centroidal(voronoi)
centroidal()所属R语言包：voronoi
Centroidal Voronoi Diagram
质心Voronoi图
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Iteratively searches for the centroidal Voronoi diagram by shifting each point to the weighted centroid of its cell, re-tessellating, shifting each point to its new weighted centroid, and repeating until convergence.
迭代搜索的质心Voronoi图，把各点，其单元的加权质心，重新镶嵌，每个点转移到新的加权质心，并重复直到收敛。
用法----------Usage----------
centroidal(x, eps = .01, max.iter = 100, f = NULL, antideriv.x = NULL,
antideriv.y = NULL, divisions = 15, rw = NULL, verbose = 0)
参数----------Arguments----------
参数：x
An M-by-2 matrix or data frame representing a point pattern, or an object of class deldir or ve.
M的2矩阵或数据框代表一个点图案，或一个对象类deldir或ve。
参数：eps
The algorithm will stop when the maximum distance moved by any point between iterations is less than eps.
该算法将停止时的最大迭代点之间的任何移动的距离小于eps。
参数：max.iter
Specifies the maximum number of iterations, provided the eps criterion is not met.
指定的最大迭代次数，提供eps不满足条件。
参数：f
A function taking two arguments over which the centroidal Voronoi diagram is constructed.
函数两个参数的重心Voronoi图的构造。
参数：antideriv.x
A function taking two arguments that is the antiderivative of f with respect to its first argument. Specification of antideriv.x is optional, but will improve efficiency if specified.
函数两个参数，这是它的第一个参数就反导的f。 antideriv.x规范是可选的，但如果指定的话，会提高工作效率。
参数：antideriv.y
A function taking two arguments that is the antiderivative of f with respect to its second argument. Specification of antideriv.y is optional, but will improve efficiency if specified.
函数两个参数，这是它的第二个参数就反导的f。 antideriv.y规范是可选的，但如果指定的话，会提高工作效率。
参数：divisions
A scalar which controls the number of subintervals over which a Riemann sum is computed. Higher values produce more precise centroid location calculations.
一个标量，它控制的子区间数的黎曼计算的。较高的值会产生更精确的计算质心位置。
参数：rw
An optional vector of length 4 describing the corners of the rectangular space of the data. The values should be in the order of (xmin, xmax, ymin, ymax).
一个可选的矢量的长度为4描述的数据的矩形空间的角部。值应该是在顺序（XMIN，XMAX，YMIN，YMAX）。
参数：verbose
If set to an integer value greater than 0, the user will be notified upon the completion of every verbose iterations.
如果设置为大于0的值的整数，用户将收到的每verbose迭代完成后。
Details
详细信息----------Details----------
The function centroidal iteratively searches for the centroidal Voronoi diagram by shifting each point to the weighted centroid of its cell, re-tessellating, and shifting each point to its new weighted centroid. If f is set to NULL, each location in the space has equal weight, and the resulting centroid calculations merely involve finding the geometric center of any given cell. If f is specified, each location v=(x, y) has weight assigned by f(v). Given such weights, calculation of the weighted centroid for cell C proceeds as
的功能centroidal迭代搜索的重心，其单元的加权质心，再棋盘，把每个点，每一个点转移到新的加权质心Voronoi图。如果f被设置成NULL，在该空间的每个位置具有相同的权重，并且所得到的质心计算只是涉及找到的几何中心的任何给定的小区。如果f指定，每个位置v=(x, y)有重量分配的f(v)。鉴于这种电池C所得款项的权重，计算的加权质心
值----------Value----------
The output object is of class ve, which itself is a list with the following items: <table summary="R valueblock"> <tr valign="top"><td>p </td> <td> A matrix of the points.</td></tr> <tr valign="top"><td>z </td> <td> A vector of the Voronoi estimates at the points.</td></tr> <tr valign="top"><td>T </td> <td> A deldir object for the points.</td></tr> <tr valign="top"><td>est </td> <td> Set to NULL. See ve.</td></tr>
输出对象是类ve，这本身就是一个列表以下项目：<table summary="R valueblock"> <tr valign="top"> <TD>p </ TD > <TD>矩阵之分。</ TD> </ TR> <tr valign="top"> <TD>z </ TD>的Voronoi <td>一个向量的点估计</ TD> </ TR> <tr valign="top"> <TD>T </ TD> <TD> Adeldir对象的点。</ TD> </ TR > <tr valign="top"> <TD> est </ TD> <TD>设置为NULL。见ve。</ TD> </ TR>
</table> Appended to the ve list are: <table summary="R valueblock"> <tr valign="top"><td>iter</td> <td> The number of iterations performed.</td></tr> <tr valign="top"><td>max.dist</td> <td> A vector containing the maximum distance moved by any point at each iteration.</td></tr> </table>
</ TABLE>附加ve列表中：<table summary="R valueblock"> <tr valign="top"> <TD> iter</ td> <td>使用数量的迭代进行。</ TD> </ TR> <tr valign="top"> <TD>max.dist </ TD> <TD>一个向量的最大距离所提出的任何一点，在每一次迭代。</ TD> </ TR> </ TABLE>
（作者）----------Author(s)----------
Travis A. Gerke and Christopher D. Barr
参考文献----------References----------
Q. Du, V. Faber and M. Gunzburger. Centroidal Voronoi Tesselations: Applications and Algorithms. SIAM Review 41:637-676, 1999.
C.G. Wager, B.A. Coull and N. Lange. Modelling Spatial Intensity for Replicated Inhomogeneous Point Patterns in Brain Imaging. J.R. Statist. Soc. B, 66:429-446, 2004.
C.D Barr and F.P Schoenberg. On the Voronoi Estimator for the Intensity of an Inhomogeneous Planar Poisson Process. Biometrika, 1:1-15, 2010.
参见----------See Also----------
polygon.adapt, integrate.box
polygon.adapt，integrate.box
实例----------Examples----------
#=====> Uniform Function <=====#[=>统一功能=====＃]
obj <- deldir(runif(10), runif(10))
c.obj <- centroidal(x = obj, eps = .001)
par(mfrow=c(1,2))
plot(obj, wlines="tess", main="Original Tessellation")
plot(c.obj$T, wlines="tess", main="Centroidal Tessellation")
#=====> Polynomial Function <=====#[=>多项式函数=====＃]
f <- function(x, y) x^4 + y^4
antideriv.x <- function(x, y) x^5/5 + x*y^4
antideriv.y <- function(x, y) y*x^4 + y^5/5
obj <- deldir(runif(10), runif(10))
c.obj <- centroidal(x = obj, eps = .005, f = f,
antideriv.x = antideriv.x,
antideriv.y = antideriv.y,
divisions = 10, verbose = 5)
par(mfrow=c(1,2))
plot(obj, wlines="tess", main="Original Tessellation")
plot(c.obj$T, wlines="tess", main="Centroidal Tessellation")
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
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发表于 2012-10-1 16:26:42
