从边界点创建闭合多边形

Question

我有一系列经度 - 纬度点，用于定义区域的边界。我想基于这些点创建一个多边形，并在地图上绘制多边形并填充它。目前，我的多边形似乎由连接所有点的许多补丁组成，但是点的顺序不正确，当我尝试填充多边形时，我得到一个奇怪的外观区域（参见附件）。

我根据多边形的中心对经度 - 纬度点（mypolyXY数组）进行排序，但我的猜测是这不正确：

cent=(np.sum([p[0] for p in mypolyXY])/len(mypolyXY),np.sum([p[1] for p in mypolyXY])/len(mypolyXY))
# sort by polar angle
mypolyXY.sort(key=lambda p: math.atan2(p[1]-cent[1],p[0]-cent[0]))

我使用

绘制点位置（黑色圆圈）和我的多边形（彩色色块）

scatter([p[0] for p in mypolyXY],[p[1] for p in mypolyXY],2)
p = Polygon(mypolyXY,facecolor=colors,edgecolor='none')
ax.add_artist(p)

我的问题是：如何根据经度 - 纬度点数组关闭多边形？

更新 我测试了一些关于如何绘制多边形的更多信息。我删除了排序例程，只是按照它们在文件中出现的顺序使用了数据。这似乎改善了结果，但正如@tcaswell所提到的，多边形形状仍然在削弱自己（见新图）。我希望可能有一个路径/多边形例程可以解决我的问题，并在多边形的边界内合并所有形状或路径。建议非常欢迎。

更新2：

我现在有一个基于@Rutger Kassies和Roland Smith建议的脚本的工作版本。我最后使用org阅读了Shapefile，它工作得相当好。它适用于标准的lmes_64.shp文件但是当我使用更详细的LME文件时，每个LME可能包含多个多边形，这个脚本崩溃了。我必须找到一种方法来合并相同的LME名称的各种多边形，以使其工作。我附上了我的剧本，以防万一有人会看一下。我非常感谢有关如何改进此脚本或使其更通用的评论。此脚本创建多边形并提取我从netcdf文件中读取的多边形区域内的数据。输入文件的网格为-180到180和-90到90。

import numpy as np
import math
from pylab import *
import matplotlib.patches as patches
import string, os, sys
import datetime, types
from netCDF4 import Dataset
import matplotlib.nxutils as nx
from mpl_toolkits.basemap import Basemap
import ogr
import matplotlib.path as mpath
import matplotlib.patches as patches


def getLMEpolygon(coordinatefile,mymap,index,first):

    ds = ogr.Open(coordinatefile)
    lyr = ds.GetLayer(0)
    numberOfPolygons=lyr.GetFeatureCount()

    if first is False:
        ft = lyr.GetFeature(index)
        print "Found polygon:",  ft.items()['LME_NAME']
        geom = ft.GetGeometryRef()

        codes = []
        all_x = []
        all_y = []
        all_XY= []

        if (geom.GetGeometryType() == ogr.wkbPolygon):
          for i in range(geom.GetGeometryCount()):

            r = geom.GetGeometryRef(i)
            x = [r.GetX(j) for j in range(r.GetPointCount())]
            y = [r.GetY(j) for j in range(r.GetPointCount())]

            codes += [mpath.Path.MOVETO] + (len(x)-1)*[mpath.Path.LINETO]
            all_x += x
            all_y += y
            all_XY +=mymap(x,y)


        if len(all_XY)==0:
            all_XY=None
            mypoly=None
        else:
            mypoly=np.empty((len(all_XY[:][0]),2))
            mypoly[:,0]=all_XY[:][0]
            mypoly[:,1]=all_XY[:][3]
    else:
        print "Will extract data for %s polygons"%(numberOfPolygons)
        mypoly=None
    first=False
    return mypoly, first, numberOfPolygons


def openCMIP5file(CMIP5name,myvar,mymap):
    if os.path.exists(CMIP5name):
        myfile=Dataset(CMIP5name)
        print "Opened CMIP5 file: %s"%(CMIP5name)
    else:
        print "Could not find CMIP5 input file %s : abort"%(CMIP5name)
        sys.exit()
    mydata=np.squeeze(myfile.variables[myvar][-1,:,:]) - 273.15
    lonCMIP5=np.squeeze(myfile.variables["lon"][:])
    latCMIP5=np.squeeze(myfile.variables["lat"][:])

    lons,lats=np.meshgrid(lonCMIP5,latCMIP5)

    lons=lons.flatten()
    lats=lats.flatten()
    mygrid=np.empty((len(lats),2))
    mymapgrid=np.empty((len(lats),2))

    for i in xrange(len(lats)):
        mygrid[i,0]=lons[i]
        mygrid[i,1]=lats[i]
        X,Y=mymap(lons[i],lats[i])
        mymapgrid[i,0]=X
        mymapgrid[i,1]=Y

    return mydata, mygrid, mymapgrid

def drawMap(NUM_COLORS):

    ax = plt.subplot(111)
    cm = plt.get_cmap('RdBu')
    ax.set_color_cycle([cm(1.*j/NUM_COLORS) for j in range(NUM_COLORS)])
    mymap = Basemap(resolution='l',projection='robin',lon_0=0)

    mymap.drawcountries()

    mymap.drawcoastlines()
    mymap.fillcontinents(color='grey',lake_color='white')
    mymap.drawparallels(np.arange(-90.,120.,30.))
    mymap.drawmeridians(np.arange(0.,360.,60.))
    mymap.drawmapboundary(fill_color='white')

    return ax, mymap, cm

"""Edit the correct names below:"""

LMEcoordinatefile='ShapefileBoundaries/lmes_64.shp'
CMIP5file='tos_Omon_CCSM4_rcp85_r1i1p1_200601-210012_regrid.nc'

mydebug=False
doPoints=False
first=True


"""initialize the map:"""
mymap=None
mypolyXY, first, numberOfPolygons = getLMEpolygon(LMEcoordinatefile, mymap, 0,first)
NUM_COLORS=numberOfPolygons
ax, mymap, cm = drawMap(NUM_COLORS)


"""Get the CMIP5 data together with the grid"""
SST,mygrid, mymapgrid = openCMIP5file(CMIP5file,"tos",mymap)

"""For each LME of interest create a polygon of coordinates defining the boundaries"""
for counter in xrange(numberOfPolygons-1):

    mypolyXY,first,numberOfPolygons = getLMEpolygon(LMEcoordinatefile, mymap,counter,first)

    if mypolyXY != None:
        """Find the indices inside the grid that are within the polygon"""
        insideBoolean = plt.mlab.inside_poly(np.c_[mymapgrid[:,0],mymapgrid[:,1]],np.c_[mypolyXY[:,0],mypolyXY[:,1]])
        SST=SST.flatten()
        SST=np.ma.masked_where(SST>50,SST)

        mymapgrid=np.c_[mymapgrid[:,0],mymapgrid[:,1]]
        myaverageSST=np.mean(SST[insideBoolean])

        mycolor=cm(myaverageSST/SST.max())
        scaled_z = (myaverageSST - SST.min()) / SST.ptp()
        colors = plt.cm.coolwarm(scaled_z)

        scatter([p[0] for p in mypolyXY],[p[1] for p in mypolyXY],2)

        p = Polygon(mypolyXY,facecolor=colors,edgecolor='none')
        ax.add_artist(p)

        if doPoints is True:

            for point in xrange(len(insideBoolean)):
                pointX=mymapgrid[insideBoolean[point],0]
                pointY=mymapgrid[insideBoolean[point],1]
                ax.scatter(pointX,pointY,8,color=colors)
                ax.hold(True)


if doPoints is True:
    colorbar()
print "Extracted average values for %s LMEs"%(numberOfPolygons)
plt.savefig('LMEs.png',dpi=300)
plt.show()

附上最终图片。感谢您的帮助。

干杯，特隆德

Answer 1

拥有一系列积分是不够的。您需要知道点的顺序。通常，多边形的点按顺序给出。所以你从第一点到第二点绘制一条线，然后从第二点到第三点画一条线。

如果您的列表不按顺序排列，则需要额外的信息才能生成顺序列表。

shapefile（参见documentation）包含一个形状列表，如Null形状，Point，PolyLine，Polygon，其变体还包含Z和M（度量）坐标。所以只是倾销积分是不行的。你必须将它们分成不同的形状并渲染你感兴趣的形状。在这种情况下，可能是PolyLine或Polygon。有关这些形状的数据格式，请参阅上面的链接。请记住，文件的某些部分是big-endian，而其他部分是little-endian。真是一团糟。

我建议使用struct模块来解析二进制.shp文件，因为根据文档，单个Polygon 的点按顺序，并且它们形成一个封闭的链（最后一点与第一个点相同）。

您可以尝试使用当前坐标列表的另一件事是从一个点开始，然后在列表中查找相同的点。这些相同点之间的所有内容都应该是一个多边形。这可能不是万无一失的，但看看它能给你带来多大的帮助。

Answer 2

我建议使用原始的Shapefile，它采用适合存储多边形的格式。作为OGR的替代方法，您可以使用Shapely，或将多边形导出为Wkt等。

import ogr
import matplotlib.path as mpath
import matplotlib.patches as patches
import matplotlib.pyplot as plt

ds = ogr.Open('lmes_64.shp')
lyr = ds.GetLayer(0)
ft = lyr.GetFeature(38)
geom = ft.GetGeometryRef()
ds = None

codes = []
all_x = []
all_y = []

if (geom.GetGeometryType() == ogr.wkbPolygon):
  for i in range(geom.GetGeometryCount()):

    r = geom.GetGeometryRef(i)
    x = [r.GetX(j) for j in range(r.GetPointCount())]
    y = [r.GetY(j) for j in range(r.GetPointCount())]

    codes += [mpath.Path.MOVETO] + (len(x)-1)*[mpath.Path.LINETO]
    all_x += x
    all_y += y

if (geom.GetGeometryType() == ogr.wkbMultiPolygon):
  codes = []
  for i in range(geom.GetGeometryCount()):
    # Read ring geometry and create path
    r = geom.GetGeometryRef(i)
    for part in r:
      x = [part.GetX(j) for j in range(part.GetPointCount())]
      y = [part.GetY(j) for j in range(part.GetPointCount())]
      # skip boundary between individual rings
      codes += [mpath.Path.MOVETO] + (len(x)-1)*[mpath.Path.LINETO]
      all_x += x
      all_y += y

carib_path = mpath.Path(np.column_stack((all_x,all_y)), codes)    
carib_patch = patches.PathPatch(carib_path, facecolor='orange', lw=2)

poly1 = patches.Polygon([[-80,20],[-75,20],[-75,15],[-80,15],[-80,20]], zorder=5, fc='none', lw=3)
poly2 = patches.Polygon([[-65,25],[-60,25],[-60,20],[-65,20],[-65,25]], zorder=5, fc='none', lw=3)


fig, ax = plt.subplots(1,1)

for poly in [poly1, poly2]:
    if carib_path.intersects_path(poly.get_path()):
        poly.set_edgecolor('g')
    else:
        poly.set_edgecolor('r')

    ax.add_patch(poly)

ax.add_patch(carib_patch)
ax.autoscale_view()

如果你想要非常简单的Shapefile处理，还要结帐Fiona（OGR的包装器）。

Answer 3

这里有一篇博文，介绍shapefile和底图：http://www.geophysique.be/2013/02/12/matplotlib-basemap-tutorial-10-shapefiles-unleached-continued/

如果您希望尝试一下，cartopy也可能是一种选择。绘制shapefile中的数据非常简单：

import matplotlib.pyplot as plt

import cartopy.crs as ccrs
import cartopy.io.shapereader as shpreader

# pick a shapefile - Cartopy makes it easy to access Natural Earth
# shapefiles, but it could be anything
shapename = 'admin_1_states_provinces_lakes_shp'
states_shp = shpreader.natural_earth(resolution='110m',
                                      category='cultural', name=shapename)

# states_shp is just a filename to a shapefile
>>> print states_shp
/Users/pelson/.local/share/cartopy/shapefiles/natural_earth/cultural/110m_admin_1_states_provinces_lakes_shp.shp

# Create the mpl axes of a PlateCarree map
ax = plt.axes(projection=ccrs.PlateCarree())

# Read the shapes from the shapefile into a list of shapely geometries.
geoms = shpreader.Reader(states_shp).geometries()

# Add the shapes in the shapefile to the axes
ax.add_geometries(geoms, ccrs.PlateCarree(),
                  facecolor='coral', edgecolor='black')

plt.show()