射影几何

本文以n维射影几何为基础，用范畴与函子的观点讨论了射影几何中对偶原理与范畴论中对偶原理的一致性，同时还给出了互相对偶的对象NP与N（P）的构造。

In the paper we discuss consistency property of duality principles in the projective geometry categorical theory , and give constitution of dual objects N_p N_ ( p ) .

首先，从射影几何的角度出发，介绍了2D射影矩阵，给出求解该矩阵的求精算法；

First , we inducted the homogeneous matrix using projective geometry , and derived the appropriate algorithms to solve this matrix .

只是运用射影几何的性质，通过简单的几何关系，对非标定单摄像机拍摄的单幅图像，求解其从2D图像平面到真实的3D平面的非线性单映射关系。

The nonlinear mapping between 2D image plane and the plane in the 3D world is conformed depending on property of projective geometry and relation of 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

The Analysis of the Function and the place of Pascal Theorem in projective Geometry

用射影几何方法探讨Desargues逆命题

On the converse proposition of Desargues with projective geometry

利用射影几何方法在小缺陷码中，NMDS码是链条件码；

NMDS codes are all the ones satisfying the chain condition ;

阐述了射影几何原理、相机成像模型、图像预处理、特征点检测技术、特征点匹配技术、相机标定技术等基本理论方法。本文提出一种基于图像分块的多尺度Harris特征点检测算法。

The theory is expatiated about imaging camera model , image pretreatment , detecting feature points , matching feature points , camera calibration etc.A multi-scale Harris algorithm for feature point detecting based on image sub-block is proposed .

它满足Hilbert几何公里体系中的结合公理；如果是有序域上的射影几何，则更满足顺序公理。

Defines the projective geometry on field and proves that it satisfies the axiom of incidence of the Hilbert axiom system of geometry , and if it is the projective geometry on an ordered field , then if satisfies the axiom of order .

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。

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 .

代数结构与几何基础Ⅰ&域上的射影几何

Algebraic Structure and Geometry Foundation ⅰ── Projective Geometry on a Field

光正交码的有限射影几何设计方法

A Method of Construction Optical Orthogonal Codes from Finite Projective Geometries

射影几何在画法几何解题中的应用

Application of Projective Geometry to Solving Problems in Drawing Geometry

射影几何教学中反例的运用

The Application of Counter Examples in Teaching of Projection Geometry

射影几何对中学几何的指导作用

The guiding effect of projective geometry on middle school geometry

基于射影几何意义下的投影重建是目前物体三维重建中经常采用的方法。

The 3 D projective reconstruction is often adopted from multiple uncalibrated images .

试论射影几何方法的形成和发展

On the formation and evolution of projective geometry methods

射影几何对共点共线问题的指导作用

Directing Effect of Projective Geometry on the Problems of Cointersection Lines and Collinear Points

矢量在平面射影几何中的应用

Application of vector to plane projective geometry

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。

By the theory of harmonic conjugate in projective geometry , midpoints of two parallel edges are determined .

简述了有限射影几何及有限域在组合设计中的意义及其对组合设计理论发展的推动作用。

State briefly the motivation that finite projective plan and finite field offer to the development of combinatorial design .

此内容可以作为射影几何教学中理论联系实际的典型例题。

This can be considered as a typical example of integrating theory with practice in the projection geometry teaching .

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。

According to the fUndamental theorem of coniC In projective geometry any five points can decide one conic section .

17世纪法国数学家笛沙格在射影几何方面的工作具有创造性成就。

Desargues who was a French mathematician in 17th century had made creative achievement in the aspect of projective geometry .

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。

Single view metrology compute the 3D coordinate of a point based on the projective geometry 's characteristic of cross-ratio invariability .

以射影几何、透视理论的基本原理为基础，探讨了根据平面立体，二次曲面及自由曲线的透视草图重建三维几何模型的若干问题。

Sketch reconstruction of different models including planar models , conical surfaces and freeform curves are discussed based on the perspective theory .

文章利用射影几何方法确定了满足近链条件的4维3元码的所有重量谱。

In this paper , by using the projective method , we determined all the weight hierarchies of codes satisfying the Near-Chain condition .

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。

Cross ratio and element at infinity are two important concepts with projective geometry and primary tools in considerate projective property of figures .

采用代数方法证明了射影几何的时偶原则及二次曲线的对偶定理。

In this paper , tbe authors proved the principle of duality of projective geometry and the dual theorem of curve of second degree .

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。

Developed from the theory of projective geometry , this paper made a detailed research on the basic theory of the image-based plane measurement technique .

给出了射影几何中关于二阶曲线渐近线的几个等价定义，并探讨了根据不同定义的二阶曲线渐近线的应用。

This paper investigates a few of equivalent definitions about asymptotes of a curve of second order and presentes some methods of obtaining these asymptotes .