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Although detail removal can be carried out in the process of filleting operation and its inverse operation, entities such as vertices, edges and faces with which the simplification operations handle directly lack engineering features, so that the simplification fails to satisfy all the needs of engineering applications.

通过"弧化-还原"，虽然可以实现几何形体的简化，但是这种几何简化是在点、线和面低层次的几何元素上进行的，几何简化的工程意义不明显，难以保证实际应用中的分析几何模型简化的有效性。

When you are satisfied with it, use the grabber to move the vertices up a bit.

缩放到满意的效果后，使用grabber来移动该顶点上一点。

With i being the greatest lower bound on the number of latter points in the interior of any TLP with exactly v vertices, i(5)=i(6)=1,i(7)=i(8)=4 , it is proved that i increases without bound as ...

证明了随着TLP顶点数的增加，内格点数无限增加。并得出在允许旋转 180°条件下，有任意内格点数的三角形TLP，任意格点四边形都是TLP。

A map is said to be Hamiltonian if all the vertices of the map are on one circuit.

一个地图称为哈密尔顿的若其上的所有顶点都在一个圈上。

Compared with the global harmonic mapping method, this approach has the following advantages.(1) The efficiency of the algorithm is greatly improved. The computational cost involved no longer increases exponentially with the number of vertices of the meshes to be fused.(2) The algorithm is robust as the ambiguity in graph structure combination is alleviated.(3) The detail of the cut mesh is fully kept.(4) The topology restriction of the original algorithm is eliminated.

与原有的基于全局调和映射的融合方法相比，新方法的算法效率大幅度提升，求解时间不再随融合模型顶点数的增加而呈指数增长；减少了二维网格拓扑合并中奇异情况出现的概率，提高了算法的稳定性；被剪切网格的细节得到完整保留；消除了原算法对融合区域拓扑的限制。

A efficient encoding for piecewise linear approximation vertices based on hexagonal neighborhood system approach is proposed.

在后继帧的编码中，以初始时空分割为基础，采用前向运动补偿、非线性内插等算法，跟踪均匀时空区域的时域变化，维持帧间时空分割的一致性。

We present an efficient approach for generating the correspondence between two homeomorphic 3D polyhedral models. The user can select vertices on the polyhedra to decompose the boundary of each polyhedron into the same number of morphing patches. Further, the user can specify the feature points on the morphing patch pairs to improve the morph. After the morphing patch pairs are be mapped to 2D regular polygons, they are merged and reconstructed to generate a morph. In the main procedures of our approach, we propose an easy mapping method and a foldover-free warping technique. And we also propose a most efficient merging algorithm. The merging can be completed in O.

我们的对应演算法主要的流程架构是(1)设计一套良好的介面提供给使用者在物体表面上点选圈选点；(2)利用最短路径将圈选点作两两相连，以切割勿体表面；(3)利用Relaxation的方式进行摊平的目的；(4)利用Warping技术以增进使用者的便利性，因此无须圈选太多快patch以精确对齐物体的特徵，同时还提供一套自行避免相交情况的演算法以保证不相交；(5)我们研发出一套极快速的merge演算法，其利用最小轮廓涵盖结构而有效地达成区域搜寻与区域merge，因此在效率上达到O；(6)最后藉由Remesh与3D位置资讯的建立，重构出对应的结果整体而言，透过本论文所研发的对应演算法将不用花费太多的执行时间，因此符合经济效益。

At the same time, by subdividing an icosahedron and projecting all its vertices onto the unit sphere from the center, we can get a spherical triangle mesh with subdivision topology.

然后，将一个正多面体进行细分并将每一次细分所产生的新顶点投影到单位球面上，如此生成一个细分网格。

There may be several Steiner trees for a given set of initial vertices.

可能有几个斯坦纳树为一组给定的初始点。

Let G = V(G,E be a simple graph with |V| vertices and |E| edges. Let |V|= p,|E|= q, if there exists f: V →{1,2,...,p} be an injective mapping, and define an inducedfunction f":E→{1,2,...,q} by setting f"=|f-f| for all∈E. If f maps E onto {1,2,...,q}, then f is said to be a Skolem-graceful labeling of G, the graph G is said to be a Skolem-graceful graph.

对一个给定的简单图G=V(G，E，|V|和|E|分别是图G的顶点数和边数，令|V|=p，|E|=q，如果存在一个一一映射f：V→{1，2，…，p}，使得对所有边∈E，由f′=|f-f|所导出的映射函数f′：E→{1，2，…，q}是一一对应关系，则称f是图G的一个Skolem优美标号，图G被称为Skolem优美图。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。