2D polgon

class Polygon2(vertices=None, close=True)[source]

Class to represent 2D (planar) polygons

Note

Uses Matplotlib primitives to perform transformations and intersections.

__init__(vertices=None, close=True)[source]

Create planar polygon from vertices

Parameters

vertices (ndarray(2, N), optional) – vertices of polygon, defaults to None
close (bool) – closes the polygon, replicates the first vertex, defaults to True

Create a polygon from a set of points provided as columns of the 2D array vertices. A closed polygon is created so the last vertex should not equal the first.

Example:

>>> from spatialmath import Polygon2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])

Warning

The points must be sequential around the perimeter and counter clockwise, otherwise moments will be negative.

Note

The polygon is represented by a Matplotlib Path

__len__()[source]

Number of vertices in polygon

Returns: number of vertices
Return type: int

Example:

>>> from spatialmath import Polygon2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> len(p)
3

__str__()[source]

Polygon to string

Returns: brief summary of polygon
Return type: str

Example:

>>> from spatialmath import Polygon2
>>> import numpy as np
>>> p = Polygon2(np.array([[1, 3, 2], [2, 2, 4]]))
>>> print(p)
Polygon2 with 4 vertices

animate(T, **kwargs)[source]

Animate a polygon

Parameters

T (SE2) – new pose of Polygon
kwargs – options passed to Matplotlib Patch

The plotted polygon is moved to the pose given by T. The pose is always with respect to the initial vertices when the polygon was constructed. The vertices of the polygon will be updated to reflect what is plotted.

If the polygon has already plotted, it will keep the same graphical attributes. If new attributes are given they will replace those given at construction time.

Seealso: plot()
Return type: None

area()[source]

Area of polygon

Returns: area
Return type: float

Example:

>>> from spatialmath import Polygon2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> p.area()
2.0

Seealso: moment()

bbox()[source]

Bounding box of polygon

Returns: bounding box as [xmin, xmax, ymin, ymax]
Return type: ndarray(4)

Example:

>>> from spatialmath import Polygon2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> p.bbox()
array([1., 2., 3., 4.])

centroid()[source]

Centroid of polygon

Returns: centroid
Return type: ndarray(2)

Example:

>>> from spatialmath import Polygon2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> p.centroid()
array([2.    , 2.6667])

Seealso: moment()

contains(p, radius=0.0)[source]

Test if point is inside polygon

Parameters

p (array_like(2)) – point
radius (float, optional) – Add an additional margin to the polygon boundary, defaults to 0.0

Returns

True if point is contained by polygon

Return type

bool

radius can be used to inflate the polygon, or if negative, to deflated it.

Example:

>>> from spatialmath import Polygon2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> p.contains([0, 0])
False
>>> p.contains([2, 3])
True

Warning

Returns True if the point is on the edge of the polygon but False if the point is one of the vertices.

Warning

For a polygon with clockwise ordering of vertices the sign of radius is flipped.

Seealso: matplotlib.contains_point()

edges()[source]

Iterate over polygon edge segments

Creates an iterator that returns pairs of points representing the end points of each segment.

Return type: Iterator

intersects(other)[source]

Test for intersection

Parameters: other (Polygon2 or Line2 or list(Polygon2) or list(Line2)) – object to test for intersection
Returns: True if the polygon intersects other
Return type: bool
Raises: ValueError –

Returns true if the polygon intersects the the given polygon or 2D line. If other is a list, test against all in the list and return on the first intersection.

moment(p, q)[source]

Moments of polygon

Parameters

p (int) – moment order x
q (int) – moment order y

Returns the pq’th moment of the polygon

\[M(p, q) = \sum_{i=0}^{n-1} x_i^p y_i^q\]

Example:

>>> from spatialmath import Polygon2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> p.moment(0, 0)  # area
2.0
>>> p.moment(3, 0)
18.0

Note is negative for clockwise perimeter.

Return type: float

plot(ax=None, **kwargs)[source]

Plot polygon

Parameters

ax (Axes, optional) – axes in which to draw the polygon, defaults to None
kwargs – options passed to Matplotlib Patch

A Matplotlib Patch is created with the passed options **kwargs and added to the axes.

Examples:

>>> from spatialmath.base import plotvol2, plot_polygon
>>> plotvol2(5)
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> p.plot(fill=False)
>>> p.plot(facecolor="g", edgecolor="none")  # green filled triangle

(Source code, png, hires.png, pdf)

(Source code, png, hires.png, pdf)

Seealso: animate() matplotlib.PathPatch()
Return type: None

radius()[source]

Radius of smallest enclosing circle

Returns: radius
Return type: float

This is the radius of the smalleset circle, centred at the centroid, that encloses all vertices.

Example:

>>> from spatialmath import Polygon2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> p.radius()
1.3333333333333335

transformed(T)[source]

A transformed copy of polygon

Parameters: T (SE2) – planar transformation
Returns: transformed polygon
Return type: Polygon2

Returns a new polgyon whose vertices have been transformed by T.

Example:

>>> from spatialmath import Polygon2, SE2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> p.vertices()
array([[1., 3., 2.],
       [2., 2., 4.]])
>>> p.transformed(SE2(10, 0, 0)).vertices() # shift by x+10
array([[11., 13., 12.],
       [ 2.,  2.,  4.]])

vertices(unique=True)[source]

Vertices of polygon

Parameters: unique (bool, optional) – return only the unique vertices , defaults to True
Returns: vertices
Return type: ndarray(2,n)

Returns the set of vertices. The polygon is always closed, that is, the first and last vertices are the same. The unique option does not include the last vertex.

Example: