顶点坐标

先将3D物体模型转换到仿射不变空间，然后把顶点坐标转换到球面坐标，利用球面坐标来嵌入水印。

First , a transformation of the model to an affine invariant space was finished prior to watermark embedding .

航迹由B样条曲线得到，以代表航迹的B样条曲线的控制顶点坐标值作为染色体的基因位进行浮点数编码。

The flight path is obtained by a B-spline curve whose control vertexes are considered as the genes of chromosome via floating point coding .

本文还提出了一种平行四边形预测方法来压缩顶点坐标。

This paper proposes a parallelogram prediction method for vertex coordinate compression .

该算法利用了分数阶傅立叶变换双域表达特性的灵活性，将水印嵌入到直线顶点坐标集合的分数阶傅立叶变换频谱中。

The watermark is embedded into the fractional Fourier transform spectrum of vertex set .

算法根据矢量地图对数据精度的特殊要求提出了相应的水印嵌入条件，并通过修改地图中相邻顶点坐标间的差值来嵌入水印信息。

According to the vector map 's special requirement to data precision , an embedding condition is firstly presented .

对常见的利用顶点坐标加水印的空域算法进行了分析，提出了将水印信息嵌入到最能反映网格模型特征的关键点坐标的水印算法。

After analyzing the methods for spatial domain , we proposed a new watermarking algorithm that adds watermarking into a mesh .

兼有上、下界约束混料凸多面体的面数与顶点坐标的一种计算方法

A computing method of f he number of lateral sides and the coordinates of vertices of a mixture CONVEX-POLYHEDRON having lower and upper bounds

将这一算法应用于名片识别系统，利用从系统中获取的倾斜角度和顶点坐标，得到了很好的校正效果。

Applying the algorithm to business card recognition system and using the skew angle and the border gained from the system , excellent corrected results will be obtained .

最后，进行小波逆变换，得到含有水印信息的虚拟图像，根据虚拟图像中的象素值就可以得到一组新的控制顶点坐标。

Finally , the marked virtual images are gotten with inverse wavelet transform and a new group of control points is obtained based on the pixel value of the virtual image .

建立纹理坐标和形状模型顶点坐标之间的一一映射关系，可以实现建模工作在视觉上的要求，完成三维人脸建模整体工作。

Established the one to one coordinate mapping between texture and shape of the model , it may accomplish the model in vision , all the 3D face modeling work will be over .

该方法可以有效地实现各种复杂空间操作，避免了直接基于顶点坐标计算各种空间操作的值时对效率的影响。

Different types of spatial operations can be implemented effectively founded on this approach . The approach avoids the influence of efficiency when to compute spatial operations through the list of vertexes directly .

研究了物流配送方面的三个问题：（1）基于顶点坐标的车辆有容量限制的单配送中心车辆路径安排问题：该问题以最小化车辆行驶距离为目标。

Three problems in logistics distribution are studied : ( 1 ) To minimize the traveling distance of vehicles , capacitated single-depot vehicle routing problem ( SDVRP ) based on coordinates of points is studied .

本系统对球面三角形的计算问题如：球面三角形的三顶点坐标，球面三角形的面积、周长、角的大小、边的长度等都得到了解决，并且设计的时间复杂度较优。

The system can solve these calculative problems such as three-peak coordinates of spherical triangle , spherical triangle 's area and perimeter , angle size and side length etc , and temporal complication of design is rather superior .

该方法不直接插值顶点坐标，而是将源曲线与目标曲线视为定义在公共定义域上的标量场，并在梯度域进行梯度场操纵。

By viewing the source curve and the target one as scalar fields defined on the common domain , our algorithm has the distinctive feature that it generates blending sequences via manipulating gradient fields instead of interpolating node coordinates .

利用二次曲线的主方向、中心或顶点坐标，给出了使得曲线的简化方程由其不变量和半不变量表示的直角坐标变换公式。

By use of principal directions and coordinates of center or apex of a quadric cure , a Descartes ' orthogonal coordinate transformation formula such as the reduced equation of the cure is expressed in terms of its invariants and semi invariants .

一种利用三角形单元顶点坐标来求静矩、惯性矩、惯性积的方法，可用于求复杂形状截面的静矩、惯性矩及惯性积。

: The unit of coordinate of the vertex on the triangle can find the moment of area , moment of inertia and the product of inertia on the cross - section , by which the problems on the cross - section of complex shape can also be solved .

它们均由多边形表示，并给定其重心和各顶点的坐标。

They are polygons , specified by the coordinates of a centre of mass and their vertices .

为了提高算法的抗剪切攻击能力，算法将顶点按坐标区域分组，在工程图中重复嵌入相同的水印信息。

In order to enhance the robustness against entities ' deleting , vertices are divided into groups due to coordinate position , and the watermark is embedded repeatedly .

只传输一次顶点的坐标，对于各不同精度模型仅传送模型的顶点索引值，索引值的数据量远远小于高精度的坐标数据量，这样就大量减少了数据的传输量。

The vertices ' coordinates are transmitted only once , and the different models are represented by the vertices ' index whose data volume is much smaller than the vertices ' coordinates , so the data volume to be transmitted is reduced remarkably .

一元二次函数在闭区间上一定有最大值与最小值，依其图像顶点横坐标与这一闭区间的相对位置的不同，求最大值与最小值的解法亦略有不同。

There are maximum and minimum surely in a closed interval for the quadratic function with an argument . Depend on the relative position apex of its picture with the closes interval , the solutions of the maximum and minimum is also slightly different .

对于给定人脸模型，我们首先计算每个顶点的拉普拉斯坐标。

For the given facial model , we calculate the Laplacian coordinates of all the vertices firstly .

你也可以创建这样的纹理：它依赖于顶点在特定坐标轴上的位置（通常是高度）。

You may also create textures that are dependent on the vertex position in respect to a certain axis ( height dependent ) .

若已知矩形边的实际长度，可以恢复出相机在三维空间中的实际位置和矩形顶点的空间坐标；

Meanwhile , the camera 's real position and the rectangular vertices in 3D space can be recovered if the edge lengths of the rectangle are known .

此算法可以自然扩展到由三角面片构成的任意三维曲面，以三角面片作为合成单元，合成后直接输出每个顶点的纹理坐标。

It is natural to extend this algorithm to 3D triangular mesh and use triangles as units for texture synthesis . The texture coordinates for each vertex are outputted as the synthesis result , which saves a lot of memory .

在表情合成时，保持所有顶点的拉普拉斯坐标不变，由表情特征点的位移以及选取的固定点，计算人脸模型上其他所有顶点的新位置，从而合成新的人脸表情。

During the expression synthesis , we preserve the vertices ' Laplacian coordinates . With the displacements of the facial feature points and the positions of the fixed points , all the new positions of the facial model are evaluated , which correspond to a new facial expression .

推导出用三顶点的测地坐标计算地球椭球面上三角形面积的公式。

The formula for area of triangle on ellipsoid by means of geodesic coordinate is derived in this paper .

本方法通过边折叠网格简化，使简化后的模型尽可能保持原模型的外形特征，其顶点最终成为微分坐标变形的控制点。

This method , by triangle mesh simplification through edge collapse , tries to make the simplified model maintain the features of the original shape , and to make the vertices become the control points of mesh deformation finally .

在现有的代表性三角形网格压缩方法中，先采用一定的网格遍历方法来压缩连接信息，同时用遍历路径上的相邻顶点来对每个顶点的几何坐标进行平行四边形预测，以压缩几何信息。

In the state of the art mesh compression schemes , the connectivity is encoded using some kinds of traversal method , the geometry is encoded using parallelogram prediction along the traversal path .

提出的新算法中，凸共面四边形是在模型顶点的局部邻域内通过对顶点坐标的细微扰动构造得出。

In the proposed method , coplanar convex quadrilaterals are constructed by slightly disturbing the geometry of vertices located in a local neighborhood .

通过对简化网格中顶点指定仿射变换矩阵，采用高斯牛顿法迭代求解出仿射变换各参数值，更新原始模型中所有顶点的坐标，渲染得到变形后的三维形状。

By specifying affine transformations for the rest points in the reduced mesh , the matrix parameter elements are computed by Gauss-Newton iteration and then the coordinates of all the vertexes in the original shape are calculated and updated .