bluemira.utilities.positioning

A collection of tools used for position interpolation.

Classes

XZGeometryInterpolator

Abstract base class for 2-D x-z geometry interpolation to normalised [0, 1] space.

PathInterpolator

Sets up an x-z path for a point to move along.

RegionInterpolator

Sets up an x-z region for a point to move within.

PositionMapper

Positioning tool for use in optimisation

Module Contents

class bluemira.utilities.positioning.XZGeometryInterpolator(geometry: bluemira.geometry.wire.BluemiraWire)

Bases: abc.ABC

Inheritance diagram of bluemira.utilities.positioning.XZGeometryInterpolator

Abstract base class for 2-D x-z geometry interpolation to normalised [0, 1] space.

By convention, normalised x-z space is oriented counter-clockwise w.r.t. [0, 1, 0].

Parameters:

geometry (bluemira.geometry.wire.BluemiraWire) – Geometry to interpolate with

geometry
_get_xz_coordinates(num_pts)

Get discretised x-z coordinates of the geometry.

Returns:

The xz coordinates

abstract to_xz(l_values: numpy.typing.ArrayLike) → tuple[float, float] | tuple[numpy.ndarray, numpy.ndarray]

Convert parametric-space ‘L’ values to physical x-z space.

Parameters:

l_values (numpy.typing.ArrayLike)

Return type:

tuple[float, float] | tuple[numpy.ndarray, numpy.ndarray]

abstract to_L(x: numpy.typing.ArrayLike, z: numpy.typing.ArrayLike) → float | numpy.ndarray

Convert physical x-z space values to parametric-space ‘L’ values.

Parameters:

  • x (numpy.typing.ArrayLike)

  • z (numpy.typing.ArrayLike)

Return type:

float | numpy.ndarray

property dimension: int
Abstractmethod:

Return type:

int

The dimension of the parametric space

class bluemira.utilities.positioning.PathInterpolator(geometry: bluemira.geometry.wire.BluemiraWire)

Bases: XZGeometryInterpolator

Inheritance diagram of bluemira.utilities.positioning.PathInterpolator

Sets up an x-z path for a point to move along.

The path is treated as flat in the x-z plane.

Parameters:

geometry (bluemira.geometry.wire.BluemiraWire)

to_xz(l_values: numpy.typing.ArrayLike) → tuple[float, float] | tuple[numpy.ndarray, numpy.ndarray]

Convert parametric-space ‘L’ values to physical x-z space.

Returns:

The xz coordinates

Parameters:

l_values (numpy.typing.ArrayLike)

Return type:

tuple[float, float] | tuple[numpy.ndarray, numpy.ndarray]

to_L(x: numpy.typing.ArrayLike, z: numpy.typing.ArrayLike) → float | numpy.ndarray

Convert physical x-z space values to parametric-space ‘L’ values.

Returns:

The normalised coordinates

Parameters:

  • x (numpy.typing.ArrayLike)

  • z (numpy.typing.ArrayLike)

Return type:

float | numpy.ndarray

property dimension: int

Dimension of the parametric space of the PathInterpolator

Return type:

int

class bluemira.utilities.positioning.RegionInterpolator(geometry: bluemira.geometry.wire.BluemiraWire)

Bases: XZGeometryInterpolator

Inheritance diagram of bluemira.utilities.positioning.RegionInterpolator

Sets up an x-z region for a point to move within.

The region is treated as a flat x-z surface.

The normalisation occurs by cutting the shape in two axes and normalising over the cut length within the region.

Currently this is limited to convex polygons.

Generalisation to all polygons is possible but unimplemented and possibly quite slow when converting from normalised to real coordinates.

When the point position provided is outside the given region the point will be moved to the closest edge of the region.

The mapping from outside to the edge of the region is not strictly defined. The only certainty is that the point will be moved into the region.

Parameters:

geometry (bluemira.geometry.wire.BluemiraWire) – Region to interpolate within

z_min
z_max
_check_geometry_feasibility(geometry: bluemira.geometry.wire.BluemiraWire)

Checks the provided region is convex.

This is a current limitation of RegionInterpolator not providing a ‘smooth’ interpolation surface.

Parameters:

geometry (bluemira.geometry.wire.BluemiraWire) – Region to check

Raises:

PositionerError – When geometry is not a convex

to_xz(l_values: numpy.typing.ArrayLike | tuple[float, float] | tuple[numpy.ndarray, numpy.ndarray]) → tuple[float, float] | tuple[numpy.ndarray, numpy.ndarray]

Convert parametric-space ‘L’ values to physical x-z space.

Parameters:

l_values (numpy.typing.ArrayLike | tuple[float, float] | tuple[numpy.ndarray, numpy.ndarray]) – Coordinates in normalised space

Returns:

  • x – x coordinate in real space

  • z – z coordinate in real space

Raises:

PositionerError – When loop is not a Convex Hull

Return type:

tuple[float, float] | tuple[numpy.ndarray, numpy.ndarray]

to_L(x: numpy.typing.ArrayLike, z: numpy.typing.ArrayLike) → tuple[float, float] | tuple[numpy.ndarray, numpy.ndarray]

Convert physical x-z space values to parametric-space ‘L’ values.

Parameters:

  • x (numpy.typing.ArrayLike) – x coordinate in real space

  • z (numpy.typing.ArrayLike) – z coordinate in real space

Returns:

  • l_1 – Coordinate 1 in normalised space

  • l_2 – Coordinate 2 in normalised space

Raises:

GeometryError – When loop is not a Convex Hull

Return type:

tuple[float, float] | tuple[numpy.ndarray, numpy.ndarray]

_intersect_filter(x: float, l_1: float, intersect: bluemira.geometry.plane.BluemiraPlane) → tuple[float, float]

Checks where points are based on number of intersections with a plane. Should initially be called with a plane involving z.

No intersection could mean above 1 edge therefore a plane in xy is checked before recalling this function. If there is one intersection point we are on an edge (either bottom or top), if there is two intersection points we are in the region, otherwise the region is not a convex hull.

Parameters:
Returns:

  • l_1 – Coordinate 1 in normalised space

  • l_2 – Coordinate 2 in normalised space

Raises:

PositionerError – When geometry is not a convex

Return type:

tuple[float, float]

property dimension

Dimension of the parametric space of the RegionInterpolator

class bluemira.utilities.positioning.PositionMapper(interpolators: dict[str, XZGeometryInterpolator])

Positioning tool for use in optimisation

Parameters:

interpolators (dict[str, XZGeometryInterpolator]) – The ordered list of geometry interpolators

interpolators
_check_length(thing)

Check that something is the same length as the number of available interpolators.

Raises:

PositionerError – the number of iterators is not equal to the number of objects

_vector_to_list(l_values)

Convert a vector of l_values into a ragged list if necessary

Returns:

The list of normalised values

to_xz(l_values: numpy.ndarray) → numpy.typing.NDArray[numpy.float64]

Convert a set of parametric-space values to physical x-z coordinates.

Parameters:

l_values (numpy.ndarray) – The set of parametric-space values to convert

Returns:

  • x – Array of x coordinates

  • z – Array of z coordinates

Return type:

numpy.typing.NDArray[numpy.float64]

to_xz_dict(l_values: numpy.ndarray) → dict[str, numpy.ndarray]

Convert a set of parametric space values to physical coordinates in a dictionary form.

Parameters:

l_values (numpy.ndarray) – The set of parametric-space values to convert

Return type:

Dictionary of x-z values corresponding to each interpolator

to_L(x: numpy.ndarray, z: numpy.ndarray) → numpy.ndarray

Convert a set of physical x-z coordinates to parametric-space values.

Parameters:

  • x (numpy.ndarray) – The x coordinates to convert

  • z (numpy.ndarray) – The z coordinates to convert

Returns:

The set of parametric-space values

Return type:

l_values

property dimension: int

The total dimension of the parametric space

Return type:

int

property interpolator_names: list[str]

The names of the interpolators

Return type:

list[str]