问如何将非矩形和非网格的数据显示为具有gnuplot的地图？

EN

### Delaunay triangulation (gnuplot implementation attempt, requires gnuplot 5.4)
reset session

# get some test data
Random=0        # set to 0 to read data from existing FILE
if (Random) {
    FILE = "tbTriangulationRandom.dat"
    set print FILE
    do for [i=0:99] {
        print sprintf("%g %g %g",x=invnorm(rand(0))*10,y=invnorm(rand(0))*10,x*y)
    }
    set print
}
else {
    FILE = "tbTriangulationTest.dat"
}

# sort data by x increasing values and if x is identical by increasing y values
set table $Data
    plot '<sort -n -k 1 -k 2 '.FILE u 1:2:3 w table
unset table

# definition of quite a few variables and functions
colX       = 1         # x column
colY       = 2         # y column
colZ       = 3         # z column
N          = |$Data|   # number of points
EDGES      = ''        # list of (inner) edges 
HULL       = ''        # list of hull segments
TRIANGLES  = ''        # list of triangles
HULLPOINTS = ''        # list of hullpoints
array Px[N]            # set point array size
array Py[N]            # set point array size
array Pz[N]            # set point array size

newEdge(p1,p2)      = sprintf(" %d %d ",p1,p2)
Edge(n)             = sprintf(" %s %s ",word(EDGES,2*n-1),word(EDGES,2*n))
EdgeP(n,p)          = int(word(EDGES,2*n-2+p))
changeEdge(n,p1,p2) = (_edge=Edge(n), _pos = strstrt(EDGES,_edge), _pos ? \
                       EDGES[1:_pos-1].newEdge(p1,p2). \
                       EDGES[_pos+strlen(_edge):strlen(EDGES)] : EDGES)

TriangleCount(n)      = words(TRIANGLES)/3
TriangleN(n)          = sprintf(" %s %s %s ", \
                        word(TRIANGLES,3*n-2),word(TRIANGLES,3*n-1),word(TRIANGLES,3*n))
newTriangle(p1,p2,p3) = p1<p2 && p2<p3 ? sprintf(" %d %d %d ",p1,p2,p3) : \
                        p1<p3 && p3<p2 ? sprintf(" %d %d %d ",p1,p3,p2) : \
                        p2<p1 && p1<p3 ? sprintf(" %d %d %d ",p2,p1,p3) : \
                        p2<p3 && p3<p1 ? sprintf(" %d %d %d ",p2,p3,p1) : \
                        p3<p1 && p1<p2 ? sprintf(" %d %d %d ",p3,p1,p2) : \
                                         sprintf(" %d %d %d ",p3,p2,p1)
changeTA(n,p1,p2,p3)  = (TA=TriangleN(n), _pos = strstrt(TRIANGLES,TA), _pos ? \
                         TRIANGLES[1:_pos-1].newTriangle(p1,p2,p3). \
                         TRIANGLES[_pos+strlen(TA):strlen(TRIANGLES)] : TRIANGLES)

TAp(n,p)              = int(word(TRIANGLES,3*n-3+p))
TAx(n,p)              = Px[TAp(n,p)]                  # x-coordinate of point p of triangle n
TAy(n,p)              = Py[TAp(n,p)]                  # y-coordinate of point p of triangle n

HullP(n,p)            = int(word(HULL,2*n-2+p))   # hull segment point number
HScount(n)            = int(words(HULL))/2        # number of hull segments
getHullPoints(n)      = (_tmp = '', sum [_i=1:words(HULL)] ((_s=' '.word(HULL,_i).' ', _tmp = \
                         strstrt(_tmp,_s) ? _tmp : _tmp._s ), 0), _tmp)
removeFromHull(seg)   = (seg, _pos = strstrt(HULL,seg), _pos ? \
                         HULL[1:_pos-1].HULL[_pos+strlen(seg):strlen(HULL)] : HULL)

# orientation of 3 points, either -1=clockwise, 0=collinear, 1=counterclockwise
Orientation(p1,p2,p3) = sgn((Px[p2]-Px[p1])*(Py[p3]-Py[p1]) - (Px[p3]-Px[p1])*(Py[p2]-Py[p1]))

# check for intersection of segment p1-p2 with segment p3-p4, 0=no intersection, 1=intersection
IntersectCheck(p1,p2,p3,p4) = (Orientation(p1,p3,p2)==Orientation(p1,p4,p2)) || \
                                 (Orientation(p3,p1,p4)==Orientation(p3,p2,p4)) ? 0 : 1

Sinus(p1,p2)          = (_dx=Px[p2]-Px[p1], _dy=Py[p2]-Py[p1], _dy/sqrt(_dx**2 + _dy**2))

### Macros for later use
# Creating inner edges datablock macro
CreateEdgeDatablock = '\
set print $EDGES; \
do for [i=1:words(EDGES)/2] { \
    p1 = int(word(EDGES,2*i-1)); \
    p2 = int(word(EDGES,2*i)); \
    print sprintf("%g %g %g %g %d %d",Px[p1],Py[p1],Px[p2]-Px[p1],Py[p2]-Py[p1],p1,p2) \
}; \
set print '

# Creating hull datablock macro
CreateHullDatablock = '\
set print $HULL; \
do for [i=1:words(HULL)/2] { \
    p1 = int(word(HULL,2*i-1)); \
    p2 = int(word(HULL,2*i));   \
    print sprintf("%g %g %g %g %d %d",Px[p1],Py[p1],Px[p2]-Px[p1],Py[p2]-Py[p1],p1,p2) \
}; \
set print '

# plotting everything
PlotEverything = '\
plot $EDGES u 1:2:3:4 w vec lw 1.0 lc "red" nohead, \
      $HULL u 1:2:3:4 w vec lw 1.5 lc "blue" nohead, \
      $Data u 1:2 w p pt 7 ps 0.5 lc "black", \
      $Data u 1:2:($0+1) w labels offset 0.5,0.5 '

# put datpoints into arrays
set table $Dummy
    plot $Data u (Px[int($0)+1]=column(colX),Py[int($0)+1]=column(colY),Pz[int($0)+1]=column(colZ),'') w table
unset table

# get first m>=3 points which are not all collinear
HULL = HULL.newEdge(1,2)                # add first 2 points to hull in any case
do for [p=3:N] {
    if (Orientation(p-2,p-1,p)==0) {    # orientation==0 if collinear
        HULL = HULL.newEdge(p-1,p)
    }    
    else { break }                      # stop if first >=3 non-collinear points found
}
HPcountInit = words(getHullPoints(0))   # get initial number of hull points

# actual plotting starts from here

set offset 1,1,1,1
set key noautotitle
set palette rgb 33,13,10
set rmargin screen 0.8

plot $Data u 1:2 w p pt 7 ps 0.5 lc "black", \
        '' u 1:2:($0+1) w labels offset 0.5,0.5

set label 1 at graph 0.02,0.97 "Adding points... "

# loop all data points
do for [p=HPcountInit+1:N] {
    print sprintf("### Adding P%d",p)
    HPlist = getHullPoints(0)
    HPcount = words(HPlist)
    set print $NewConnections   # initalize/empty datablock for new connections
        print ""
    set print
    do for [hpt in HPlist] {          # loop and check all hull points
        hp = int(hpt)
        # print sprintf("Check hull point P%d", hp)
        c = 0
        do for [hs=1:HScount(0)] {               # loop all hull segments
            hp1 = HullP(hs,1)
            hp2 = HullP(hs,2)
            # print sprintf("Check %d-%d with %d-%d", hp1, hp2, hp, p)
            if (p!=hp1 && p!=hp2 && hp!=hp1 && hp!=hp2) {
                c = c || IntersectCheck(hp1,hp2,hp,p)
                if (c) { break }
            }
        }
        if (c==0) {                 # if no intersections with hull
            set print $NewConnections append            # add new connections to datablock
                print sprintf("%g %g", hp, Sinus(p,hp))
            set print
        }
    }
  
    # sort datablock clockwise (a bit cumbersome in gnuplot)
    set table $ConnectSorted
        plot $NewConnections u 1:2:2 smooth zsort    # requires gnuplot 5.4.0
    set table $Dummy
        plot Connect='' $ConnectSorted u (Connect=Connect.sprintf(" %d",$1),'') w table
    unset table
    
    # add new edges
    Ccount = int(words(Connect))
    do for [i=1:Ccount-1] {
        p1 = int(word(Connect,i))
        p2 = int(word(Connect,i+1))
        TRIANGLES = TRIANGLES.sprintf(" %d %d %d ", p1<p2?p1:p2, p2<p1?p1:p2, p)  # numbers in ascending order
        if (i==1) { HULL=HULL.newEdge(p1,p) }
        if (i>1 && i<Ccount) { EDGES = EDGES.newEdge(p1,p) }
        if (i==Ccount-1) { 
            HULL  = HULL.newEdge(p2,p)
        }
        if (p!=HPcountInit+1) {          # remove hull segments, except initial ones
            NewEdge = p1<p2 ? sprintf(" %d %d ",p1,p2) : sprintf(" %d %d ",p2,p1)
            # print sprintf("Remove %s",NewEdge)
            HULL = removeFromHull(NewEdge)
            EDGES = EDGES.NewEdge
            @CreateEdgeDatablock
            @CreateHullDatablock
            @PlotEverything
        }
    }
}


# flip diagonal of a quadrangle if Det(p1,p2,p3,p4) and Orientation(p1,p2,p3) have the same sign
#
m11(p1,p4) = Px[p1]-Px[p4]
m21(p2,p4) = Px[p2]-Px[p4]
m31(p3,p4) = Px[p3]-Px[p4]

m12(p1,p4) = Py[p1]-Py[p4]
m22(p2,p4) = Py[p2]-Py[p4]
m32(p3,p4) = Py[p3]-Py[p4]

m13(p1,p4) = (Px[p1]-Px[p4])**2 + (Py[p1]-Py[p4])**2
m23(p2,p4) = (Px[p2]-Px[p4])**2 + (Py[p2]-Py[p4])**2
m33(p3,p4) = (Px[p3]-Px[p4])**2 + (Py[p3]-Py[p4])**2

Det(p1,p2,p3,p4) = m11(p1,p4)*(m22(p2,p4)*m33(p3,p4) - m32(p3,p4)*m23(p2,p4)) + \
                   m12(p1,p4)*(m23(p2,p4)*m31(p3,p4) - m33(p3,p4)*m21(p2,p4)) + \
                   m13(p1,p4)*(m21(p2,p4)*m32(p3,p4) - m31(p3,p4)*m22(p2,p4))

# create triangle data
set print $Triangles
    do for [i=1:TriangleCount(0)] {
        print sprintf("%g %g",TAx(i,1),TAy(i,1))
        print sprintf("%g %g",TAx(i,2),TAy(i,2))
        print sprintf("%g %g",TAx(i,3),TAy(i,3))
        print sprintf("%g %g",TAx(i,1),TAy(i,1))
        print ""
    }
unset print

@CreateEdgeDatablock
@CreateHullDatablock
@PlotEverything

set label 1 "Flipping diagonals... "

###
# loop edges and check if need to flip. If on edge was flipped, start over again.
flip = 0
flipCount = 0
flippedAtLeastOnce = 1
while (flippedAtLeastOnce) {
    flippedAtLeastOnce=0
    do for [e=1:words(EDGES)/2] {               # loop all inner edges
        # find the 2 triangles with this edge
        p1 = EdgeP(e,1)
        p2 = EdgeP(e,2)
        found = 0
        do for [t=1:TriangleCount(0)] {         # loop all triangles
            tap1 = TAp(t,1)
            tap2 = TAp(t,2)
            tap3 = TAp(t,3)
            p = p1==tap1 ? p2==tap2 ? tap3 : p2==tap3 ? tap2 : 0 : p1==tap2 ? p2==tap3 ? tap1 : 0 : 0
            # print sprintf("%d %d %d: %d",tap1,tap2,tap3,p)
            if (p!=0) {
                if (found==1) { 
                    ta2=t; p4=p; 
                    flip  = sgn(Det(p1,p2,p3,p4))==Orientation(p1,p2,p3)
                    flippedAtLeastOnce = flippedAtLeastOnce || flip
                    if (flip) {
                        flipCount = flipCount+1
                        print sprintf("Flip % 3d: %d-%d with %d-%d",flipCount,p1,p2,p3,p4)
                        EDGES     = changeEdge(e,p3,p4)
                        TRIANGLES = changeTA(ta1,p1,p3,p4)
                        TRIANGLES = changeTA(ta2,p2,p3,p4)
                        @CreateEdgeDatablock
                        @CreateHullDatablock
                        @PlotEverything
                        break           # start over again
                    }
                }
                if (found==0) { ta1=t; p3=p; found=1}
            }
        }
    }
}
###

# create quadrangles datablock
Center2x(p1,p2)    = (Px[p1]+Px[p2])/2.          # x-center of 2 points
Center2y(p1,p2)    = (Py[p1]+Py[p2])/2.          # y-center of 2 points
Center3x(p1,p2,p3) = (Px[p1]+Px[p2]+Px[p3])/3.   # x-center between 3 points
Center3y(p1,p2,p3) = (Py[p1]+Py[p2]+Py[p3])/3.   # x-center between 3 points

set print $QUADRANGLES
    do for [i=1:TriangleCount(0)] {
        do for [p=0:2] {
            z = Pz[TAp(i,p+1)]
            tap1 = TAp(i,p+1)
            tap2 = TAp(i,(p+1)%3+1)
            tap3 = TAp(i,(p+2)%3+1)
            print sprintf("%g %g %g", Px[tap1], Py[tap1], z)
            print sprintf("%g %g %g", Center2x(tap1,tap2), Center2y(tap1,tap2), z)
            print sprintf("%g %g %g", Center3x(tap1,tap2,tap3), Center3y(tap1,tap2,tap3), z)
            print sprintf("%g %g %g", Center2x(tap1,tap3), Center2y(tap1,tap3), z)
            print sprintf("%g %g %g", Px[tap1], Py[tap1], z)
            print ''
        }

    }
set print

set label 1 "Coloring areas."

plot $QUADRANGLES u 1:2:3 w filledcurves closed lc palette, \
     $EDGES u 1:2:3:4 w vec lw 1.0 lc "grey" nohead, \
     $HULL u 1:2:3:4 w vec lw 1.5 lc "blue" nohead, \
     $Data u 1:2:3 w p pt 7 ps 0.5 lc palette
### end of code