Aim to study the relations between the thought of gaussian intrinsic differential geometry and gauss ' s earlier research on non - euclidean geometry 摘要目的分析与研究高斯关于非欧几何的研究和内蕴微分几何思想之间的联系。
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 结果总结分析了高斯建立的内蕴微分几何的思想和渊源，揭示了其与非欧几何学的内在联系。
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 在三维空间中，空间对象的定义基础是欧几里得几何，服从欧几里得公理，但利用计算机系统处理严格服从欧几里得公理的空间对象必定会带来一些问题。
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 纵观几何学发展的历史，可以称得上波澜壮阔：一方面，从古希腊时代的欧氏综合几何，到近代解析几何等多种几何的发展，以及用变换的方法处理几何的埃尔朗根纲领，到20世纪拓扑学、高维空间理论等几何学的新发展，这一切都在不断丰富人们对几何学的认识；另一方面，从欧几里得第一次使用公理化方法把几何学组织成一个逻辑演绎体系，到罗巴切夫斯基非欧几何的发现，以及希尔伯特形式公理体系的建立，极大地发展了公理化思想方法，不管是几何学的内容还是方法都发生了质的飞跃。
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 虽然它的独立与发展相对于其他一些古老的数学学科如分析学，代数学，欧氏几何学和数论要晚了许多，但经过一百多年，特别是20世纪40年代到70年代的蓬勃发展，一般拓扑学日趋成熟与完善。
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 它利用摄像机拍摄场景或物体不同角度的图象，根据不同图象之间的几何关系估计摄像机的外部参数(即摄像机的位置和方向)恢复场景在射影空间的几何模型，再利用自定标技术估计摄像机的内部参数并进而完成场景在欧氏空间的重建。
