在R上获得样条曲面

Question

如何生成b样条曲面,让我们说:

x=attitude$rating
y=attitude$complaints
z=attitude$privileges

样条基础上的x和y.z是控制点集.

Answer 1

据我了解，您有x，y和z数据，并且想在x和y上使用双变量样条插值，并使用z作为控制点。您可以interp(...)在akima包中使用。

library(akima)
spline <- interp(x,y,z,linear=FALSE)
# rotatable 3D plot of points and spline surface
library(rgl)
open3d(scale=c(1/diff(range(x)),1/diff(range(y)),1/diff(range(z))))
with(spline,surface3d(x,y,z,alpha=.2))
points3d(x,y,z)
title3d(xlab="rating",ylab="complaints",zlab="privileges")
axes3d()

由于x，y和x是高度相关的，因此图本身对您的数据集就没有兴趣。

编辑对OP评论的回复。

如果要使用b样条曲线曲面，请尝试mba.surf(...)使用不幸命名的MBA程序包。

library(MBA)
spline <- mba.surf(data.frame(x,y,z),100,100)

library(rgl)
open3d(scale=c(1/diff(range(x)),1/diff(range(y)),1/diff(range(z))))
with(spline$xyz,surface3d(x,y,z,alpha=.2))
points3d(x,y,z)
title3d(xlab="rating",ylab="complaints",zlab="privileges")
axes3d()

Answer 2

 require(rms)  # Harrell's gift to the R world.

 # Better to keep the original names and do so within a dataframe.
 att <- attitude[c('rating','complaints','privileges')]
 add <- datadist(att)  # records ranges and descriptive info on data
 options(datadist="add")  # need these for the rms functions

#  rms-`ols` function (ordinary least squares) is a version of `lm`
 mdl <- ols( privileges ~ rcs(rating,4)*rcs(complaints,4) ,data=att)
# Predict is an rms function that works with rms's particular classes
 pred <- Predict(mdl, 'rating','complaints')
# bplot calls lattice functions; levelplot by default; this gives a "3d" plot
 bplot(pred, yhat~rating+complaints, lfun=wireframe)

它是一个交叉的限制三次样条模型.如果您想要使用您喜欢的样条函数,那么请务必尝试一下.我对rcs- 函数运气不错.

这样可以提供更加开放的网格,计算点数更少:

pred <- Predict(mdl, 'rating','complaints', np=25)
bplot(pred, yhat~rating+complaints, lfun=wireframe)
png()
bplot(pred, yhat~rating+complaints, lfun=wireframe)
dev.off()

您可以使用jhoward所示的rgl方法.str(pred)的顶部看起来像:

 str(pred)
Classes ‘Predict’ and 'data.frame': 625 obs. of  5 variables:
 $ rating    : num  43 44.6 46.2 47.8 49.4 ...
 $ complaints: num  45 45 45 45 45 ...
 $ yhat      : num  39.9 39.5 39.1 38.7 38.3 ...
 $ lower     : num  28 28.3 27.3 25 22 ...
 $ upper     : num  51.7 50.6 50.9 52.4 54.6 ...
snipped

library(rgl)
open3d()
with(pred, surface3d(unique(rating),unique(complaints),yhat,alpha=.2))
with(att, points3d(rating,complaints,privileges, col="red"))
title3d(xlab="rating",ylab="complaints",zlab="privileges")
axes3d()
aspect3d(x=1,z=.05)

一旦你意识到没有关于该模型的不适当推断的极端数据,就很好地说明了外推的危险性.rms-package有一个perimeter函数,绘图函数有一个perim参数,周边对象可以传递给它.