如何绘制（x，y，z）点以显示其密度 [英] How to plot (x,y,z) points showing their density

问题描述

我的数据文件是围绕轴原点的一组（x，y，z）点。它们代表一种措施失败的点。
这些点位于此

问题是该图未显示出错误的出处可能发生。
如果可能的话，我想显示点密度的变化。

我不知道是否可以改变点的颜色点或赋予它们透明性，并尝试表示密度最高的位置。

如果无法表示3D点的密度，则可以采用另一种方法在三个平面（x = 0，y，z），（x，y = 0，z），（x，y，z = 0）中绘制点的投影密度。

致谢

编辑：

我可以用不同的颜色绘制成功点（ 0 ）和错误点（ 1 ）的位置我的实验。此

，但该图未显示点的密度。
例如，在Mathematica中，这些数据样本的密度图为

如何使用 Gnuplot 获得密度图？ Mathematica可能正在对中间的点进行插值并将其值设置为0到1之间，但我不知道如何使用Gnuplot来实现。

解决方案

@ user1993416，我想您可以使用gnuplot做一些事情。您可能需要使用参数 Delta 。使用我8岁的计算机，大约需要1000点积分。 2分钟。

关注代码：

  ### 3D密度图
重置会话
设置项wxt 
 
 N = 1000＃数据点数量
 Delta = 2＃半框宽度
 
 TimeStart = time（0.0）
＃创建虚拟对象一些虚拟数据
设置样本N 
设置表$ Data 
图'+'u（invnorm（rand（0）））:( invnorm （rand（0）））:( invnorm（rand（0）））与表
取消表
 
＃将数据文件/数据集放入数组
 stats $ Data nooutput 
 RowCount = STATS_records 
数组ColX [RowCount] 
数组ColY [RowCount] 
数组ColZ [RowCount] 
数组ColC [RowCount] 
为[i = 1：RowCount] {
设置表格$ Dummy 
图$ Data u（ColX [$ 0 + 1] = $ 1,0）:( ColY [$ 0 + 1] = $ 2,0）:( ColZ [$ 0 + 1] = $ 3,0），其中表
未设置表
} 
 
＃查看每个数据点及其周围的
为[i = 1： RowCount] {
 print sprintf（ Datapoint％g of％g，i，RowCount）
 x0 = ColX [i] 
 y0 = ColY [i] 
 z0 = ColZ [i] 
＃计算距离感兴趣数据点周围$ Delta的数据点
设置表$ Occurrences 
图$ Data u（（abs（x0- $ 1）< Delta） & （abs（y0- $ 2）< Delta）& （abs（z0- $ 3）< Delta）？ 1：0）:( 1）平滑频率
未设置表
＃从$ Occurrences中提取数字，该数字将用于为数据点
设置表着色$ Dummmy 
图$ Occurrences u（c0 = $ 2,0）：（$ 0）每个:: 1 :: 1，其中表
未设置表
 ColC [i] = c0 
} 
 
 ＃再次将数组放入数据集中
 set print $ Data 
做[i = 1：RowCount] {
 print sprintf（％g\t％g\t％g \t％g，ColX [i]，ColY [i]，ColZ [i]，ColC [i]）
} 
 set print 
 
 TimeEnd = time（ 0.0）
 print sprintf（ Duration：％.3f sec，TimeEnd-TimeStart）
 
设置调色板rgb 33,13,10 
 splot $ Data u 1：2： 3：4 wp ps 1 pt 7 lc调色板z notitle 
 
设置终端gif动画延迟30 
设置输出 Density.gif 
 Amin = 40 
 Amax = 60 
 AFrames = 25 
 [i = 0：AFrames] {
 print sprintf（ Frame％g，Angle：％.1f，i，sin（2 * pi * i / AFrames）*（Amax-Amin）+ Amin）
 set view 45，（sin（2 * pi * i / AFrames）*（Amax-Amin）+ Amin）
 replot 
} 
设置输出
  

应导致：

My data file is a set of (x,y,z) points located around the axis origin. They represent points where a kind of measure has failed. These points are in this link.

Gnuplot can plot them,

set encoding iso_8859_1
set term postscript eps enhanced color size 4.7in,4in
set xlabel "X"
set ylabel "Y"
set zlabel "Z"
set output "test_gp.eps"
set style line 1 lc rgb '#0060ad' pt 7 ps 0.5 lt 1 lw 0.5 # --- blue
set style fill  transparent solid 0.15 noborder
splot "data.dat" u 1:2:3 w p ls 1 title "P_{error}"

with the resulting plot

The problem is that the figure does not show where the error is more likely to occur. I would like to show the variations in the density of points if it is possible.

I do not know if it is possible to vary the color of the points or give them transparency and try to represent the locations with the most density of points.

If a representation of the density of 3D points is not possible, another way could be to make a projection density of the points in the three planes (x=0,y,z), (x,y=0,z), (x,y,z=0).

Regards

EDIT:

I can plot with different colors the success (0) and error (1) point locations of my experiment. The file in this link has a 4th column with all data samples ( 0's and 1's).

The splot figure

splot "data_all.dat" u 1:2:3:4 w points ls 1 palette title "P_{error}"

is

but this figure is not showing the density of points. For example, in Mathematica the density plot of these data samples is

How could I get the density plot with Gnuplot?. It is likely that Mathematica is doing an interpolation of the points in the middle and give them values between 0 and 1, but I do not know how to achieve it with Gnuplot.

解决方案

@user1993416, I guess you can do something with gnuplot. You might need to play with the parameter Delta. With my 8 year old computer 1000 points need approx. 2 minutes.

The followig code:

### 3D density plot
reset session
set term wxt

N = 1000      # number of datapoints
Delta = 2    # half boxwidth

TimeStart = time(0.0)
# create dummy some dummy data
set samples N
set table $Data
    plot '+' u (invnorm(rand(0))):(invnorm(rand(0))):(invnorm(rand(0))) with table
unset table

# put the datafile/dataset into arrays
stats $Data nooutput
RowCount = STATS_records
array ColX[RowCount]
array ColY[RowCount]
array ColZ[RowCount]
array ColC[RowCount]
do for [i=1:RowCount] {
set table $Dummy
    plot $Data u (ColX[$0+1]=$1,0):(ColY[$0+1]=$2,0):(ColZ[$0+1]=$3,0) with table
unset table
}

# look at each datapoint and its sourrounding
do for [i=1:RowCount] {
    print sprintf("Datapoint %g of %g",i,RowCount)
    x0 = ColX[i]
    y0 = ColY[i]
    z0 = ColZ[i]
    # count the datapoints with distances <Delta around the datapoint of interest
    set table $Occurrences
        plot $Data u ((abs(x0-$1)<Delta) & (abs(y0-$2)<Delta) & (abs(z0-$3)<Delta) ? 1 : 0):(1) smooth frequency
    unset table
    # extract the number from $Occurrences which will be used to color the datapoint
    set table $Dummmy
        plot $Occurrences u (c0=$2,0):($0) every ::1::1 with table
    unset table
    ColC[i] = c0
}

# put the arrays into a dataset again
set print $Data
do for [i=1:RowCount] {
    print sprintf("%g\t%g\t%g\t%g",ColX[i],ColY[i],ColZ[i],ColC[i])
}
set print

TimeEnd = time(0.0)
print sprintf("Duration: %.3f sec",TimeEnd-TimeStart)

set palette rgb 33,13,10
splot $Data u 1:2:3:4 w p ps 1 pt 7 lc palette z notitle

set terminal gif animate delay 30
set output "Density.gif"
Amin = 40
Amax = 60
AFrames = 25
do for [i=0:AFrames] {
    print sprintf("Frame %g, Angle: %.1f", i, sin(2*pi*i/AFrames)*(Amax-Amin)+Amin)
    set view 45,(sin(2*pi*i/AFrames)*(Amax-Amin)+Amin)
    replot
}
set output

should result in:

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