python - 使用 matplotlib 求解多边形中的点

Question

我正在寻找一种算法来检查一个点是否在多边形内。

我目前正在使用 mplPath 和 contains_point() 但它在某些情况下似乎不起作用。

2016 年 9 月 16 日编辑:

好的，所以我通过简单地检查该点是否也在边缘来改进我的代码。不过，对于矩形和领结示例，我仍然存在一些问题:

新代码:

#for PIP problem
import matplotlib.path as mplPath
import numpy as np
#for plot
import matplotlib.pyplot as plt


def plot(poly,points):
    bbPath = mplPath.Path(poly)
    #plot polygon
    plt.plot(*zip(*poly))

    #plot points
    xs,ys,cs = [],[],[]
    for point in points:
        xs.append(point[0])
        ys.append(point[1])
        color = inPoly(poly,point)
        cs.append(color)
        print point,":", color
    plt.scatter(xs,ys, c = cs , s = 20*4*2)

    #setting limits
    axes = plt.gca()
    axes.set_xlim([min(xs)-5,max(xs)+50])
    axes.set_ylim([min(ys)-5,max(ys)+10])

    plt.show()

def isBetween(a, b, c): #is c between a and b ?
    crossproduct = (c[1] - a[1]) * (b[0] - a[0]) - (c[0] - a[0]) * (b[1] - a[1])
    if abs(crossproduct) > 0.01 : return False   # (or != 0 if using integers)

    dotproduct = (c[0] - a[0]) * (b[0] - a[0]) + (c[1] - a[1])*(b[1] - a[1])
    if dotproduct < 0 : return False

    squaredlengthba = (b[0] - a[0])*(b[0] - a[0]) + (b[1] - a[1])*(b[1] - a[1])
    if dotproduct > squaredlengthba: return False

    return True

def get_edges(poly):
    # get edges
    edges = []
    for i in range(len(poly)-1):
        t = [poly[i],poly[i+1]]
        edges.append(t)
    return edges

def inPoly(poly,point):
    if bbPath.contains_point(point) == True:
        return 1
    else:
        for e in get_edges(poly):
            if isBetween(e[0],e[1],point):
                return 1
    return 0
# TESTS ========================================================================
#set up poly
polys = {
1 : [[10,10],[10,50],[50,50],[50,80],[100,80],[100,10],[10,10]], # test rectangulary shape
2 : [[20,10],[10,20],[30,20],[20,10]], # test triangle
3 : [[0,0],[0,10],[20,0],[20,10],[0,0]], # test bow-tie
4 : [[0,0],[0,10],[20,10],[20,0],[0,0]] # test rect
}

#points to check
points = {
1 : [(10,25),(50,75),(60,10),(20,20),(20,60),(40,50)], # rectangulary shape test pts
2 : [[20,10],[10,20],[30,20],[-5,0],[20,15]] , # triangle  test pts
3 : [[0,0],[0,10],[20,0],[20,10],[10,0],[10,5],[15,5]],  # bow-tie shape test pts
4 : [[0,0],[0,10],[20,0],[20,10],[10,0],[10,5],[15,5]]  # rect shape test pts
}

#print bbPath.contains_points(points) #0 if outside, 1 if inside
for data in zip(polys.itervalues(),points.itervalues()):
    plot(data[0],data[1])

新代码的输出:

旧代码:

#for PIP problem
import matplotlib.path as mplPath
import numpy as np
#for plot
import matplotlib.pyplot as plt

#set up poly
array = np.array([[10,10],[10,50],[50,50],[50,80],[100,80],[100,10]])
bbPath = mplPath.Path(array)

#points to check
points = [(10,25),(50,75),(60,10),(20,20),(20,60),(40,50)]


print bbPath.contains_points(points) #0 if outside, 1 if inside

#plot polygon
plt.plot(*zip(*array))

#plot points
xs,ys,cs = [],[],[]
for point in points:
    xs.append(point[0])
    ys.append(point[1])
    cs.append(bbPath.contains_point(point))
plt.scatter(xs,ys, c = cs)

#setting limits
axes = plt.gca()
axes.set_xlim([0,120])
axes.set_ylim([0,100])

plt.show()

我想出了以下 .如您所见，红色包围的三个点被指示为在多边形(蓝色)之外，而我希望它们在多边形内部。

我还尝试更改路径 bbPath.contains_points(points, radius = 1.) 的半径值，但这没有任何区别。

欢迎任何帮助。

编辑:

这个问题的答案中提出的算法的屏幕截图似乎表明它在其他情况下失败。

Answer 1

好吧，我终于设法改用 shapely 来完成它。

#for PIP problem
import matplotlib.path as mplPath
import numpy as np
#for plot
import matplotlib.pyplot as plt
import shapely.geometry as shapely

class MyPoly(shapely.Polygon):
    def __init__(self,points):
        super(MyPoly,self).__init__(points)
        self.points = points
        self.points_shapely = [shapely.Point(p[0],p[1]) for p in points]

def convert_to_shapely_points_and_poly(poly,points):
    poly_shapely = MyPoly(poly)
    points_shapely = [shapely.Point(p[0],p[1]) for p in points]
    return poly_shapely,points_shapely

def plot(poly_init,points_init):
    #convert to shapely poly and points
    poly,points = convert_to_shapely_points_and_poly(poly_init,points_init)

    #plot polygon
    plt.plot(*zip(*poly.points))

    #plot points
    xs,ys,cs = [],[],[]
    for point in points:
        xs.append(point.x)
        ys.append(point.y)
        color = inPoly(poly,point)
        cs.append(color)
        print point,":", color
    plt.scatter(xs,ys, c = cs , s = 20*4*2)

    #setting limits
    axes = plt.gca()
    axes.set_xlim([min(xs)-5,max(xs)+50])
    axes.set_ylim([min(ys)-5,max(ys)+10])

    plt.show()


def isBetween(a, b, c): #is c between a and b ?
    crossproduct = (c.y - a.y) * (b.x - a.x) - (c.x - a.x) * (b.y - a.y)
    if abs(crossproduct) > 0.01 : return False   # (or != 0 if using integers)

    dotproduct = (c.x - a.x) * (b.x - a.x) + (c.y - a.y)*(b.y - a.y)
    if dotproduct < 0 : return False

    squaredlengthba = (b.x - a.x)*(b.x - a.x) + (b.y - a.y)*(b.y - a.y)
    if dotproduct > squaredlengthba: return False

    return True

def get_edges(poly):
    # get edges
    edges = []
    for i in range(len(poly.points)-1):
        t = [poly.points_shapely[i],poly.points_shapely[i+1]]
        edges.append(t)
    return edges


def inPoly(poly,point):
    if poly.contains(point) == True:
        return 1
    else:
        for e in get_edges(poly):
            if isBetween(e[0],e[1],point):
                return 1
    return 0


# TESTS ========================================================================
#set up poly
polys = {
1 : [[10,10],[10,50],[50,50],[50,80],[100,80],[100,10],[10,10]], # test rectangulary shape
2 : [[20,10],[10,20],[30,20],[20,10]], # test triangle
3 : [[0,0],[0,10],[20,0],[20,10],[0,0]], # test bow-tie
4 : [[0,0],[0,10],[20,10],[20,0],[0,0]], # test rect clockwise
5 : [[0,0],[20,0],[20,10],[0,10],[0,0]] # test rect counter-clockwise
}

#points to check
points = {
1 : [(10,25),(50,75),(60,10),(20,20),(20,60),(40,50)], # rectangulary shape test pts
2 : [[20,10],[10,20],[30,20],[-5,0],[20,15]] , # triangle  test pts
3 : [[0,0],[0,10],[20,0],[20,10],[10,0],[10,5],[15,5]],  # bow-tie shape test pts
4 : [[0,0],[0,10],[20,0],[20,10],[10,0],[10,5],[15,2],[30,8]],  # rect shape test pts
5 : [[0,0],[0,10],[20,0],[20,10],[10,0],[10,5],[15,2],[30,8]]  # rect shape test pts
}

#print bbPath.contains_points(points) #0 if outside, 1 if inside
for data in zip(polys.itervalues(),points.itervalues()):
    plot(data[0],data[1])