基本解释：对偶地图
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A brief proof to the key theory "The dual graph T of a simple polygon triangulation S is a tree" is given in the proof of theory "A simple polygon triangulation S is 3-Color".对“简单多边形三角形化图S是可以3-色”的定理证明中用到的关键定理:“简单多边形三角形化图S的对偶图T是一棵树”作了十分简化的证明,从而简化了3-色问题及Art Gallery问题Watchman定理的证明。
Based on the triangulation of the state space of a robot, a dual graph was constructed following the target attractive principle, and then a path planning algorithm was presented to find a sequence of adjacent triangles that were traversed by the shortest path.对机器人的状态空间进行三角划分,根据目标吸引原理来建立其对偶图,针对对偶图提出路径规划算法得到最短路径穿越的三角形序列。
A second section presents the dual graph method and show its shortages.通过对增设虚拟边网络连通性表达法和对偶图网络连通性表达法的描述和它们所面临问题的分析研究，说明这两种方法在交通网络连通性表达上，尤其是在引进交通转弯限制时所显示出来的需要大量处理工作的问题，提出了一种新的网络连通性表达法，作者称为“边标号法”，此法避免了对交通网络增设虚拟边或进行点边转化所带来的大量工作量问题，在对交通网络图不作任何修改的情况下，清楚而有效地表达出网络的连通特性。
Firstly it presents the traditional direct graph method and dual graph method, and describes the main problems.提出了一种新的网络连通性表达法，称为“边标号法”，从算法的角度解决了增设虚拟边网络连通性表达法和对偶图网络连通性表达法所带来的大量工作量问题，在对交通网络图不作任何修改的情况下，清楚而有效地表达出网络的连通特性，体现出了边标号法的优越性，并用一个具体实例通过程序实现了该方法。
Relationship between bandwidth sums of graph and its dual hypergraph;图带宽和与其对偶超图带宽和的关系
In this papers,it mainly presents a necessary and sufficient condition on dual hypergraphs and studies its property.给出超图H的对偶超图是保形的充要条件,对它的性质进行了探讨,同时对具有保形性的超图的边数进行了研究。
The paper gives the necessary and sufficient condition of self-dual graphs, all of self-dual graphs can be structured with this necessary and sufficient codition.给出自对偶图的充要条件,并利用此充要条件,能构造出所有自对偶图。
Reverse nearest neighbor query based on Voronoi diagram and delaunay graph基于Voronoi图及其对偶图的反最近邻查询
4-colouring of dual G(p,q,f) of a 32-face sphere development32面体展开图的对偶图G(p,q,f)的4着色
Dual Hopf Algebras from a Quiver and Dual Quiver Quantum Groups由箭图构造的对偶Hopf代数和量子群
Congruence Classes of Minimum Coverings of Complete Graph with Even Length Cycle偶圈对完全图最小覆盖的若干同余类
Image Denoising and Image Decomposition Based on Dual Method;基于对偶方法的图像去噪和图像分解算法
SAR Image De-Noising Algorithm Based on Dual-Tree Complex Wavelet Domain Image Fusion基于对偶树复小波域图像融合的SAR图像去噪
Electromagnetic Response to Gravitational Wave: Classical Description and Its Quantum Duality;引力波的电磁响应：经典图象及其量子对偶性
Image Denoising Based on Dual Tree Complex Wavelet Transform基于对偶树复小波的图像去噪技术研究
Total Variation-based Primal-dual Active-set Algorithms for Image Restoration基于全变差的本原对偶有效集图像复原算法
Image restoration algorithm based on primal-dual hybrid gradient descent method基于原—对偶混合梯度下降法的图像恢复算法
A complete bipartite graph is a simple bipartite graph with bipartition.完全偶图是具有二分类的简单偶图。
Worship of idols.偶像崇拜对偶像的崇拜
SO(2) Duality Theory of Electric Dipole and Magnetic Dipole Radiation;电偶极和磁偶极辐射的SO(2)对偶理论
Duality Transformation Research Based on Graph Representation and Its Application in Engineering;基于图表示的对偶转换的研究及其在工程中的应用
Neighborhood Adaptive Image Denoising Using Dual-Tree Complex Wavelet Transform基于对偶树复数小波变换的邻域自适应的图像降噪
A Primal-dual Active-set Method for Modified Bound Constrained Image Restoration Problems原对偶积极集法求解改进的有界约束图像恢复问题
Residual Error Hypercomplex Symplectic Decomposition Approach to Multispectral and Panchromatic Image Fusions残差超复数偶对分解的多光谱和全色图像融合方法
Of, relating to, or marked by antithesis.对偶的对偶的，有关对偶的，有对照标志的
