puncturedfem.ClosedContour

List of edges forming a closed contour.

Assumed to be simple with edges listed successively.

Attributes:

Name	Type	Description
`edges`	`list[Edge]`	List of edges forming the contour.
`num_edges`	`int`	Number of edges in the contour.
`edge_orient`	`list[int]`	List of orientations of the edges, where +1 indicates the edge is oriented in the same direction as the contour and -1 indicates the edge is oriented in the opposite direction.
`interior_point`	`Vert`	A point in the interior of the contour.
`num_pts`	`int`	Number of sampled points on the contour.
`vert_idx`	`list[int]`	Index of the starting point of each edge.
`local_vert_idx`	`list[int]`	Index of the starting point of each edge, relative to the edge.
`closest_vert_idx`	`np.ndarray`	Index of the closest vertex for each sampled point on the contour.

`init(cell_id, edges=None, edge_orients=None)`

Initialize a ClosedContour object.

Parameters:

Name	Type	Description	Default
`cell_id`	`int`	The MeshCell id of the contour. (This is the MeshCell id of the MeshCell that the contour is part of the boundary of.)	required
`edges`	`Optional[list[Edge]]`	List of edges forming the contour.	`None`
`edge_orients`	`Optional[list[int]]`	List of orientations of the edges, where +1 indicates the edge is oriented in the same direction as the contour and -1 indicates the edge is oriented in the opposite direction.	`None`

`add_edge(e, edge_orient)`

Add an edge to the contour.

Parameters:

Name	Type	Description	Default
`e`	`Edge`	The edge to add to the contour.	required
`edge_orient`	`int`	Orientation of the edge, where +1 indicates the edge is oriented in the same direction as the contour and -1 indicates the edge is oriented in the opposite direction.	required

`add_edges(edges, edge_orients)`

Add a list of edges to contour.

Parameters:

Name	Type	Description	Default
`edges`	`list[Edge]`	List of edges to add to the contour.	required
`edge_orients`	`list[int]`	List of orientations of the edges, where +1 indicates the edge is oriented in the same direction as the contour and -1 indicates the edge is oriented in the opposite direction.	required

Raises:

Type	Description
`ValueError`	If the number of edges and orientations do not match.

`deparameterize()`

Delete the sampled points of the edges comprising the contour.

`dot_with_normal(comp1, comp2)`

Return the dot product (comp1, comp2) * unit_normal.

Parameters:

Name	Type	Description	Default
`comp1`	`np.ndarray`	First component of the vector to dot with the normal.	required
`comp2`	`np.ndarray`	Second component of the vector to dot with the normal.	required

Returns:

Type	Description
`numpy.ndarray`	Array of dot products (comp1, comp2) * unit_normal for each sampled point on the contour, having the same length as the number of sampled points on the contour.

Raises:

Type	Description
`NotParameterizedError`	If the edges have not been sampled.

`dot_with_tangent(comp1, comp2)`

Return the dot product (comp1, comp2) * unit_tangent.

Parameters:

Name	Type	Description	Default
`comp1`	`np.ndarray`	First component of the vector to dot with the tangent.	required
`comp2`	`np.ndarray`	Second component of the vector to dot with the tangent.	required

Returns:

Type	Description
`numpy.ndarray`	Array of dot products (comp1, comp2) * unit_tangent for each sampled point on the contour, having the same length as the number of sampled points on the contour.

Raises:

Type	Description
`NotParameterizedError`	If the edges have not been sampled.

`evaluate_function_on_contour(fun)`

Return fun(x) for each sampled point on contour.

Parameters:

Name	Type	Description	Default
`fun`	`Func_R2_R`	Function of two real variables returning a real value.	required

Returns:

Type	Description
`numpy.ndarray`	Array of function values at each sampled point on the contour, having the same length as the number of sampled points on the contour.

`find_closest_local_vertex_index()`

Determine the index of the nearest index.

Specifically determine the sampled point index of the starting point of the closest vertex to each sampled point on the contour. Stores the result in the attribute closest_vert_idx.

Raises:

Type	Description
`NotParameterizedError`	If the edges have not been sampled.

`find_interior_point()`

Find a single point in the interior of the contour.

Stores the result in the attribute interior_point.

Raises:

Type	Description
`NotParameterizedError`	If the edges have not been sampled.
`InteriorPointError`	If an interior point cannot be found.

`find_local_vert_idx()`

Determine the sampled point index of the starting point of each edge.

Stores the result in the attribute vert_idx.

Raises:

Type	Description
`NotParameterizedError`	If the edges have not been sampled.

`find_num_pts()`

Determine the total number of sampled points on the contour.

This is the sum of the number of sampled points on each edge, neglecting the last point on each edge (since it is repeated on the next edge). Stores the result in the attribute num_pts.

Raises:

Type	Description
`NotParameterizedError`	If the edges have not been sampled.

`get_distance_to_boundary(x, y)`

Get the minimum distance to sampled points on the contour.

Parameters:

Name	Type	Description	Default
`x`	`float`	x-coordinate of the point.	required
`y`	`float`	y-coordinate of the point.	required

Returns:

Type	Description
`float`	The minimum distance to the contour.

Raises:

Type	Description
`NotParameterizedError`	If the edges have not been sampled.

`get_sampled_points()`

Return the x1 and x2 coordinates of the boundary points.

Returns:

Type	Description
`tuple[numpy.ndarray, numpy.ndarray]`	Tuple containing the x1 and x2 coordinates of the boundary points.

Raises:

Type	Description
`NotParameterizedError`	If the edges have not been sampled.

`integrate_over_closed_contour(vals)`

Quadrature to approximate the integral of vals over the contour.

Parameters:

Name	Type	Description	Default
`vals`	`np.ndarray`	Array of values to integrate over the contour, having the same length as the number of sampled points on the contour.	required

Returns:

Type	Description
`float`	Approximation of the integral of vals over the contour.

`integrate_over_closed_contour_preweighted(vals_dx_norm)`

Quadrature to approximate the integral of vals over the contour.

Assumes vals_dx_norm is already multiplied by the norm of the derivative of the curve parameterization.

Parameters:

Name	Type	Description	Default
`vals_dx_norm`	`np.ndarray`	Array of values to integrate over the contour, already multiplied by the norm of the derivative of the curve parameterization.	required

Returns:

Type	Description
`float`	Approximation of the integral of val over the contour.

Raises:

Type	Description
`NotParameterizedError`	If the edges have not been sampled.
`SizeMismatchError`	If vals_dx_norm is not a vector or is not the same length as the number of sampled points on the contour.

`is_in_interior_contour(x, y)`

Return which points lie in the interior of the contour.

Return a boolean array indicating whether each point (x[i], y[i]) is inside the contour.

Parameters:

Name	Type	Description	Default
`x`	`np.ndarray`	x-coordinates of the points.	required
`y`	`np.ndarray`	y-coordinates of the points.	required

Returns:

Type	Description
`numpy.ndarray`	Boolean array indicating whether each point is inside the contour, having the same shape as x and y.

Raises:

Type	Description
`SizeMismatchError`	If x and y do not have the same shape.

`is_parameterized()`

Check if the edges of the contour have been sampled.

Returns:

Type	Description
`bool`	True if all edges are parameterized, False otherwise.

`multiply_by_dx_norm(vals)`

Return vals multiplied by the norm of the derivative of the curve.

Returns f multiplied against the norm of the derivative of the curve parameterization.

Parameters:

Name	Type	Description	Default
`vals`	`np.ndarray`	Array of values to multiply by the norm of the derivative of the curve parameterization.	required

Returns:

Type	Description
`numpy.ndarray`	Array of values multiplied by the norm of the derivative of the curve parameterization, having the same length as the number of sampled points on the contour.

Raises:

Type	Description
`NotParameterizedError`	If the edges have not been sampled.

`parameterize(quad_dict)`

Sample each edge of the contour.

Parameters:

Name	Type	Description	Default
`quad_dict`	`QuadDict`	Dictionary of quadrature rules.	required

`set_mesh_id(cell_id)`

Set the cell_id of the contour.

This is the global index of the MeshCell that the contour is part of the boundary of.

Parameters:

Name	Type	Description	Default
`cell_id`	`int`	The MeshCell id of the contour.	required

Raises:

Type	Description
`TypeError`	If cell_id is not a positive integer.

puncturedfem.ClosedContour

__init__(cell_id, edges=None, edge_orients=None)

add_edge(e, edge_orient)

add_edges(edges, edge_orients)

deparameterize()

dot_with_normal(comp1, comp2)

dot_with_tangent(comp1, comp2)

evaluate_function_on_contour(fun)

find_closest_local_vertex_index()

find_interior_point()

find_local_vert_idx()

find_num_pts()

get_distance_to_boundary(x, y)

get_sampled_points()

integrate_over_closed_contour(vals)

integrate_over_closed_contour_preweighted(vals_dx_norm)

is_in_interior_contour(x, y)

is_parameterized()

multiply_by_dx_norm(vals)

parameterize(quad_dict)

set_mesh_id(cell_id)

`init(cell_id, edges=None, edge_orients=None)`

`add_edge(e, edge_orient)`

`add_edges(edges, edge_orients)`

`deparameterize()`

`dot_with_normal(comp1, comp2)`

`dot_with_tangent(comp1, comp2)`

`evaluate_function_on_contour(fun)`

`find_closest_local_vertex_index()`

`find_interior_point()`

`find_local_vert_idx()`

`find_num_pts()`

`get_distance_to_boundary(x, y)`

`get_sampled_points()`

`integrate_over_closed_contour(vals)`

`integrate_over_closed_contour_preweighted(vals_dx_norm)`

`is_in_interior_contour(x, y)`

`is_parameterized()`

`multiply_by_dx_norm(vals)`

`parameterize(quad_dict)`

`set_mesh_id(cell_id)`