用shapely判断两个图形的包含相交关系

shapely介绍

• z轴在实例化对象时可以使用，但图形分析中没有用，所有的操作都在x-y平面完成
• shapely拥有（点、曲线、面 interior, boundary, exterior）这样的概念
  • 点的内部是一个点、没有边界、所有其他点都是外部
  • 曲线的内部是沿线的无数个电、边界是两个端点、外部是其他所有的点
  • 面的内部是面上的无数个点、边界是一个或多个曲线、外部是其他所有点

shapely安装

我之前的博客已经介绍过shapely的安装，有兴趣的朋友可以去看看。

shapely的导入

from shapely.geometry import Point, LineString, Polygon 

Point、LineString、Polygon的通用属性

object.area 返回对象的面积 object.bounds 返回包含对象的x、y的最大值最小值的元组 object.length 返回对象的长度 object.geom_type 返回图形的类型 字符串 object.distance(other) 返回两个对象的最小距离 object.hausdorff_distance(other) 返回两个对象之间的哈多夫距离 object.representative_point() 返回一个保证在对象上的点 

Point对象

point = Point(0, 1) # 创建点对象，可以是三维的 print(point.area) # 0.0 print(point.length) # 0.0 print(point.bounds) # (0.0, 1.0, 0.0, 1.0) print(point.geom_type) # Point print(point.coords) # 
    print(point.coords[:]) # [(0.0, 1.0)] print(list(point.coords)) # [(0.0, 1.0)] print(point.x, point.y) # 0.0 1.0 

0.0 0.0 (0.0, 1.0, 0.0, 1.0) Point <shapely.coords.CoordinateSequence object at 0x00000201F7A18518> [(0.0, 1.0)] [(0.0, 1.0)] 0.0 1.0 

LineString对象

# 可以自己相交 line = LineString([(0, 0), (1, 1)]) print(line.area) # 0.0 print(line.length) # 1.30951 print(line.bounds) # (0.0, 0.0, 1.0, 1.0) print(line.geom_type) # LineString print(line.coords) # 
    print(line.coords[:], type(line.coords[:])) # [(0.0, 0.0), (1.0, 1.0)] 
    

0.0 1.30951 (0.0, 0.0, 1.0, 1.0) LineString <shapely.coords.CoordinateSequence object at 0x0000028D59BC0518> [(0.0, 0.0), (1.0, 1.0)] <class 'list'> 

Polygon对象

# 可以传入两个参数，第一个是有序的外边缘轮廓，第二个是无序的内边缘轮廓，多边形内所有的环形最多只能有一个焦点，否则都是无效的 poly = Polygon([(0, 0), (-1, 1), (2, 1), (3, -2)]) print(poly.area) print(poly.length) print(poly.bounds) x_min, y_min, x_max, y_max = poly.bounds print(x_min, y_min, x_max, y_max) print(poly.geom_type) print(poly.exterior.coords) print(poly.exterior.coords[:]) print(poly.interiors) print(poly.interiors[:]) 

5.0 11.5464 (-1.0, -2.0, 3.0, 1.0) -1.0 -2.0 3.0 1.0 Polygon <shapely.coords.CoordinateSequence object at 0x0000018A43B629E8> [(0.0, 0.0), (-1.0, 1.0), (2.0, 1.0), (3.0, -2.0), (0.0, 0.0)] <shapely.geometry.polygon.InteriorRingSequence object at 0x0000018A4398DB70> [] 

box对象

from shapely.geometry import box # box可以穿件矩形多边形，ccw参数选择顺时针或逆时针 b = box(0, 1, 2, 3, ccw=False) # 是以前两个参数作为左下角的点，后两个参数作为右上角的点 print(b.geom_type) print(b.bounds) print(b.exterior.coords[:]) # 获取多边形点的顺序 print(sgp.orient(b, sign=1)) # 顺时针 print(sgp.orient(b, sign=-1)) # 逆时针 

Polygon (1.0, 0.0, 2.0, 3.0) [(1.0, 0.0), (1.0, 3.0), (2.0, 3.0), (2.0, 0.0), (1.0, 0.0)] POLYGON ((1 0, 2 0, 2 3, 1 3, 1 0)) POLYGON ((1 0, 1 3, 2 3, 2 0, 1 0)) 

一元判定

# has_z 判断是否有z坐标 p = Point(0, 0) print(p.has_z) # False p = Point(0, 0, 0) print(p.has_z) # True # is_ccw 判断是否是逆时针的 lr = LinearRing([(1, 0), (1, 1), (0, 0)]) print(lr.is_ccw) # True lr.coords = list(lr.coords)[::-1] print(lr.is_ccw) # False # is_empty 返回TRUE如果内部和边界都是空 p = Point() print(p.is_empty) # True p = Point(0, 0) print(p.is_empty) # False # is_ring 闭合返回TRUE  line = LineString([(0, 0), (1, 1), (1, 0)]) print(line.is_ring) # False line = LineString([(0, 0), (1, 1), (1, 0), (0, 0)]) print(line.is_ring) # True lr = LinearRing([(0, 0), (1, 1), (1, 0)]) print(lr.is_ring) # True lr = LinearRing([(0, 0), (1, 1), (1, 0), (0, 0)]) print(lr.is_ring) # True # is_simple 自己不相交，返回TRUE line = LineString([(0, 0), (1, 1), (1, -1), (0, 1)]) print(line.is_simple) # False line = LineString([(0, 0), (0, 1), (1, 1), (1, 0)]) print(line.is_simple) # True is_valid LinearRing 不相交或者只有一个交点是有效的 Polygon 同上 Note:可以写成验证装饰器，根据特定内容判断他是否是有效的 

二元判定

object.__eq__(other) # 类型和坐标点相同返回TRUE object.equals(other) #boundary, interior, and exterior完全相同返回TRUE object.almost_equals(other[, decimal=6]) # 近似相等返回TRUE decimal是小数点的位数完全相同 object.contains(other) # other里没有点在object的exterior，且other的interior里至少有一个点在object的interior object.crosses(other) # object的interior与other的interior相交，且不包含他 object.disjoint(other) # object的interior和boundary 和other的interior和boundary都不想交 返回True object.intersects(other) # object的interior或者boundary和other的interior或者boundary相交 返回TRUE object.overlaps(other) # object的interior或者boundary和other的interior或者boundary相交，且不包含他, 返回TRUE object.touches(other) # other和object至少有一个共同的点，且他们的interior不相交 

object.__eq__(other) # 类型和坐标点相同返回TRUE,和左边点顺序有关

object = LineString([(0, 0), (1, 1)]) other = LineString([(0, 0), (1, 1)]) print(object.__eq__(other)) # True object = Point((0, 0)) other = Point((0, 0)) print(object.__eq__(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 0), (0, 1), (1, 1)]) print(object.__eq__(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 1), (1, 1), (0, 0)]) print(object.equals(other)) # False 

object.equals(other) #boundary, interior, and exterior完全相同返回TRUE，和坐标点顺序无关

object = LineString([(0, 0), (1, 1)]) other = LineString([(0, 0), (1, 1)]) print(object.equals(other)) # True object = Point((0, 0)) other = Point((0, 0)) print(object.equals(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 0), (0, 1), (1, 1)]) print(object.equals(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 1), (1, 1), (0, 0)]) print(object.equals(other)) # True 

object.almost_equals(other[, decimal=6]) 近似相等返回TRUE decimal是小数点的位数完全相同,和坐标点的顺序有关

object = LineString([(0, 0), (1, 1)]) other = LineString([(0, 0), (1, 1)]) print(object.almost_equals(other)) # True object = Point((0, 0)) other = Point((0, 0)) print(object.almost_equals(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 0), (0, 1), (1, 1)]) print(object.almost_equals(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 1), (1, 1), (0, 0)]) print(object.almost_equals(other)) # False 

object.contains(other) other里没有点在object的exterior，且other的interior里至少有一个点在object的interior,和坐标点的顺序无关

object = LineString([(0, 0), (1, 1)]) other = LineString([(0, 0), (1, 1)]) print(object.contains(other)) # True object = Point((0, 0)) other = Point((0, 0)) print(object.contains(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 0), (0, 1), (1, 1)]) print(object.contains(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 1), (1, 2), (0, 0)]) print(object.contains(other)) # False 

object.crosses(other) object的interior与other的interior相交，且不包含他,该判断只适用于图形与线之间的判定

object = LineString([(0, 0), (1, 1)]) other = LineString([(0, 0), (1, 1)]) print(object.crosses(other)) # False object = LineString([(0, 0), (2, 2)]) other = LineString([(0, 0), (1, 1)]) print(object.crosses(other)) # False object = Point((0, 0)) other = Point((0, 0)) print(object.crosses(other)) # False object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 0), (0, 1), (1, 1)]) print(object.crosses(other)) # False object = Polygon([(0, 0), (0, 1), (1, 1), (1, 0)]) other = LineString([(0.5, 0.5), (2, 2)]) print(object.crosses(other)) # True print(other.crosses(object)) # True object = Polygon([(0, 0), (0, 1), (1, 1), (1, 0)]) other = Polygon([(0.5, 0.5), (0.5, 2), (2, 2), (2, 0.5)]) print(object.crosses(other)) # False print(other.crosses(object)) # False 

object.disjoint(other) object的interior和boundary 和other的interior和boundary都不想交 返回True，完全不相交才返回True，有一个点都不行

object = LineString([(0, 0), (1, 1)]) other = LineString([(0, 0), (1, 1)]) print(object.disjoint(other)) # False object = LineString([(0, 0), (1, 1)]) other = LineString([(2, 2), (3, 3)]) print(object.disjoint(other)) # True object = Point((0, 0)) other = Point((1, 1)) print(object.disjoint(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 0), (0, -1), (-1, -1)]) print(object.disjoint(other)) # False，，有一个点相交了，都不想交才是True object = Polygon([(0, 0), (0, 1), (1, 1), (1, 0)]) other = LineString([(2, 2), (3, 3)]) print(object.disjoint(other)) # True print(other.disjoint(object)) # True object = Polygon([(0, 0), (0, 1), (1, 1), (1, 0)]) other = Polygon([(2,2), (2,4), (4,4), (4, 2)]) print(object.disjoint(other)) # True print(other.disjoint(object)) # True 

object.intersects(other) object的interior或者boundary和other的interior或者boundary相交 返回TRUE

object = LineString([(0, 0), (1, 1)]) other = LineString([(0, 0), (1, 1)]) print(object.intersects(other)) # True object = LineString([(0, 0), (1, 1)]) other = LineString([(1, 1), (0, 0)]) print(object.intersects(other)) # True object = Point((0, 0)) other = Point((1, 1)) print(object.intersects(other)) # False object = Polygon([(0, 0), (0, 1), (1, 1)]) other = Polygon([(0, 0), (0, -1), (-1, -1)]) print(object.intersects(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1), (1, 0)]) other = LineString([(0, 0), (3, 3)]) print(object.intersects(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1), (1, 0)]) other = Polygon([(2,2), (2,4), (4,4), (4, 2)]) print(object.intersects(other)) # False 

object.touches(other) other和object至少有一个共同的点，且他们的interior不相交，也就是说在边界上

object = LineString([(0, 0), (1, 1)]) other = LineString([(1, 1), (2, 2)]) print(object.touches(other)) # True object = LineString([(0, 0), (1, 1)]) other = Point(0, 0) print(object.touches(other)) # True object = Point((0, 0)) other = Point((0, 0)) print(object.touches(other)) # False object = Polygon([(0, 0), (0, 1), (1, 1), (1, 0)]) other = Point((0, 0)) print(object.touches(other)) # True object = Polygon([(0, 0), (0, 1), (1, 1), (1, 0)]) other = LineString([(0.1, 0), (0.2, 0)]) print(object.touches(other)) # True print(other.touches(object)) # True