方法后的特點是:關系描述清楚，節省存儲空間，方便查找和交互修改形體.在介紹單鏈中三表（面表、邊表、頂點表）所含的幾何信息細節、以及單鏈的三表之間的表示面、邊、頂點拓撲關系的指針的鄰接多重連接方式之後，本文給出了以c語言數組方式簡明描述的數據結構實例
  9. In comparison to previous methods, this approach conveys much richer information : curve topology, affine geometry and local intensity are combined together to seek correspondences

    然而往往面臨以下困難：第一，顯著特徵往往存在於圖像和形狀曲線的高頻部分，因此很難被句法或大尺度的特徵描述子所捕捉。
  10. In the area of pure mathematics, topics include number theory, abstract algebra, real and complex analysis, functional analysis, differential geometry, topology, and differential equations

    在純數學的范疇，可供選讀的科目包括數論、抽象代數、實和復分析、泛函分析、微分幾何、拓撲學及微分方程理論等。
  11. Although its independence and development were late more relative to some other antique mathematical course such as analytics, algebra, euclidean geometry and number theory, through over one hundred years, especially the vivid development from the 1940s to the 1970s, general topology are getting increasingly mature and perfect

    雖然它的獨立與發展相對于其他一些古老的數學學科如分析學，代數學，歐氏幾何學和數論要晚了許多，但經過一百多年，特別是20世紀40年代到70年代的蓬勃發展，一般拓撲學日趨成熟與完善。
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