regions

regions

Region classes for the cxregions package.

This module contains all region-related classes including the base JuliaRegion class and specific region types like Interior1CRegion, Exterior1CRegion, and Annulus.

Attributes

Name	Description
lefthalfplane	Left half-plane region (Re(z) < 0).
lowerhalfplane	Lower half-plane region (Im(z) < 0).
righthalfplane	Right half-plane region (Re(z) > 0).
unitdisk	Unit disk region (|z| < 1).
upperhalfplane	Upper half-plane region (Im(z) > 0).

Classes

Name	Description
Annulus	An annulus (ring-shaped region) between two circles.
Exterior1CRegion	Simply connected exterior region.
ExteriorRegion	Exterior region with multiple inner boundaries.
Interior1CRegion	Simply connected interior region.
InteriorConnectedRegion	Multiply connected interior region.
JuliaRegion	Base class for wrapping Julia region objects from ComplexRegions.jl.

Annulus

regions.Annulus(outer, inner=None, center=0j)

An annulus (ring-shaped region) between two circles.

This represents the region between an inner and outer circle.

Parameters

Name	Type	Description	Default
outer	float, Circle, or juliacall.AnyValue	Outer radius, outer circle, or Julia Annulus object	required
inner	float or Circle	Inner radius or inner circle	None
center	complex	Center point (if constructing from radii), default is 0	0j

Attributes

Name	Type	Description
inner	Circle	Inner boundary circle
outer	Circle	Outer boundary circle

Examples

>>> # Annulus from radii
>>> annulus1 = Annulus(2, 1, center=0)
>>> # Annulus from circles
>>> from cxregions.curves import Circle
>>> inner_circle = Circle(0, 1)
>>> outer_circle = Circle(0, 2)
>>> annulus2 = Annulus(outer_circle, inner_circle)

Methods

Name	Description
isfinite	Check if the annulus is finite.
modulus	Compute the modulus of the annulus.

isfinite

regions.Annulus.isfinite()

Check if the annulus is finite.

Returns

Name	Type	Description
	bool	Always returns True for annuli

modulus

regions.Annulus.modulus()

Compute the modulus of the annulus.

Returns

Name	Type	Description
	float	The modulus (related to the ratio of radii)

Exterior1CRegion

regions.Exterior1CRegion(boundary)

Simply connected exterior region.

This represents the region outside a single closed curve, extending to infinity.

Parameters

Name	Type	Description	Default
boundary	ClosedCurve, ClosedPath, or juliacall.AnyValue	The boundary curve of the region	required

Attributes

Name	Type	Description
boundary	ClosedCurve or ClosedPath	The boundary curve of the region

Examples

>>> from cxregions.curves import Circle
>>> circle = Circle(0, 1)
>>> exterior = Exterior1CRegion(circle)

Methods

Name	Description
isfinite	Check if the region is finite.

isfinite

regions.Exterior1CRegion.isfinite()

Check if the region is finite.

Returns

Name	Type	Description
	bool	True if the boundary is finite, False otherwise

ExteriorRegion

regions.ExteriorRegion(inner)

Exterior region with multiple inner boundaries.

This represents the region outside multiple closed curves, extending to infinity.

Parameters

Name	Type	Description	Default
inner	list of ClosedCurve/ClosedPath or juliacall.AnyValue	The inner boundary curves	required

Attributes

Name	Type	Description
inner	list of ClosedCurve/ClosedPath	The inner boundary curves

Examples

>>> from cxregions.curves import Circle
>>> circle1 = Circle(0, 1)
>>> circle2 = Circle(3, 0.5)
>>> exterior = ExteriorRegion([circle1, circle2])

Methods

Name	Description
isfinite	Check if the region is finite.

isfinite

regions.ExteriorRegion.isfinite()

Check if the region is finite.

Returns

Name	Type	Description
	bool	Always returns False for exterior regions

Interior1CRegion

regions.Interior1CRegion(boundary)

Simply connected interior region.

This represents the region inside a single closed curve.

Parameters

Name	Type	Description	Default
boundary	ClosedCurve, ClosedPath, or juliacall.AnyValue	The boundary curve of the region	required

Attributes

Name	Type	Description
boundary	ClosedCurve or ClosedPath	The boundary curve of the region

Examples

>>> from cxregions.curves import Circle
>>> circle = Circle(0, 1)
>>> interior = Interior1CRegion(circle)

Methods

Name	Description
isfinite	Check if the region is finite.

isfinite

regions.Interior1CRegion.isfinite()

Check if the region is finite.

Returns

Name	Type	Description
	bool	True if the boundary is finite, False otherwise

InteriorConnectedRegion

regions.InteriorConnectedRegion(outer, inner=[])

Multiply connected interior region.

This represents the region inside an outer boundary but outside inner boundaries.

Parameters

Name	Type	Description	Default
outer	ClosedCurve, ClosedPath, or juliacall.AnyValue	The outer boundary curve	required
inner	list of ClosedCurve/ClosedPath	The inner boundary curves (holes)	[]

Attributes

Name	Type	Description
outer	ClosedCurve or ClosedPath	The outer boundary curve
inner	list of ClosedCurve/ClosedPath	The inner boundary curves

Examples

>>> from cxregions.curves import Circle
>>> outer_circle = Circle(0, 2)
>>> inner_circle = Circle(0, 1)
>>> region = InteriorConnectedRegion(outer_circle, [inner_circle])

Methods

Name	Description
isfinite	Check if the region is finite.

isfinite

regions.InteriorConnectedRegion.isfinite()

Check if the region is finite.

Returns

Name	Type	Description
	bool	True if all boundaries are finite, False otherwise

JuliaRegion

regions.JuliaRegion(julia_obj)

Base class for wrapping Julia region objects from ComplexRegions.jl.

This class provides a Python interface to Julia region objects, which represent areas in the complex plane bounded by curves.

Parameters

Name	Type	Description	Default
julia_obj	juliacall.AnyValue	A Julia region object from ComplexRegions.jl	required

Attributes

Name	Type	Description
julia	juliacall.AnyValue	The underlying Julia region object

Methods

Name	Description
contains	Check if a point is contained in the region.
get	Get a field from the underlying Julia object.
innerboundary	Get the inner boundary curves of the region.
intersect	Compute the intersection of this region with another.
outerboundary	Get the outer boundary curves of the region.
union	Compute the union of this region with another.

contains

regions.JuliaRegion.contains(z=None)

Check if a point is contained in the region.

Parameters

Name	Type	Description	Default
z	complex	Point to test for containment	None

Returns

Name	Type	Description
	bool	True if z is in the region, False otherwise

get

regions.JuliaRegion.get(field)

Get a field from the underlying Julia object.

Parameters

Name	Type	Description	Default
field	str	Name of the field to retrieve	required

Returns

Name	Type	Description
	Any	The value of the requested field

innerboundary

regions.JuliaRegion.innerboundary()

Get the inner boundary curves of the region.

Returns

Name	Type	Description
	JuliaPath or list of JuliaPath	Inner boundary curve(s) of the region

intersect

regions.JuliaRegion.intersect(other)

Compute the intersection of this region with another.

Parameters

Name	Type	Description	Default
other	JuliaRegion	Another region to intersect with	required

Returns

Name	Type	Description
	JuliaRegion	Intersection of the two regions

outerboundary

regions.JuliaRegion.outerboundary()

Get the outer boundary curves of the region.

Returns

Name	Type	Description
	JuliaPath or list of JuliaPath	Outer boundary curve(s) of the region

union

regions.JuliaRegion.union(other)

Compute the union of this region with another.

Parameters

Name	Type	Description	Default
other	JuliaRegion	Another region to union with	required

Returns

Name	Type	Description
	JuliaRegion	Union of the two regions

Functions

Name	Description
Jordan	Construct a Jordan curve from a ClosedPath or ClosedCurve object.
between	Construct the region between two closed curves.
disk	Construct a disk as an interior region.
exterior	Construct the exterior region of a closed curve.
get_julia	Extract the Julia object from a Python wrapper.
halfplane	Construct a half-plane as an interior region from a Line.
interior	Construct the interior region of a closed curve.
wrap_jl_region	Wrap a Julia region object in the appropriate Python class.

Jordan

regions.Jordan(c)

Construct a Jordan curve from a ClosedPath or ClosedCurve object.

Parameters

Name	Type	Description	Default
c	ClosedPath, ClosedCurve, or juliacall.AnyValue	A closed curve or path object	required

Returns

Name	Type	Description
	ClosedPath or ClosedCurve	The input object if already a Jordan curve, or wrapped appropriately

Raises

Name	Type	Description
	ValueError	If the argument is not a valid closed curve or path

between

regions.between(curve1, curve2)

Construct the region between two closed curves.

Parameters

Name	Type	Description	Default
curve1	ClosedCurve or ClosedPath	First boundary curve	required
curve2	ClosedCurve or ClosedPath	Second boundary curve	required

Returns

Name	Type	Description
	InteriorConnectedRegion	Region between the two curves

Examples

>>> from cxregions.curves import Circle
>>> outer = Circle(0, 2)
>>> inner = Circle(0, 1)
>>> region = between(outer, inner)

disk

regions.disk(center, radius)

Construct a disk as an interior region.

Parameters

Name	Type	Description	Default
center	complex	Center of the disk	required
radius	float	Radius of the disk	required

Returns

Name	Type	Description
	Interior1CRegion	Disk region

Examples

>>> disk_region = disk(1+1j, 2)

exterior

regions.exterior(curve)

Construct the exterior region of a closed curve.

Parameters

Name	Type	Description	Default
curve	ClosedCurve or ClosedPath	Boundary curve	required

Returns

Name	Type	Description
	Exterior1CRegion	Exterior region of the curve

Examples

>>> from cxregions.curves import Circle
>>> circle = Circle(0, 1)
>>> region = exterior(circle)

get_julia

regions.get_julia(p)

Extract the Julia object from a Python wrapper.

Parameters

Name	Type	Description	Default
p	JuliaCurve, JuliaPath, or other	Python wrapper object or raw Julia object	required

Returns

Name	Type	Description
	juliacall.AnyValue or other	The underlying Julia object, or the input if not a wrapper

halfplane

regions.halfplane(l)

Construct a half-plane as an interior region from a Line.

Parameters

Name	Type	Description	Default
l	Line	Line that forms the boundary of the half-plane	required

Returns

Name	Type	Description
	Interior1CRegion	Half-plane region

Examples

>>> from cxregions.curves import Line
>>> line = Line(0, direction=1)
>>> hp = halfplane(line)

interior

regions.interior(curve)

Construct the interior region of a closed curve.

Parameters

Name	Type	Description	Default
curve	ClosedCurve or ClosedPath	Boundary curve	required

Returns

Name	Type	Description
	Interior1CRegion	Interior region of the curve

Examples

>>> from cxregions.curves import Circle
>>> circle = Circle(0, 1)
>>> region = interior(circle)

wrap_jl_region

regions.wrap_jl_region(jul)

Wrap a Julia region object in the appropriate Python class.

Parameters

Name	Type	Description	Default
jul	juliacall.AnyValue	A Julia region object from ComplexRegions.jl	required

Returns

Name	Type	Description
	JuliaRegion	The appropriate Python region wrapper

Raises

Name	Type	Description
	ValueError	If the argument is not a Julia object or not a recognized region type