Gnuplot多点轴，一个方向的等值线

我试着用参数m和n再现一幅显示横向电磁（TEM）模式强度分布的图像。我使用了曲面图的4x4多点矩阵。结果令我满意。为了完整起见：

如何添加轴，而不是为每个绘图单独设置标题

有没有一种方法可以像原始图像那样只在一个方向上显示曲面上的等值线

原作者省略了多点图的下半部分，以强调对称性。我不确定这是否真的说明了这一点。我应该展示完整的矩阵还是你能想出更好的方法

解决方案 谢谢大家。根据您的建议，我现在有以下图片：

从Qt端子输出以下代码：

m=n=3           # max. 3
THETA=2.5

set hidden3d trianglepattern 2 
set isosamples 50
set xrange [-THETA:THETA]
set yrange [-THETA:THETA]
set view 70,55,,.5
unset border
unset key
unset tics

H0(x)=1
H1(x)=2*x
H2(x)=4*x**2-2
H3(x)=8*x**3-12*x

set multiplot layout n+1,m+1 upwards margins .14,.9,.14,.9 spacing .05 \ 
        title 'Intensitätsverteilungen der Laguerre-Gauß-Moden' font ",16"
do for [i=0:n] for [j=0:m] { 
        eval sprintf("splot (H%d(sqrt(2)*y)*exp(-y**2))**2\
                          * (H%d(sqrt(2)*x)*exp(-x**2))**2\
                                with lines lc %d", i, j, abs(i-j)+1)
}
set origin 0,0
set size 1,1
unset margins
set title ' '
set arrow from 0,-.5 to graph 1,0
set arrow from -.5,0 to graph 0,1
set label at .5, .5 "dreh-\nsymmetrisch" center rotate by -37
set arrow from .7,0 to .1,.6
set tics out nomirror
set xtics 0, 1, n
set ytics 0, 1, m
set xrange [-.5:n+.5]
set yrange [-.5:m+.5]
set xlabel offset graph .5,0 "n"
set ylabel offset graph 0,.5 "m" norotate
plot NaN
unset multiplot

我没有手动添加轴，而是在顶部绘制了一个适当缩放的二维绘图。因此，参数m和n的轴比例不是3。为了支持更高阶，必须添加相应的Hermite多项式Hn（x）；n=1，2，3。。。并且可能需要调整multiplot的边距

提供

set hidden3d trianglepattern 2

被证明是仅在一个方向上显示等值线的最简单方法

颜色应该有助于形成成对的旋转对称图形。有人可能会争论美学，但信息有望得到传达

---

尝试以下方法并根据您的需要进行调整。当然还有改进的余地

对1。为多点打印使用一些边距，并通过需要调整的箭头和标签绘制线条

到2。将数据放入数据块中，并使用zerrorfill绘制它（请参阅帮助zerrorfill）

到3。我想说这是品味的问题。为什么作者只显示TEM01，只有一个例子？为什么不全部展示

代码：

### isolines only in one direction
reset session
# set term wxt size 900,950   # or some other terminal and sizes

unset key
unset tics
set border 0
set view 55,55,1.0,0.5

set style fill solid 0.0
do for [i=1:99] {
    set linetype i lw 0.5 lc rgb "black"
}

THETA=2.5
set xrange [-THETA:THETA]
set yrange [-THETA:THETA]

H0(x)=1
H1(x)=2*x
H2(x)=4*x**2-2
H3(x)=8*x**3-12*x

m=n=3
set multiplot layout n+1,m+1 upwards \
    title 'Intensitätsverteilungen der Laguerre-Gauß-Moden' \
    margins screen 0.1, screen 0.95, screen 0.15, screen 0.9

    do for [i=0:n] for [j=0:m] {
    #    if (i >= j || i == 0 && j == 1) {   # uncommenting this line skips TEM02,03,12,13,23 
            # eval sprintf("set title 'TEM_{%d%d}'", i, j)    # uncomment to show title
             eval sprintf("f(x,y) = (H%d(sqrt(2)*y)*exp(-y**2))**2 \
                              * (H%d(sqrt(2)*x)*exp(-x**2))**2", i, j)
            # data to datablock
            set print $Data
                c=20.0
                do for [iii=-c:c] {
                    do for [jjj=-c:c] {
                        x=iii/c*THETA
                        y=jjj/c*THETA
                        print sprintf("%g %g %g",x,y,f(x,y))
                    }
                print ""  # add empty line
                print ""  # add empty line
                }
            set print
            splot $Data using 1:2:3:(0):3 with zerrorfill 

    #    } else { set multiplot next }      # uncommenting this line skips TEM02,03,12,13,23 

    }
    unset title

    # arrows and labels 
    A1x0=0.16; A1x1=0.95; A1y=0.05;  A1grid=0.225
    A2x=0.05;  A2y0=0.20; A2y1=0.95; A2grid=0.20
    TicL=0.01
    set arrow 1 from screen A1x0,A1y to screen A1x1,A1y lw 3
    set label 1 "n" at screen A1x1,A1y offset 0,-1 font ",14"
    set arrow 2 from screen A2x,A2y0 to screen A2x,A2y1 lw 3
    set label 2 "m" at screen A2x,A2y1 offset -4,0 font ",14"
    do for [i=0:3] {
        set label i+3 sprintf("%d",i) at screen A1x0+i*A1grid,A1y offset -0.7,-1.5 font ",14"
        set arrow i+3 from screen A1x0+i*A1grid,A1y to screen A1x0+i*A1grid,A1y-TicL lw 2 nohead
        set label i+7 sprintf("%d",i) at screen A2x,A2y0+i*A2grid offset -4,0 font ",14"
        set arrow i+7 from screen A2x,A2y0+i*A2grid to screen A2x-TicL,A2y0+i*A2grid lw 2nohead
    }
    plot NaN   # plot nothing but to add the arrows and labels
unset multiplot
### end of code

结果：

### isolines only in one direction
reset session
# set term wxt size 900,950   # or some other terminal and sizes

unset key
unset tics
set border 0
set view 55,55,1.0,0.5

set style fill solid 0.0
do for [i=1:99] {
    set linetype i lw 0.5 lc rgb "black"
}

THETA=2.5
set xrange [-THETA:THETA]
set yrange [-THETA:THETA]

H0(x)=1
H1(x)=2*x
H2(x)=4*x**2-2
H3(x)=8*x**3-12*x

m=n=3
set multiplot layout n+1,m+1 upwards \
    title 'Intensitätsverteilungen der Laguerre-Gauß-Moden' \
    margins screen 0.1, screen 0.95, screen 0.15, screen 0.9

    do for [i=0:n] for [j=0:m] {
    #    if (i >= j || i == 0 && j == 1) {   # uncommenting this line skips TEM02,03,12,13,23 
            # eval sprintf("set title 'TEM_{%d%d}'", i, j)    # uncomment to show title
             eval sprintf("f(x,y) = (H%d(sqrt(2)*y)*exp(-y**2))**2 \
                              * (H%d(sqrt(2)*x)*exp(-x**2))**2", i, j)
            # data to datablock
            set print $Data
                c=20.0
                do for [iii=-c:c] {
                    do for [jjj=-c:c] {
                        x=iii/c*THETA
                        y=jjj/c*THETA
                        print sprintf("%g %g %g",x,y,f(x,y))
                    }
                print ""  # add empty line
                print ""  # add empty line
                }
            set print
            splot $Data using 1:2:3:(0):3 with zerrorfill 

    #    } else { set multiplot next }      # uncommenting this line skips TEM02,03,12,13,23 

    }
    unset title

    # arrows and labels 
    A1x0=0.16; A1x1=0.95; A1y=0.05;  A1grid=0.225
    A2x=0.05;  A2y0=0.20; A2y1=0.95; A2grid=0.20
    TicL=0.01
    set arrow 1 from screen A1x0,A1y to screen A1x1,A1y lw 3
    set label 1 "n" at screen A1x1,A1y offset 0,-1 font ",14"
    set arrow 2 from screen A2x,A2y0 to screen A2x,A2y1 lw 3
    set label 2 "m" at screen A2x,A2y1 offset -4,0 font ",14"
    do for [i=0:3] {
        set label i+3 sprintf("%d",i) at screen A1x0+i*A1grid,A1y offset -0.7,-1.5 font ",14"
        set arrow i+3 from screen A1x0+i*A1grid,A1y to screen A1x0+i*A1grid,A1y-TicL lw 2 nohead
        set label i+7 sprintf("%d",i) at screen A2x,A2y0+i*A2grid offset -4,0 font ",14"
        set arrow i+7 from screen A2x,A2y0+i*A2grid to screen A2x-TicL,A2y0+i*A2grid lw 2nohead
    }
    plot NaN   # plot nothing but to add the arrows and labels
unset multiplot
### end of code

关于点2（一个方向的等值线），我发现使用

zerrorfill

可以做到：

w = 2.5
set xrange [-w:w]
set yrange [-w:w]
set view 55,55,1.
set ticslevel 0

H1(x) = 2*x
H2(x) = 4*x**2-2
f(x,y) = (H2(sqrt(2)*y)*exp(-y**2))**2\
                          * (H1(sqrt(2)*x)*exp(-x**2))**2

splot for [i=-25:25] '+' us (y=i/10.):1:(z=f(x,y)):(0):(z) w zerrorfill  fc "white" lc "black" t ""

不太好，这是我第一次尝试：

set hidden3d
w = 2.5
set xrange [-w:w]
set yrange [-w:w]
set view 55,55,1.
set ticslevel 0

set iso 100,200
set palette defined (0 "white", 1 "black")
set cbrange[0:1]

H1(x) = 2*x
H2(x) = 4*x**2-2
f(x,y) = (H2(sqrt(2)*y)*exp(-y**2))**2\
                          * (H1(sqrt(2)*x)*exp(-x**2))**2

splot '++' us 1:2:(f(x,y)-0.05):(0) w l palette, i=0,\
      "++" us 1:2:(i=i+1, f(x,y)/(i%2==0)):(1) w l palette

---

第一个plot对象负责隐藏的部分，它是白色的。第二个绘图对象具有黑线；使用

（i%2==0）的除法

为每第二行创建

nan

s，产生一个方向上的抑制线。

要仅在一个方向上显示曲面上的等值线，请使用

设置hidden3d三角形模式2

和

设置isosamples 50

。