Polylines¶

class py123d.geometry.Polyline2D[source]¶

Represents a interpolatable 2D polyline.

Example

>>> import numpy as np
>>> from py123d.geometry import Polyline2D
>>> polyline = Polyline2D.from_array(np.array([[0.0, 0.0], [1.0, 1.0], [2.0, 0.0]]))
>>> polyline.length
2.8284271247461903
>>> polyline.interpolate(np.sqrt(2))
Point2D(array=[1. 1.])

Public Data Attributes:

`linestring`	The shapely LineString representation of the polyline.
`array`	The numpy array representation of shape (N, 2), indexed by `Point2DIndex`.
`polyline_se2`	The `PolylineSE2` representation of the polyline, with inferred yaw angles.
`length`	Returns the length of the polyline.

Inherited from ArrayMixin

`array`	The array representation of the geometric entity.
`shape`	Return the shape of the array.

Public Methods:

`from_linestring`(linestring)	Creates a `Polyline2D` from a Shapely LineString.
`from_array`(array[, copy])	Creates a `Polyline2D` from a (N, 2) or (N, 3) shaped numpy array.
`interpolate`(distances[, normalized])	Interpolates the `Polyline2D` at the given distances.
`project`(point[, normalized])	Projects a point onto the polyline and returns the distance along the polyline to the closest point.

Inherited from ArrayMixin

`from_array`(array[, copy])	Create an instance from a NumPy array.
`from_list`(values)	Create an instance from a list of values.
`tolist`()	Convert the array to a Python list.
`to_list`()	Convert the array to a Python list.
`copy`()	Return a copy of the object with a copied array.

classmethod from_linestring(linestring)[source]¶

Creates a Polyline2D from a Shapely LineString. If the LineString has Z-coordinates, they are ignored.

Parameters:: linestring (LineString) – A shapely LineString object.
Return type:: Polyline2D
Returns:: A Polyline2D instance.

classmethod from_array(array, copy=True)[source]¶

Creates a Polyline2D from a (N, 2) or (N, 3) shaped numpy array. Assumes […,:2] slices are XY coordinates.

Parameters:

polyline_array – A numpy array of shape (N, 2) or (N, 3), e.g. indexed by Point2DIndex or Point3DIndex.
array (ndarray[tuple[Any, ...], dtype[float64]])
copy (bool)

Raises:

ValueError – If the input array is not of the expected shape.

Return type:

Polyline2D

Returns:

A Polyline2D instance.

property linestring: LineString¶: The shapely LineString representation of the polyline.

property array: ndarray[tuple[Any, ...], dtype[float64]]¶: The numpy array representation of shape (N, 2), indexed by Point2DIndex.

property polyline_se2: PolylineSE2¶: The PolylineSE2 representation of the polyline, with inferred yaw angles.

property length: float¶: Returns the length of the polyline.

interpolate(distances, normalized=False)[source]¶

Interpolates the Polyline2D at the given distances.

Parameters:

distances (Union[float, ndarray[tuple[Any, ...], dtype[float64]]]) – Array-like or float distances along the polyline to interpolate.
normalized (bool)

Return type:

Union[Point2D, ndarray[tuple[Any, ...], dtype[float64]]]

Returns:

The interpolated point(s) on the polyline.

project(point, normalized=False)[source]¶

Projects a point onto the polyline and returns the distance along the polyline to the closest point.

Parameters:

point (Union[Point, Point2D, PoseSE2, ndarray[tuple[Any, ...], dtype[float64]]]) – The point to project onto the polyline.
normalized (bool) – Whether to return the normalized distance, defaults to False.

Return type:

ndarray[tuple[Any, ...], dtype[float64]]

Returns:

The distance along the polyline to the closest point.

copy()¶

Return a copy of the object with a copied array.

Return type:: ArrayMixin

classmethod from_list(values)¶

Create an instance from a list of values.

Return type:: Self
Parameters:: values (list)

property shape: tuple¶: Return the shape of the array.

to_list()¶

Convert the array to a Python list.

Return type:: list

tolist()¶

Convert the array to a Python list.

Return type:: list

class py123d.geometry.PolylineSE2[source]¶

Represents a interpolatable SE2 polyline.

Example

>>> import numpy as np
>>> from py123d.geometry import PolylineSE2
>>> polyline_se2 = PolylineSE2.from_array(np.array([[0.0, 0.0, 0.0], [1.0, 1.0, np.pi/4], [2.0, 0.0, 0.0]]))
>>> polyline_se2.length
2.8284271247461903
>>> polyline_se2.interpolate(np.sqrt(2))
PoseSE2(array=[1.         1.         0.78539816])

Public Data Attributes:

`linestring`	The shapely LineString representation of the polyline.
`array`	The numpy array representation of shape (N, 3), indexed by `PoseSE2Index`.
`length`	Returns the length of the polyline.

Inherited from ArrayMixin

`array`	The array representation of the geometric entity.
`shape`	Return the shape of the array.

Public Methods:

`from_linestring`(linestring)	Creates a `PolylineSE2` from a shapely LineString.
`from_array`(polyline_array)	Creates a `PolylineSE2` from a numpy array.
`interpolate`(distances[, normalized])	Interpolates the polyline at the given distances.
`project`(point[, normalized])	Projects a point onto the polyline and returns the distance along the polyline to the closest point.

Inherited from ArrayMixin

`from_array`(array[, copy])	Create an instance from a NumPy array.
`from_list`(values)	Create an instance from a list of values.
`tolist`()	Convert the array to a Python list.
`to_list`()	Convert the array to a Python list.
`copy`()	Return a copy of the object with a copied array.

classmethod from_linestring(linestring)[source]¶

Creates a PolylineSE2 from a shapely LineString. The yaw angles are inferred from the LineString coordinates.

Parameters:: linestring (LineString) – The LineString to convert.
Return type:: PolylineSE2
Returns:: A PolylineSE2 representing the same path as the LineString.

classmethod from_array(polyline_array)[source]¶

Creates a PolylineSE2 from a numpy array.

Parameters:: polyline_array (ndarray[tuple[Any, ...], dtype[float32]]) – The input numpy array representing, either indexed by Point2DIndex or PoseSE2Index.
Raises:: ValueError – If the input array is not of the expected shape.
Return type:: PolylineSE2
Returns:: A PolylineSE2 representing the same path as the input array.

property linestring: LineString¶: The shapely LineString representation of the polyline.

property array: ndarray[tuple[Any, ...], dtype[float64]]¶: The numpy array representation of shape (N, 3), indexed by PoseSE2Index.

property length: float¶: Returns the length of the polyline.

interpolate(distances, normalized=False)[source]¶

Interpolates the polyline at the given distances.

Parameters:

distances (Union[float, ndarray[tuple[Any, ...], dtype[float64]]]) – The distances along the polyline to interpolate.
normalized (bool) – Whether the distances are normalized (0 to 1), defaults to False

Return type:

Union[PoseSE2, ndarray[tuple[Any, ...], dtype[float64]]]

Returns:

The interpolated StateSE2 or an array of interpolated states, according to

project(point, normalized=False)[source]¶

Projects a point onto the polyline and returns the distance along the polyline to the closest point.

Parameters:

point (Union[Point, Point2D, PoseSE2, ndarray[tuple[Any, ...], dtype[float64]]]) – The point to project onto the polyline.
normalized (bool) – Whether to return the normalized distance, defaults to False.

Return type:

ndarray[tuple[Any, ...], dtype[float64]]

Returns:

The distance along the polyline to the closest point.

copy()¶

Return a copy of the object with a copied array.

Return type:: ArrayMixin

classmethod from_list(values)¶

Create an instance from a list of values.

Return type:: Self
Parameters:: values (list)

property shape: tuple¶: Return the shape of the array.

to_list()¶

Convert the array to a Python list.

Return type:: list

tolist()¶

Convert the array to a Python list.

Return type:: list

class py123d.geometry.Polyline3D[source]¶

Represents a interpolatable 3D polyline.

Example

>>> import numpy as np
>>> from py123d.geometry import Polyline3D
>>> polyline_3d = Polyline3D.from_array(np.array([[0.0, 0.0, 0.0], [1.0, 1.0, 1.0], [2.0, 0.0, 0.0]]))
>>> polyline_3d.length
3.4641016151377544
>>> polyline_3d.interpolate(np.sqrt(3))
Point3D(array=[1. 1. 1.])

Public Data Attributes:

`linestring`	The shapely LineString representation of the 3D polyline.
`array`	The numpy array representation of shape (N, 3), indexed by `Point3DIndex`.
`polyline_2d`	The `Polyline2D` representation of the 3D polyline.
`polyline_se2`	The `PolylineSE2` representation of the 3D polyline.
`length`	Returns the length of the 3D polyline.

Inherited from ArrayMixin

`array`	The array representation of the geometric entity.
`shape`	Return the shape of the array.

Public Methods:

`from_linestring`(linestring)	Creates a `Polyline3D` from a shapely LineString.
`from_array`(array)	Creates a `Polyline3D` from a numpy array.
`interpolate`(distances[, normalized])	Interpolates the 3D polyline at the given distances.
`project`(point[, normalized])	Projects a point onto the 3D polyline and returns the distance along the polyline to the closest point.

Inherited from ArrayMixin

`from_array`(array[, copy])	Create an instance from a NumPy array.
`from_list`(values)	Create an instance from a list of values.
`tolist`()	Convert the array to a Python list.
`to_list`()	Convert the array to a Python list.
`copy`()	Return a copy of the object with a copied array.

classmethod from_linestring(linestring)[source]¶

Creates a Polyline3D from a shapely LineString. If the LineString does not have Z-coordinates, the coordinate is zero-padded.

Parameters:: linestring (LineString) – The input LineString.
Return type:: Polyline3D
Returns:: A Polyline3D instance.

classmethod from_array(array)[source]¶

Creates a Polyline3D from a numpy array.

Parameters:: array (ndarray[tuple[Any, ...], dtype[float64]]) – A numpy array of shape (N, 3) representing 3D points, e.g. indexed by Point3DIndex.
Return type:: Polyline3D
Returns:: A Polyline3D instance.

property linestring: LineString¶: The shapely LineString representation of the 3D polyline.

property array: ndarray[tuple[Any, ...], dtype[float64]]¶: The numpy array representation of shape (N, 3), indexed by Point3DIndex.

property polyline_2d: Polyline2D¶: The Polyline2D representation of the 3D polyline.

property polyline_se2: PolylineSE2¶: The PolylineSE2 representation of the 3D polyline.

property length: float¶: Returns the length of the 3D polyline.

interpolate(distances, normalized=False)[source]¶

Interpolates the 3D polyline at the given distances.

Parameters:

distances (Union[float, ndarray[tuple[Any, ...], dtype[float64]]]) – A float or numpy array of distances along the polyline.
normalized (bool) – Whether to interpret the distances as fractions of the length.

Return type:

Union[Point3D, ndarray[tuple[Any, ...], dtype[float64]]]

Returns:

A Point3D instance or a numpy array of shape (N, 3) representing the interpolated points.

project(point, normalized=False)[source]¶

Projects a point onto the 3D polyline and returns the distance along the polyline to the closest point.

Parameters:

point (Union[Point, Point2D, Point3D, ndarray[tuple[Any, ...], dtype[float64]]]) – The point to project.
normalized (bool) – Whether to return normalized distances, defaults to False.

Return type:

ndarray[tuple[Any, ...], dtype[float64]]

Returns:

The distance along the polyline to the closest point.

copy()¶

Return a copy of the object with a copied array.

Return type:: ArrayMixin

classmethod from_list(values)¶

Create an instance from a list of values.

Return type:: Self
Parameters:: values (list)

property shape: tuple¶: Return the shape of the array.

to_list()¶

Convert the array to a Python list.

Return type:: list

tolist()¶

Convert the array to a Python list.

Return type:: list