projective geometry

1. In this paper, the existence theorem of midpoint chord of quadratic curve, as well as its proof, is given via methods of projective geometry and polarity principle.
   文章利用射影几何方法及配极原理给出二次曲线中点弦存在性定理的证明。
2. By using the projective geometry, some schemes for generating rational curves from pencil of lines are investigated in this paper.
   采用射影几何学方法，研究从直线束生成有理曲线的技术方案。
3. The synthetic geometers were developing projective geometry.
   综合几何学家们在发展射影几何学。
4. Cross ratio and element at infinity are two important concepts with projective geometry and primary tools in considerate projective property of figures.
   交比和无穷远元素是射影几何中的两个重要概念，它们是探讨图形射影性质的主要工具。
5. According to the fUndamental theorem of coniC In projective geometry any five points can decide one conic section.
   在射影几何中，二次曲线定理告诉我们任意五点可以决定一条二次曲线。
6. Method: First, device parameters and azimuth parameters of analytic geometry model and projective geometry model of coded structured light system were analyzed and unified.
   方法：首先，比较分析编码结构光系统的解析几何模型和射影几何模型，统一了二者的设备参数、姿态和位置参数。
7. Conics Projective Geometry and Application of the Nature of the Discussion
   射影二次曲线的几何性质讨论及应用&二元二次多项式因式分解的理论
8. In this paper, the bar fixing problems of spatial four_bar mechanism are discussed applying projective geometry.
   应用画法几何探讨空间四杆机构各杆件的定位问题。
9. We shall interrupt the history of projective geometry.
   我们要把射影几何的历史断开。
10. Basing on projective geometry, the author of this paper offers a general analysis of photogrammetric geometry theory and puts forward the photogrammetric equations expressed by homogeneous projective coordinates.
    作者从射影几何的观点出发，全面分析研究了摄影测量的几何理论，首次提出了用齐次射影坐标表述的摄影测量方程组，为摄影测量提供了新的理论基础，并给出了具体的实例。
11. An Approach to the Vector in Application of Projective Geometry
    矢量法在投影几何中应用的探讨
12. Single view metrology compute the 3D coordinate of a point based on the projective geometry's characteristic of cross-ratio invariability.
    单视图测量理论主要是利用了射影几何中的交比不变性来计算图像上点的三维坐标。
13. Developed from the theory of projective geometry, this paper made a detailed research on the basic theory of the image-based plane measurement technique.
    从射影几何理论出发，论文详细研究了基于图像的平面测量的基本原理。
14. In this paper the auther puts forward the stereographic projection in which the projection plane is the equatorial plane of projection-sphere, recommends the rules about perspective mapping of plane field in projective geometry and reveals two corollaries in stereographic projection.
    本文提出了以投影圆球之赤道平面为投影平面的一种球极投影，首次引入了射影几何理论中关于平面场透视变换的双旋法则，并得到了两个关于球极投影的推论。
15. This paper adopts a method proposed recently, which uses projective geometry transform and 3D vision correspondence from multiple cameras to interpolate virtual images based on virtual viewpoint.
    本文采用了一种较新的方法，即通过基于射影几何学变换和立体视觉对应的方法插入虚拟视角的虚拟图像。
16. The Analysis of the Function and the place of Pascal Theorem in projective Geometry
    浅析Pascal定理在射影几何中的地位和作用&兼谈对编写射影几何教材的一点建议
17. Research into Effection Change Projection Plane Time about Three-Dimensional Projective Geometry
    三维画法几何中有效换面次数的研究
18. According to the projective geometry and perspective theory, this pager presents a method for drawing the virtual image in front oblique mirror. It further perfects the drawing method of virtual image.
    根据射影几何和透视理论，探讨了在正面斜镜中画虚像方法，进一步完善了关于虚像的画法。
19. In this paper, a kind of method on vector of Menelaus Theorem is given and by Menelaus Theorem several famous theorems of projective geometry are proved.
    给出了Menelaus定理的一种关于矢量的证明方法，并利用Menelaus定理证明了射影几何中的几个著名定理。
20. By the theory of harmonic conjugate in projective geometry, midpoints of two parallel edges are determined.
    根据射影几何中的调和共轭理论，确定梯形2条平行边的中点。
21. The principle using Lagrange interpolation algorithm and a scheme for information sharing based on the projective geometry are also introduced.
    本文介绍了利用拉格朗日插值算法给出的分存原理，并提出一类基于射影几何学的分存算法。
22. In this paper, some theories and methods of affine geometry and projective geometry are applied in elementary geometry, and an instructive role of higher geometry is played in the teaching of elementary geometry.
    从仿射几何和射影几何的理论与方法出发，探讨了它们在初等几何中的一些应用，有利于高等几何对初等几何教学的指导作用。
23. In this paper, by using projective geometry theory, we have separately proved Butterfly Theorem with four different methodes, ang have extended it to affine and projective geometry.
    本文利用射影几何的理论，采用了四种不同的方法，对蝴蝶定理进行了证明，并给出了仿射的和射影的若干推广。
24. In this paper, we give a new theorem on Newton lines of a complete quadrilateral, and use it to prove direct a type of proposition of common point and common line in the projective geometry.
    给出了关于完全四线形的牛顿线的一个新定理，并用该定理直接证明了射影几何中一类共点、共线命题。
25. In the calibration of the system, a plan based on the principle of cross ratio invariance in algebraic projective geometry was used to calibrate the coded light planes.
    在对编码投影光平面的标定过程中，提出利用代数射影几何中的交比不变原理对其进行标定的方案，并论述了标定原理。
26. Application of vector to plane projective geometry
    矢量在平面射影几何中的应用
27. This theorem and its corollary link with the theories of corresponding polar and pascal lines and perspective axis. The conclusion of projective geometry can be applied to analytic and elementary geometries.
    这个定理和推论将极线、巴斯加线、透视轴等相应理论联系了起来，便于将射影几何中的结论应用于解析几何和初等几何。
28. The first self-calibration method is inspired by monocular vision and is mainly based on projective geometry.
    一种是基于单目视觉技术的双目视觉自标定技术。
29. Based on the theory in projective geometry geometric invariants, by which the non-coding marker point-plane matching can be realized.
    根据射影几何学中几何不变量的相关理论，本文利用共面五点交比不变特性实现平面非编码标记点的匹配。
30. The self-calibration technology needs no calibration object and its work is based on projective geometry and the constraints of epipolar geometry.
    自标定技术则不需要标定物，利用射影不变量和极几何约束对相机进行标定，在实际应用中灵活。

noun

1. the geometry of properties that remain invariant under projection

   Synonym:    descriptive geometry