如何用Gnuplot绘制散点数据密度2D等高线图？修正色条与轴缩放问题

基于散点数据绘制2D等高线图时遇到两个问题：

1. 散点图的第三列数据已归一化至[0.0, 1.0]范围，但等高线图右侧色条显示范围为[-0.2, 1.0]；
2. 两张图的XY轴缩放比例不一致，同一数据集应保持相同缩放。

原脚本如下：

### 2D density color plot
reset session

# create some random rest data
set table $Data
    set samples 700
    plot '+' u (invnorm(rand(0))):(invnorm(rand(0))) w table
    set samples 500
    plot '+' u (invnorm(rand(0))+2):(invnorm(rand(0))+2) w table
unset table

# for each datapoint: how many other datapoints are within radius R
R = 0.5    # Radius to check
Dist(x0,y0,x1,y1) = sqrt((x1-x0)**2 + (y1-y0)**2)
set print $Density
    do for [i=1:|$Data|] {
        x0 = real(word($Data[i],1))
        y0 = real(word($Data[i],2))
        c  = 0
        stats $Data u (Dist(x0,y0,$1,$2)<=R ? c=c+1 : 0) nooutput
        d = c / (pi * R**2)             # density: points per unit area
        print sprintf("%g %g %f", x0, y0, d)
    }
set print

# Plot normalized z-values
set size ratio -1   # same screen units for x and y
set palette rgb 33,13,10

stats $Density u 3 nooutput

set table $Density_norm
plot $Density u 1:2:($3/STATS_max) w table
unset table

plot $Density_norm u 1:2:3 w p pt 7 lc palette z notitle

pause -1

# Plot 2D contours of created data points
set dgrid3d 100,100 splines
set contour surface
set cntrparam levels incremental 0.0, 0.1, 1.0
set view map
splot $Density_norm u 1:2:3 with lines lw 2 lc palette nosurface

### end of script

对应的效果图：

• 归一化数据的散点图：
• 同一归一化数据的等高线图：

针对两个问题，修正方法如下：

1. 修正色条范围问题 #

等高线图色条出现负值是因为set dgrid3d splines会对数据进行插值平滑，导致超出原始数据的[0,1]范围。直接添加set cbrange [0:1]命令，强制色条显示范围与归一化数据一致即可。

2. 修正XY轴缩放比例问题 #

散点图使用plot命令时，set size ratio -1已保证XY轴等比例，但等高线图使用splot命令时，需要额外添加set view equal xyz命令，确保XY轴的缩放比例和散点图保持一致。

修改后的完整脚本 #

### 2D density color plot
reset session

# create some random rest data
set table $Data
    set samples 700
    plot '+' u (invnorm(rand(0))):(invnorm(rand(0))) w table
    set samples 500
    plot '+' u (invnorm(rand(0))+2):(invnorm(rand(0))+2) w table
unset table

# for each datapoint: how many other datapoints are within radius R
R = 0.5    # Radius to check
Dist(x0,y0,x1,y1) = sqrt((x1-x0)**2 + (y1-y0)**2)
set print $Density
    do for [i=1:|$Data|] {
        x0 = real(word($Data[i],1))
        y0 = real(word($Data[i],2))
        c  = 0
        stats $Data u (Dist(x0,y0,$1,$2)<=R ? c=c+1 : 0) nooutput
        d = c / (pi * R**2)             # density: points per unit area
        print sprintf("%g %g %f", x0, y0, d)
    }
set print

# Plot normalized z-values
set size ratio -1   # same screen units for x and y
set palette rgb 33,13,10

stats $Density u 3 nooutput

set table $Density_norm
plot $Density u 1:2:($3/STATS_max) w table
unset table

plot $Density_norm u 1:2:3 w p pt 7 lc palette z notitle

pause -1

# Plot 2D contours of created data points
set dgrid3d 100,100 splines
set contour surface
set cntrparam levels incremental 0.0, 0.1, 1.0
set view map
set view equal xyz  # 保持XY轴缩放比例一致
set cbrange [0:1]   # 强制色条范围与归一化数据匹配
splot $Density_norm u 1:2:3 with lines lw 2 lc palette nosurface

### end of script

内容的提问来源于stack exchange，提问作者magfan