Polygons¶

scikit-geometry can handle polygons, as well as polygons with holes. Polygons can be created from lists of points.

[1]:

import skgeom as sg
from skgeom.draw import draw

[2]:

poly = sg.Polygon([sg.Point2(0, 0), sg.Point2(0, 3), sg.Point2(3, 3)])

[3]:

draw(poly)

You may also use lists of coordinates or numpy arrays to construct polygons:

[4]:

sg.Polygon([[0, 0], [0, 3], [3, 3]])

Likewise, you can access a Polygon’s vertices as either a list of Point2s or as a numpy array:

[5]:

list(poly.vertices)

[5]:

[PointC2(0, 0), PointC2(0, 3), PointC2(3, 3)]

[6]:

poly.coords

[6]:

array([[0., 0.],
       [0., 3.],
       [3., 3.]])

We can check wether a given point is inside the polygon (a negative sign means outside, positive means inside):

[7]:

poly.oriented_side(sg.Point2(1, 2))

[7]:

Sign.NEGATIVE

[8]:

poly.oriented_side(sg.Point2(2, 1))

[8]:

Sign.POSITIVE

Calculate the bounding box

[9]:

poly.bbox()

[9]:

Bbox_2(0, 0, 3, 3)

Compute the area of the polygon. Note: the sign depends on the order of the polygon (clockwise → negative, counter-clockwise → positive).

[10]:

poly.area()

[10]:

-4.5

[11]:

poly.orientation() == sg.Sign.CLOCKWISE

[11]:

True

[12]:

poly.is_convex()

[12]:

True

[13]:

poly.is_simple()

[13]:

True

Polygon with Holes¶

We can cut out an area of a Polygon by adding one or multiple holes.

[14]:

hole = sg.Polygon([
    sg.Point2(1.0, 2.0),
    sg.Point2(1.0, 2.5),
    sg.Point2(0.5, 2.5),
    sg.Point2(0.5, 2.0)]
)
poly_with_hole = sg.PolygonWithHoles(poly, [hole])

[15]:

draw(poly_with_hole)

Boolean operations on Polygons¶

scikit-geometry supports boolean operations on polygons, such as computing the union, difference and intersection between two polygons (or polygons with holes).

[16]:

poly1 = sg.Polygon([sg.Point2(3, 0), sg.Point2(3, 3), sg.Point2(0, 3), sg.Point2(0, 0)])
poly2 = sg.Polygon([sg.Point2(5, 2), sg.Point2(5, 5), sg.Point2(2, 5), sg.Point2(2, 2)])

[17]:

draw(poly1, facecolor='red')
draw(poly2, facecolor='blue')

[18]:

from skgeom import boolean_set

[19]:

draw(boolean_set.join(poly1, poly2))

[20]:

draw(boolean_set.difference(poly1, poly2))

[21]:

draw(boolean_set.symmetric_difference(poly1, poly2))

[22]:

draw(boolean_set.intersect(poly1, poly2))

Minkowski Sum of 2 Polygons¶

We can compute the minkowski sum of two polygons easily (i.e. offsetting a polygon with another polygon).

[23]:

from skgeom import minkowski

[24]:

p1 = sg.Polygon([sg.Point2(-1, -1), sg.Point2(1, -1), sg.Point2(0, 1)])
p2 = sg.Polygon([sg.Point2(3, -1), sg.Point2(5, -1), sg.Point2(5, 1), sg.Point2(3, 1)])

[25]:

draw(p1, facecolor='red')
draw(p2, facecolor='blue')

[26]:

result = minkowski.minkowski_sum(p1, p2)
draw(result)