gnuplot 等高线图阴影线

Question

我正在使用 gnuplot 绘制多个函数的等高线图。这是针对优化问题。
我有3个功能:

f(x,y)

g1(x,y)

g2(x,y)

两者 g1(x,y)和 g2(x,y)是约束条件，想在 f(x,y) 的等高线图上绘制.

这是教科书的例子:



感谢@theozh，这是我在 gnuplot 中复制它的尝试。

### contour lines with labels
reset session

f(x,y)=(x**2+y-11)**2+(x+y**2-7)**2
g1(x,y)=(x-5)**2+y**2
g2(x,y) = 4*x+y

set xrange [0:6]
set yrange [0:6]
set isosample 250, 250
set key outside

set contour base
set cntrparam levels disc 10,30,75,150,300,500,850,1500 
unset surface
set table $Contourf
    splot f(x,y)
unset table

set contour base
set cntrparam levels disc 26
unset surface
set table $Contourg1
    splot g1(x,y)
unset table

set contour base
set cntrparam levels disc 20
unset surface
set table $Contourg2
    splot g2(x,y)
unset table

set style textbox opaque noborder

set datafile commentschar " "
plot for [i=1:8] $Contourf u 1:2:(i) skip 5 index i-1 w l lw 1.5 lc var title columnheader(5)
replot $Contourg1 u 1:2:(1) skip 5 index 0 w l lw 4 lc 0 title columnheader(5)
replot $Contourg2 u 1:2:(1) skip 5 index 0 w l lw 4 lc 0 title columnheader(5)

我想复制 gnuplot 示例中的教科书图片。如何在函数上做阴影标记 g1和 g2 ，上图中的粗黑线。

@theozh 在下面提供了一个很好的解决方案。但是，该方法不适用于陡峭的曲线。举个例子

reset session
unset key

set size square

g(x,y) = -0.8-1/x**3+y

set xrange [0:4]
set yrange [0:4]
set isosample 250, 250
set key off

set contour base
unset surface

set cntrparam levels disc 0
set table $Contourg
    splot g(x,y)
unset table

set angle degree
set datafile commentschar " "

plot $Contourg u 1:2 skip 5 index 0 w l lw 2 lc 0 title columnheader(5)

set style fill transparent pattern 4
replot $Contourg u 1:2:($2+0.2) skip 5 index 0 w filledcurves lc 0 notitle 

产生下图。有没有办法使用不同的偏移量，例如 x < 1.3 的偏移 x 值和 x > 1.3 的偏移 y 值。这将产生更好的填充曲线。我正在寻找的 matlab 实现可以在这里找到: https://www.mathworks.com/matlabcentral/fileexchange/29121-hatched-lines-and-contours .



在复制@Ethans 程序时，我得到以下信息，与@Ethan 相比，dashtype 相对较粗，不知道为什么，我使用的是 gnuplot v5.2 和 wxt 终端。



当我复制@theozh 代码时，除了闭合轮廓外，它工作得很好，不知道为什么？见下面的例子:

f(x,y)=x*exp(-x**2-y**2)+(x**2+y**2)/20
g1(x,y)= x*y/2+(x+2)**2+(y-2)**2/2-2

set xrange [-7:7]
set yrange [-7:7]
set isosample 250, 250
set key outside

set contour base
unset surface

set cntrparam levels disc 4,3.5,3,2.5,2,1.5,1,0.5,0 
set table $Contourf
    splot f(x,y)
unset table

set cntrparam levels disc 0
set table $Contourg1
    splot g1(x,y)
unset table

# create some extra offset contour lines
# macro for setting contour lines
ContourCreate = '\
    set cntrparam levels disc Level; \
    set table @Output; \
        splot @Input; \
    unset table'

Level = 0.45
Input = 'g1(x,y)'
Output = '$Contourg1_ext'
@ContourCreate


# Macro for ordering the datapoints of the contour lines which might be split
ContourOrder = '\
stats @DataIn skip 6 nooutput; \
N = STATS_blank-1; \
set table @DataOut; \
    do for [i=N:0:-1] { plot @DataIn u 1:2 skip 5 index 0 every :::i::i with table }; \
unset table'

DataIn = '$Contourg1'
DataOut = '$Contourg1_ord'
@ContourOrder

DataIn = '$Contourg1_ext'
DataOut = '$Contourg1_extord'
@ContourOrder


# Macro for reversing a datablock
ContourReverse = '\
set print @DataOut; \
    do for [i=|@DataIn|:1:-1] { print @DataIn[i]}; \
set print'

DataIn = '$Contourg1_extord'
DataOut = '$Contourg1_extordrev'
@ContourReverse

# Macro for adding datablocks
ContourAdd = '\
set print @DataOut; \
    do for [i=|@DataIn1|:1:-1] { print @DataIn1[i]}; \
    do for [i=|@DataIn2|:1:-1] { print @DataIn2[i]}; \
set print'

DataIn1 = '$Contourg1_ord'
DataIn2 = '$Contourg1_extordrev'
DataOut = '$Contourg1_add'
@ContourAdd


set style fill noborder 
set datafile commentschar " "
plot \
    for [i=1:8] $Contourf u 1:2:(i) skip 5 index i-1 w l lw 1.5 lc var title columnheader(5), \
    $Contourg1 u 1:2 skip 5 index 0 w l lw 2 lc 0 title columnheader(5), \
    $Contourg1_add u 1:2 w filledcurves fs transparent pattern 5 lc rgb "black" notitle

Answer 1

另一种可能性是使用自定义破折号模式，如下所示:
顺便说一句，使用“重新绘图”来组成单个图形几乎永远不会正确。

# Additional contour levels displaced by 0.2 from the original
set contour base
set cntrparam levels disc 20.2
unset surface
set table $Contourg2d
    splot g2(x,y)
unset table

set contour base
set contour base
set cntrparam levels disc 26.2
unset surface
set table $Contourg1d
    splot g1(x,y)
unset table

set linetype 101 lc "black" linewidth 5 dashtype (0.5,5)

plot for [i=1:8] $Contourf u 1:2:(i) skip 5 index i-1 w l lw 1.5 lc var title columnheader(5), \
        $Contourg1 u 1:2:(1) skip 5 index 0 w l lw 1 lc "black" title columnheader(5), \
        $Contourg2 u 1:2:(1) skip 5 index 0 w l lw 1 lc "black" title columnheader(5), \
        $Contourg1d u 1:2:(1) skip 5 index 0 w l linetype 101 notitle, \
        $Contourg2d u 1:2:(1) skip 5 index 0 w l linetype 101 notitle

修改以显示轮廓偏移的使用，以便虚线仅位于线的一侧。