bluemira.geometry.parameterisations

Geometry parameterisations

Classes

GeometryParameterisation

A geometry parameterisation class facilitating geometry optimisation.

PrincetonD

Princeton D geometry parameterisation, with n_TF = ∞.

PrincetonDDiscrete

Princeton D geometry parameterisation, with finite n_TF.

TripleArc

Triple-arc up-down symmetric geometry parameterisation.

SextupleArc

Sextuple-arc up-down asymmetric geometry parameterisation.

PolySpline

Simon McIntosh's Poly-Bézier-spline geometry parameterisation (19 variables).

PictureFrameTools

Tools Class containing methods to produce various PictureFrame variant limbs.

PFrameSection

Picture Frame sections

PictureFrame

Picture-frame geometry parameterisation.

Module Contents

class bluemira.geometry.parameterisations.GeometryParameterisation(variables: OptVariablesFrameT, **kwargs)

Bases: abc.ABC, Generic[OptVariablesFrameT]

Inheritance diagram of bluemira.geometry.parameterisations.GeometryParameterisation

A geometry parameterisation class facilitating geometry optimisation.

Notes

Subclass this base class when making a new GeometryParameterisation, adding a set of variables with initial values, and override the create_shape method.

Parameters:

variables (OptVariablesFrameT)

__slots__ = ('_variables', 'name')
name = 'GeometryParameterisation'
_variables
property n_ineq_constraints: int

Number of inequality constraints in the GeometryParameterisation

Return type:

int

property variables: OptVariablesFrameT

The variables of the GeometryParameterisation

Return type:

OptVariablesFrameT

adjust_variable(name: str, value: float | None = None, lower_bound: float | None = None, upper_bound: float | None = None)

Adjust a variable in the GeometryParameterisation.

Parameters:

  • name (str) – Name of the variable to adjust

  • value (float | None) – Value of the variable to set

  • lower_bound (float | None) – Value of the lower bound to set

  • upper_bound (float | None) – Value of the upper to set

fix_variable(name: str, value: float | None = None)

Fix a variable in the GeometryParameterisation, removing it from optimisation but preserving a constant value.

Parameters:

  • name (str) – Name of the variable to fix

  • value (float | None) – Value at which to fix the variable (will default to present value)

f_ineq_constraint()

Inequality constraint function for the variable vector of the geometry parameterisation. This is used when internal consistency between different un-fixed variables is required.

Raises:

GeometryParameterisationError – No inequality constraints

property tolerance: numpy.typing.NDArray[numpy.float64]

Optimisation tolerance for the geometry parameterisation.

Return type:

numpy.typing.NDArray[numpy.float64]

get_x_norm_index(name: str) → int

Get the index of a variable name in the modified-length x_norm vector

Parameters:

name (str) – Variable name for which to get the index

Return type:

Index of the variable name in the modified-length x_norm vector

process_x_norm_fixed(x_norm: numpy.typing.NDArray[numpy.float64]) → list[float]

Utility for processing a set of free, normalised variables, and folding the fixed un-normalised variables back into a single list of all actual values.

Parameters:

x_norm (numpy.typing.NDArray[numpy.float64]) – Normalised vector of variable values

Return type:

List of ordered actual (un-normalised) values

abstract create_shape(label: str = '') → bluemira.geometry.wire.BluemiraWire

Make a CAD representation of the geometry.

Parameters:

label (str) – Label to give the wire

Returns:

CAD Wire of the geometry

Return type:

bluemira.geometry.wire.BluemiraWire

to_json(file: str)

Write the json representation of the GeometryParameterisation to a file.

Parameters:

file (str) – The path to the file.

classmethod from_json(file: pathlib.Path | str | TextIO) → GeometryParameterisation

Create the GeometryParameterisation from a json file.

Parameters:

file (pathlib.Path | str | TextIO) – The path to the file, or an open file handle that supports reading.

Returns:

The GeometryParameterisation from a json file.

Return type:

GeometryParameterisation

static _annotator(ax: matplotlib.pyplot.Axes, key: str, xy1: tuple[float, float], xy2: tuple[float, float], xy3: tuple[float, float], arrowstyle: str = '<|-')

Create annotation arrow with label

Parameters:

  • ax (matplotlib.pyplot.Axes) – Matplotlib axis instance

  • key (str) – label of annotation

  • xy1 (tuple[float, float]) – Tuple for first arrow point

  • xy2 (tuple[float, float]) – Tuple for second arrow point

  • xy3 (tuple[float, float]) – Tuple for arrow label location

  • arrowstyle (str)

static _angle_annotator(ax: matplotlib.pyplot.Axes, key: str, radius: float, centre: tuple[float, float], angles: tuple[float, float], centre_angle: float)

Create annotation arrow with label

Parameters:

  • ax (matplotlib.pyplot.Axes) – Matplotlib axis instance

  • key (str) – label of annotation

  • radius (float) – radius of arrow

  • centre (tuple[float, float]) – centre coordinate of arrow

  • angles (tuple[float, float])

  • centre_angle (float)

static _draw_angle_annotation(ax, start_angle: float, angle: float, label: str, origin: tuple[float, float] = (0, 0), length: float = 1.0, arc_radius: float = 0.3, label_offset: float = 0.1)

Draw two lines forming an angle, an arc for the angle, and a label.

Parameters:

  • ax – The axis to draw on.

  • start_angle (float) – angle of the first line

  • angle (float) – Angle in degrees for the second line (measured from horizontal).

  • label (str) – Label of angle

  • origin (tuple[float, float]) – (x, y) coordinates of the starting point.

  • length (float) – Length of the lines.

  • arc_radius (float) – Radius of the arc showing the angle.

  • label_offset (float) – Offset for the angle label.

_label_function(ax: matplotlib.pyplot.Axes, shape: bluemira.geometry.wire.BluemiraWire) → tuple[float, float]

Adds labels to parameterisation plots

Parameters:
Returns:

  • offset_ar_x – Suggested location for where to plot the next set of labels related to the radii in the parameterisation. (z-coordinates only)

  • offset_ar_z – Suggested location for where to plot the next set of labels related to the height in the parameterisation. (x-coordinates only)

Return type:

tuple[float, float]

plot(ax=None, *, labels=False, **kwargs)

Plot the geometry parameterisation

Parameters:

  • ax (Optional[Axes]) – Matplotlib axes object

  • labels (bool) – Label variables on figure

  • kwargs (Dict) – Passed to matplotlib Axes.plot function

Returns:

The geometry parameterisation.

class bluemira.geometry.parameterisations.PrincetonD(var_dict: bluemira.utilities.opt_variables.VarDictT | None = None)

Bases: GeometryParameterisation[PrincetonDOptVariables]

Inheritance diagram of bluemira.geometry.parameterisations.PrincetonD

Princeton D geometry parameterisation, with n_TF = ∞.

Parameters:

var_dict (bluemira.utilities.opt_variables.VarDictT | None) – Dictionary with which to update the default values of the parameterisation.

Notes

../../../../_images/index-1.svg

The dictionary keys in var_dict are:

x1: float

Radial position of inner limb [m]

x2: float

Radial position of outer limb [m]

dz: float

Vertical offset from z=0 [m]

__slots__ = ()
n_ineq_constraints: int = 1

Number of inequality constraints in the GeometryParameterisation

create_shape(label: str = '', n_points: int = 2000, *, with_tangency: bool = False) → bluemira.geometry.wire.BluemiraWire

Make a CAD representation of the Princeton D.

Parameters:

  • label (str) – Label to give the wire

  • n_points (int) – The number of points to use when calculating the geometry of the Princeton D.

  • with_tangency (bool)

Return type:

CAD Wire of the geometry

f_ineq_constraint() → numpy.typing.NDArray[numpy.float64]

Inequality constraint for PrincetonD.

Returns:

Inequality constraint for PrincetonD.

Return type:

numpy.typing.NDArray[numpy.float64]

df_ineq_constraint() → numpy.typing.NDArray[numpy.float64]

Inequality constraint gradient for PrincetonD.

Returns:

Inequality constraint gradient for PrincetonD.

Return type:

numpy.typing.NDArray[numpy.float64]

class bluemira.geometry.parameterisations.PrincetonDDiscrete(var_dict: bluemira.utilities.opt_variables.VarDictT | None = None, n_TF: int | None = None, tf_wp_width: float | None = None, tf_wp_depth: float | None = None, n_points: int = 50, tolerance: float = 0.001)

Bases: PrincetonD

Inheritance diagram of bluemira.geometry.parameterisations.PrincetonDDiscrete

Princeton D geometry parameterisation, with finite n_TF.

Parameters:

  • var_dict (bluemira.utilities.opt_variables.VarDictT | None) – Dictionary with which to update the default values of the parameterisation.

  • n_TF (int | None)

  • tf_wp_width (float | None)

  • tf_wp_depth (float | None)

  • n_points (int)

  • tolerance (float)

Raises:

GeometryParameterisationError – If n_TF is specified, tf_wp_width and tf_wp_depth must also be specified.

Notes

../../../../_images/index-2.svg

Fig. 42 Princeton D at finite n_TF

The dictionary keys in var_dict are:

x1: float

Radial position of inner limb [m]

x2: float

Radial position of outer limb [m]

dz: float

Vertical offset from z=0 [m]

Please note, when using this shape as a sweep path, you must use frenet=False. This is because of limitations in CAD, which we are trying to resolve. See #4267

__slots__ = ('_n_TF', '_n_points', '_tf_wp_depth', '_tf_wp_width', '_tolerance')
n_ineq_constraints: int = 1

Number of inequality constraints in the GeometryParameterisation

_n_TF = None
_tf_wp_width = None
_tf_wp_depth = None
_n_points = 50
_tolerance = 0.001
create_shape(label: str = '', n_points: int | None = None, *, tolerance: float | None = None, with_tangency: bool = False) → bluemira.geometry.wire.BluemiraWire

Make a CAD representation of the Princeton D.

Parameters:

  • label (str) – Label to give the wire

  • n_points (int | None) – The number of points to use when calculating the geometry of the Princeton D.

  • tolerance (float | None)

  • with_tangency (bool)

Return type:

CAD Wire of the geometry

Raises:

GeometryParameterisationError – If x2 <= x1

class bluemira.geometry.parameterisations.TripleArc(var_dict: bluemira.utilities.opt_variables.VarDictT | None = None)

Bases: GeometryParameterisation[TripleArcOptVaribles]

Inheritance diagram of bluemira.geometry.parameterisations.TripleArc

Triple-arc up-down symmetric geometry parameterisation.

Parameters:

var_dict (bluemira.utilities.opt_variables.VarDictT | None) – Dictionary with which to update the default values of the parameterisation.

Notes

../../../../_images/index-3.svg

Source: [doi:10.12688/f1000research.28224.1](https://doi.org/10.12688/f1000research.28224.1)

The dictionary keys in var_dict are:

x1: float

Radial position of inner limb [m]

dz: float

Vertical offset from z=0 [m]

sl: float

Length of inboard straigh section [m]

f1: float

radii of top and bottom left arc [m]

f2: float

radii of top and bottom middle arc [m]

a1: float

top left and bottom left arc angle [degrees]

a2: float

top middle and bottom middle arc angle [degrees]

__slots__ = ()
n_ineq_constraints: int = 1

Number of inequality constraints in the GeometryParameterisation

f_ineq_constraint() → numpy.typing.NDArray[numpy.float64]

Inequality constraint for TripleArc.

Constrain such that a1 + a2 is less than or equal to 180 degrees.

Returns:

Inequality constraint for TripleArc.

Return type:

numpy.typing.NDArray[numpy.float64]

df_ineq_constraint() → numpy.typing.NDArray[numpy.float64]

Inequality constraint gradient for TripleArc.

Returns:

Inequality constraint gradient for TripleArc.

Return type:

numpy.typing.NDArray[numpy.float64]

create_shape(label: str = '') → bluemira.geometry.wire.BluemiraWire

Make a CAD representation of the triple arc.

Parameters:

label (str) – Label to give the wire

Return type:

CAD Wire of the geometry

_label_function(ax: matplotlib.pyplot.Axes, shape: bluemira.geometry.wire.BluemiraWire) → tuple[float, float]

Adds labels to parameterisation plots

Parameters:
Returns:

Labels to parameterisation plots.

Return type:

tuple[float, float]

class bluemira.geometry.parameterisations.SextupleArc(var_dict: bluemira.utilities.opt_variables.VarDictT | None = None)

Bases: GeometryParameterisation[SextupleArcOptVariables]

Inheritance diagram of bluemira.geometry.parameterisations.SextupleArc

Sextuple-arc up-down asymmetric geometry parameterisation.

Parameters:

var_dict (bluemira.utilities.opt_variables.VarDictT | None) – Dictionary with which to update the default values of the parameterisation.

Notes

../../../../_images/index-4.svg

The dictionary keys in var_dict are:

x1: float

Radial position of inner limb [m]

z1: float

Inboard limb height [m]

r1 - r5: float

arc radius [m]

a1 - a5: float

arc angle [degrees]

__slots__ = ()
n_ineq_constraints: int = 1

Number of inequality constraints in the GeometryParameterisation

f_ineq_constraint() → numpy.typing.NDArray[numpy.float64]

Inequality constraint for SextupleArc.

Constrain such that sum of the 5 angles is less than or equal to 360 degrees.

Returns:

Inequality constraint for SextupleArc.

Return type:

numpy.typing.NDArray[numpy.float64]

df_ineq_constraint() → numpy.typing.NDArray[numpy.float64]

Inequality constraint gradient for SextupleArc.

Returns:

Inequality constraint gradient for SextupleArc.

Return type:

numpy.typing.NDArray[numpy.float64]

create_shape(label: str = '') → bluemira.geometry.wire.BluemiraWire

Make a CAD representation of the sextuple arc.

Parameters:

label (str) – Label to give the wire

Return type:

CAD Wire of the geometry

_label_function(ax: matplotlib.pyplot.Axes, shape: bluemira.geometry.wire.BluemiraWire)

Adds labels to parameterisation plots

Parameters:
class bluemira.geometry.parameterisations.PolySpline(var_dict: bluemira.utilities.opt_variables.VarDictT | None = None)

Bases: GeometryParameterisation[PolySplineOptVariables]

Inheritance diagram of bluemira.geometry.parameterisations.PolySpline

Simon McIntosh’s Poly-Bézier-spline geometry parameterisation (19 variables).

Parameters:

var_dict (bluemira.utilities.opt_variables.VarDictT | None) – Dictionary with which to update the default values of the parameterisation.

Notes

../../../../_images/index-5.svg

The dictionary keys in var_dict are:

x1: float

Radial position of inner limb [m]

x2: float

Radial position of outer limb [m]

z2: float

Outer note vertical shift [m]

height: float

Full height [m]

top: float

Horizontal shift []

upper: float

Vertical shift []

dz: float

Vertical offset [m]

flat: float

Fraction of straight outboard leg []

tilt: float

Outboard angle [degrees]

bottom: float

Lower horizontal shift []

lower: float

Lower vertical shift []

l0s - l3s: float

Tension variable segment start

l0e - l3e: float

Tension variable segment end

Tension variables control how strictly the spline adheres to the initialisation points. Low tension makes the splines smoother.

__slots__ = ()
create_shape(label: str = '') → bluemira.geometry.wire.BluemiraWire

Make a CAD representation of the poly spline.

Parameters:

label (str) – Label to give the wire

Return type:

CAD Wire of the geometry

static _make_control_points(p0: list[float], p3: list[float], theta0: list[float], theta3: list[float], l_start: float, l_end: float) → tuple[numpy.typing.NDArray[numpy.float64], numpy.typing.NDArray[numpy.float64]]

Make 2 Bézier spline control points between two vertices.

Returns:

Two Bézier spline control points.

Parameters:

  • p0 (list[float])

  • p3 (list[float])

  • theta0 (list[float])

  • theta3 (list[float])

  • l_start (float)

  • l_end (float)

Return type:

tuple[numpy.typing.NDArray[numpy.float64], numpy.typing.NDArray[numpy.float64]]

static _get_annotator_offset_z(shape: bluemira.geometry.wire.BluemiraWire, x_value: float) → float

Gives the z-offset for the annotator.

Returns:

z-Offset for the annotator.

Return type:

float

Parameters:
_label_function(ax: matplotlib.pyplot.Axes, shape: bluemira.geometry.wire.BluemiraWire)

Adds labels to parameterisation plots

Parameters:
class bluemira.geometry.parameterisations.PictureFrameTools

Tools Class containing methods to produce various PictureFrame variant limbs.

static _make_domed_leg(x_out: float, x_curve_start: float, x_mid: float, z_top: float, z_mid: float, ri: float, axis: collections.abc.Iterable[float] = (0, -1, 0), *, flip: bool = False) → bluemira.geometry.wire.BluemiraWire

Makes smooth dome for CP coils. This includes a initial straight section and a main curved dome section, with a transitioning ‘joint’ between them, producing smooth tangent curves.

Parameters:

  • x_out (float) – Radial position of outer edge of limb [m]

  • x_curve_start (float) – Radial position of straight-curve transition of limb [m]

  • x_mid (float) – Radial position of inner edge of upper/lower limb [m]

  • z_top (float) – Vertical position of top of limb dome [m]

  • z_mid (float) – Vertical position of flat section [m]

  • ri (float) – Radius of inner corner transition. Nominally 0 [m]

  • axis (collections.abc.Iterable[float]) – [x,y,z] vector normal to plane of parameterisation

  • flip (bool) – True if limb is lower limb of section, False if upper

Return type:

CAD Wire of the geometry

static _make_flat_leg(x_mid: float, x_out: float, z: float, r_i: float, r_o: float, axis: collections.abc.Iterable[float] = (0, 1, 0), *, flip: bool = False) → bluemira.geometry.wire.BluemiraWire

Makes a flat leg (top/bottom limb) with the option of one end rounded.

Parameters:

  • x_mid (float) – Radial position of inner edge of limb [m]

  • x_out (float) – Radial position of outer edge of limb [m]

  • z (float) – Vertical position of limb [m]

  • r_i (float) – Radius of inner corner [m]

  • r_o (float) – Radius of outer corner [m]

  • axis (collections.abc.Iterable[float]) – [x,y,z] vector normal to plane of parameterisation

  • flip (bool) – True if limb is lower limb of section, False if upper

Return type:

CAD Wire of the geometry

static _make_tapered_inner_leg(x_in: float, x_mid: float, z_bot: float, z_taper: float, z_top: float, r_min: float, axis: tuple[float, float, float] = (0, 1, 0)) → bluemira.geometry.wire.BluemiraWire

Makes a tapered inboard leg using a circle arc taper, symmetric about the midplane with the tapering beginning at a certain height and reaching a maximum taper at the midplane.

Parameters:

  • x_in (float) – Radial position of innermost point of limb [m]

  • x_mid (float) – Radial position of outer edge of limb [m]

  • z_bot (float) – Vertical position of bottom of limb [m]

  • z_taper (float) – Vertical position of start of tapering [m]

  • z_top (float) – Vertical position of top of limb [m]

  • r_min (float) – Minimum radius of curvature [m]

  • axis (tuple[float, float, float]) – [x,y,z] vector normal to plane of parameterisation

Return type:

CAD Wire of the geometry

Raises:

GeometryParameterisationError – Input parameters cannot create shape

_connect_to_outer_limb(top, bottom, *, top_curve: bool = False, bot_curve: bool = False) → bluemira.geometry.wire.BluemiraWire
Parameters:

  • top_curve (bool)

  • bot_curve (bool)

Return type:

bluemira.geometry.wire.BluemiraWire

_connect_straight_to_inner_limb(top: numpy.typing.NDArray[numpy.float64], bottom: numpy.typing.NDArray[numpy.float64]) → bluemira.geometry.wire.BluemiraWire
Parameters:

  • top (numpy.typing.NDArray[numpy.float64])

  • bottom (numpy.typing.NDArray[numpy.float64])

Return type:

bluemira.geometry.wire.BluemiraWire

static _inner_limb(p1: numpy.typing.NDArray[numpy.float64], p2: numpy.typing.NDArray[numpy.float64]) → bluemira.geometry.wire.BluemiraWire
Parameters:

  • p1 (numpy.typing.NDArray[numpy.float64])

  • p2 (numpy.typing.NDArray[numpy.float64])

Return type:

bluemira.geometry.wire.BluemiraWire

static _outer_limb(p1: numpy.typing.NDArray[numpy.float64], p2: numpy.typing.NDArray[numpy.float64]) → bluemira.geometry.wire.BluemiraWire
Parameters:

  • p1 (numpy.typing.NDArray[numpy.float64])

  • p2 (numpy.typing.NDArray[numpy.float64])

Return type:

bluemira.geometry.wire.BluemiraWire

class bluemira.geometry.parameterisations.PFrameSection(*args, **kwds)

Bases: enum.Enum

Inheritance diagram of bluemira.geometry.parameterisations.PFrameSection

Picture Frame sections

CURVED
FLAT
TAPERED_INNER
__call__(*args, **kwargs)

Call linked function on access

Returns:

Linked function.

class bluemira.geometry.parameterisations.PictureFrame(var_dict: bluemira.utilities.opt_variables.VarDictT | None = None, *, upper: str | PFrameSection = PFrameSection.FLAT, lower: str | PFrameSection = PFrameSection.FLAT, inner: str | PFrameSection | None = None)

Bases: GeometryParameterisation[PictureFrameOptVariables], PictureFrameTools

Inheritance diagram of bluemira.geometry.parameterisations.PictureFrame

Picture-frame geometry parameterisation.

Parameters:

  • var_dict (bluemira.utilities.opt_variables.VarDictT | None) – Dictionary with which to update the default values of the parameterisation.

  • upper (str | PFrameSection)

  • lower (str | PFrameSection)

  • inner (str | PFrameSection | None)

Notes

../../../../_images/index-6.svg

The base dictionary keys in var_dict are:

x1: float

Radial position of inner limb [m]

x2: float

Radial position of outer limb [m]

z1: float

Vertical position of top limb [m]

z2: float

Vertical position of top limb [m]

ri: float

Radius of inner corners [m]

ro: float

Radius of outer corners [m]

For curved pictures frames ‘ro’ is ignored on curved sections but there are additional keys:

z1_peak: float

Vertical position of top of limb dome [m]

z2_peak: float

Vertical position of top of limb dome [m]

x3: float

The radius to start the dome curve [m]

For tapered inner leg the additional keys are:

x4: float

Radial position of outer limb [m]

z3: float

Vertical position of top of tapered section [m]

__slots__
upper
lower
inner = None
__deepcopy__(memo) → PictureFrame

Picture Frame deepcopy

Returns:

Deepcopy of Picture Frame.

Return type:

PictureFrame

create_shape(label: str = '') → bluemira.geometry.wire.BluemiraWire

Make a CAD representation of the picture frame.

Parameters:

label (str) – Label to give the wire

Return type:

CAD Wire of the Picture Frame geometry

_make_inb_leg() → bluemira.geometry.wire.BluemiraWire
Return type:

bluemira.geometry.wire.BluemiraWire

_make_upper_lower_leg(*, make_upper_section: bool, flip: bool) → PFrameSection
Parameters:

  • make_upper_section (bool)

  • flip (bool)

Return type:

PFrameSection

_make_out_leg(top_leg: PFrameSection, bot_leg: PFrameSection) → bluemira.geometry.wire.BluemiraWire
Parameters:
Return type:

bluemira.geometry.wire.BluemiraWire

_label_function(ax, shape)

Adds labels to parameterisation plots

Parameters:

  • ax – Matplotlib axis instance

  • shape – parameterisation wire

Returns:

  • offset_ar_x – Suggested location for where to plot the next set of labels related to the radii in the parameterisation. (z-coordinates only)

  • offset_ar_z – Suggested location for where to plot the next set of labels related to the height in the parameterisation. (x-coordinates only)