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euclidean geometry 歐幾里得幾何,歐氏幾何。

euclidean space

According this technology , first we shot the scene from different angles use digital camera , then utilize the relation of epipolar geometry to estimate the exterior parameters ( the position and direction ) of cameras and to recover the scene in projective space , after this we use the technology of self - calibration to estimate the interior parameters of cameras and to recover the scene in euclidean geometry 它利用攝像機拍攝場景或物體不同角度的圖象,根據不同圖象之間的幾何關系估計攝像機的外部參數(即攝像機的位置和方向)恢復場景在射影空間的幾何模型,再利用自定標技術估計攝像機的內部參數并進而完成場景在歐氏空間的重建。

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。

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。

In three dimensions , the basis of spatial objects is euclidean geometry , it obeys euclidean axioms . this leads directly to the question how geometric constructions , as defined by the euclidean axioms , can be represented with the finite approximations available in computer systems 在三維空間中,空間對象的定義基礎是歐幾里得幾何,服從歐幾里得公理,但利用計算機系統處理嚴格服從歐幾里得公理的空間對象必定會帶來一些問題。

Results a view of better understanding origins of gaussian intrinsic differential geometry is presented , and the intrinsic relation between gauss ' s thought of intrinsic differential geometry and of his non - euclidean geometry is brought to light and discussed 結果總結分析了高斯建立的內蘊微分幾何的思想和淵源,揭示了其與非歐幾何學的內在聯系。