ConicCoordinateSystem

class coordinates.coordinate_systems.ConicCoordinateSystem(**kwargs)

3 Dimensional Conic coordinate system.

The conic coordinate system is a 3D orthogonal coordinate system derived from intersecting conical surfaces. It is defined by coordinates \((\mu, \nu, \phi)\), where:

• \(\mu \in (0, \pi)\) is the angle between a point and a reference axis

• \(\nu \in (0, \pi)\) is the angle from a second family of intersecting cones

• \(\phi \in [0, 2\pi)\) is the azimuthal angle (rotation around the z-axis)

The Cartesian coordinates are given by:

\[ \begin{align}\begin{aligned}x = a \frac{\sin(\mu) \sin(\nu)}{\cos(\mu) - \cos(\nu)} \cos(\phi)\\y = a \frac{\sin(\mu) \sin(\nu)}{\cos(\mu) - \cos(\nu)} \sin(\phi)\\z = a \frac{\sin(\mu + \nu)}{\cos(\mu) - \cos(\nu)}\end{aligned}\end{align} \]

Parameters:

a (float) – Focal distance parameter, must be nonzero.

Methods

__init__(**kwargs)	Initialize a coordinate system instance with specific parameter values.
adjust_dense_tensor_signature(tensor_field, ...)	Raise and/or lower multiple tensor slots in one call.
axes_complement(axes)	Return all axes in the coordinate system that are not present in axes.
build_axes_mask(axes)	Construct a boolean mask array indicating which axes are in axes.
compute_expression(expression, coordinates)	Evaluate a named symbolic expression over mixed coordinate inputs.
compute_expression_from_coordinates(...[, ...])	Evaluate a named expression over 1D coordinate arrays with optional fixed axes.
compute_function_from_coordinates(func, ...)	Evaluate a function over 1D coordinate arrays with optional fixed axes.
convert_axes_to_indices(axes)	Convert axis name(s) to their corresponding index or indices.
convert_indices_to_axes(axes_indices)	Convert axis index or indices to their corresponding axis name(s).
convert_to(target_system, *native_coords)	Convert coordinates from this system to another coordinate system via Cartesian intermediate.
coordinate_meshgrid(*coordinate_arrays[, ...])	Construct a coordinate-aligned meshgrid from 1D coordinate arrays.
create_coordinate_list(coordinate_arrays, /)	Assemble a list of coordinate components (arrays or scalars) in canonical axis order.
from_cartesian(*coords)	Convert Cartesian coordinates to native coordinates in this system.
from_hdf5(filename[, group_name, registry])	Save this coordinate system to HDF5.
get_axes_from_mask(mask)	Convert a boolean axis mask into a list of axis names.
get_axes_latex(axes)	Return the LaTeX representation(s) of one or more axis names.
get_axes_order(src_axes, dst_axes)	Compute the reordering indices that will reorder src_axes into the order of dst_axes.
get_axes_permutation(src_axes, dst_axes)	Compute the permutation needed to reorder src_axes into dst_axes.
get_axes_units(unit_system)	Resolve the physical units for each axis in a given unit system.
get_canonical_axes_order(src_axes)	Compute the permutation indices to reorder src_axes into sorted alphabetical order.
get_canonical_axes_permutation(axes)	Compute the permutation needed to reorder axes into the canonical order defined by the coordinate system.
get_class_expression(expression_name)	Retrieve a derived expression for this coordinate system by name.
get_conversion_transform(other)	Construct a coordinate transformation function that maps native coordinates from this coordinate system to the target coordinate system.
get_expression(expression_name)	Retrieve an instance-specific symbolic expression.
get_free_fixed([axes, fixed_axes])	Split a list of coordinate axes into fixed and free components.
get_indices_from_mask(mask)	Convert a boolean mask of length ndim back to numeric indices.
get_mask_from_axes(axes)	Return a boolean mask of shape (ndim,) with True on the positions corresponding to axes.
get_mask_from_indices(indices)	Boolean mask that is True at the supplied numeric indices.
get_numeric_expression(expression_name)	Retrieve a numerically evaluable version of a coordinate system expression given the expression name.
has_class_expression(expression_name)	Check if the coordinate system has a specific expression registered to it.
has_expression(expression_name)	Check if a symbolic expression is registered at the instance level.
in_axes_order(iterable, src_axes, dst_axes)	Reorder a sequence of values from src_axes order to dst_axes order.
in_canonical_order(iterable, src_axes)	Reorder a sequence of values from src_axes order to canonical axis order.
insert_fixed_axes(iterable, src_axes[, ...])	Insert fixed axis values into an iterable of values according to canonical axis order.
is_axes_subset(axes_a, axes_b)	Check if axes_a is a subset of axes_b.
is_axes_superset(axes_a, axes_b)	Check if axes_a is a superset of axes_b.
is_axis(axis)	Check whether the given axis name(s) exist in this coordinate system.
lambdify_expression(expression)	Convert a symbolic expression into a callable function.
list_class_expressions()	List the available coordinate system expressions.
list_expressions()	List the available instance-level expressions.
lower_index_dense(tensor_field, index, rank, ...)	Lower a single tensor index using \(g_{ab}\).
order_axes(src_axes, dst_axes)	Reorder src_axes into the order defined by dst_axes.
order_axes_canonical(src_axes)	Reorder a list of axis names into the canonical order of this coordinate system.
pprint()	Print a detailed description of the coordinate system, including its axes, parameters, and expressions.
raise_index_dense(tensor_field, index, rank, ...)	Raise a single tensor index using \(g^{ab}\).
requires_expression(value, expression, ...)	Return value if not None; otherwise evaluate compute_expression.
requires_expression_from_coordinates(value, ...)	Return value if not None; otherwise evaluate compute_expression_from_coordinates.
resolve_axes([axes, require_subset, ...])	Normalize and validate a user-supplied list of axis names.
set_expression(expression_name, expression)	Set a symbolic expression at the instance level.
substitute_expression(expression)	Replace symbolic parameters with numerical values in an expression.
to_cartesian(*coords)	Convert native coordinates to Cartesian coordinates.
to_hdf5(filename[, group_name, overwrite])	Save this coordinate system to HDF5.

Attributes

axes	The axes names present in this coordinate system.
axes_dimensions	Return the symbolic physical dimensions associated with each axis.
axes_symbols	The symbols representing each of the coordinate axes in this coordinate system.
inverse_metric_tensor	Returns the callable function for the inverse metric tensor of the coordinate system.
inverse_metric_tensor_symbol	The symbolic inverse metric tensor for this coordinate system instance.
metric_tensor	Returns the callable function for the metric tensor of the coordinate system.
metric_tensor_symbol	The symbolic array representing the metric tensor.
ndim	The number of dimensions spanned by this coordinate system.
parameter_symbols	Get the symbolic representations of the coordinate system parameters.
parameters	The parameters of this coordinate system.