paths

paths

Path classes for the cxregions package.

This module contains all path-related classes including the base JuliaPath class and specific path types like Polygon, CircularPolygon, and Rectangle.

Classes

Name	Description
CircularPolygon	A polygon with circular arc sides.
ClosedPath	A closed path that forms a Jordan curve.
JuliaPath	Base class for wrapping Julia path objects from ComplexRegions.jl.
Path	A path composed of connected curves.
Polygon	A polygon with straight sides.
Rectangle	A rectangular polygon.

CircularPolygon

paths.CircularPolygon(arg)

A polygon with circular arc sides.

This class represents a polygon where each side can be either a straight line segment or a circular arc.

Parameters

Name	Type	Description	Default
arg	list of curves or juliacall.AnyValue	List of curves (segments and arcs) that form the polygon sides, or Julia CircularPolygon object to wrap	required

Attributes

Name	Type	Description
path	ClosedPath	The underlying closed path

Examples

>>> from cxregions.curves import Arc, Segment
>>> arc1 = Arc(1, 2 + 1j, 1j)
>>> seg1 = Segment(1j, -1)
>>> arc2 = Arc(-1, -0.5j, -1j)
>>> seg2 = Segment(-1j, 1)
>>> cpoly = CircularPolygon([arc1, seg1, arc2, seg2])

Methods

Name	Description
side	Get the k-th side of the polygon.
sides	Get all sides of the polygon.

side

paths.CircularPolygon.side(k)

Get the k-th side of the polygon.

Parameters

Name	Type	Description	Default
k	int	Index of the side	required

Returns

Name	Type	Description
	JuliaCurve	The k-th side of the polygon

sides

paths.CircularPolygon.sides()

Get all sides of the polygon.

Returns

Name	Type	Description
	list of JuliaCurve	List of curves that form the polygon sides

ClosedPath

paths.ClosedPath(curves)

A closed path that forms a Jordan curve.

This class represents a closed sequence of curves that form a continuous closed path, enabling computation of winding numbers and containment tests.

Parameters

Name	Type	Description	Default
curves	list of JuliaCurve, Path, or juliacall.AnyValue	List of curves that form the closed path, or Julia ClosedPath object to wrap	required

Examples

>>> from cxregions.curves import Segment
>>> seg1 = Segment(0, 1)
>>> seg2 = Segment(1, 1+1j)
>>> seg3 = Segment(1+1j, 1j)
>>> seg4 = Segment(1j, 0)
>>> closed_path = ClosedPath([seg1, seg2, seg3, seg4])

Methods

Name	Description
isinside	Check if point z is inside the closed path.
winding	Compute the winding number around point z.

isinside

paths.ClosedPath.isinside(z)

Check if point z is inside the closed path.

Parameters

Name	Type	Description	Default
z	complex	Point to test	required

Returns

Name	Type	Description
	bool	True if z is inside the path, False otherwise

winding

paths.ClosedPath.winding(z)

Compute the winding number around point z.

Parameters

Name	Type	Description	Default
z	complex	Point around which to compute winding number	required

Returns

Name	Type	Description
	int	Winding number (positive for counterclockwise orientation)

JuliaPath

paths.JuliaPath(julia_obj)

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

This class provides a Python interface to Julia path objects, which are sequences of connected curves forming a continuous path.

Parameters

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

Attributes

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

Methods

Name	Description
angles	Get the turning angles at all vertices.
arclength	Compute the total arc length of the path.
arg	Find the parameter value corresponding to point z on the path.
closest	Find the closest point on the path to z.
conj	Return the complex conjugate of the path.
curve	Get the k-th curve in the path.
curves	Get all curves that make up the path.
dist	Compute the distance from point z to the path.
get	Get a field from the underlying Julia object.
intersect	Find intersection points with another path.
inv	Compute the inversion of the path with respect to the unit circle.
isapprox	Check if this path is approximately equal to another.
isfinite	Check if the path has finite length.
ispositive	Check if the path has positive orientation.
isreal	Check if the path lies on the real axis.
length	Get the number of curves in the path.
normal	Compute the normal vector at parameter t.
point	Evaluate the path at parameter value t.
reflect	Reflect point z across the path.
reverse	Return the path with reversed orientation.
tangent	Compute the tangent vector at parameter t.
unittangent	Compute the unit tangent vector at parameter t.
vertex	Get the k-th vertex of the path.
vertices	Get all vertices of the path.

angles

paths.JuliaPath.angles()

Get the turning angles at all vertices.

Returns

Name	Type	Description
	numpy.ndarray	Array of turning angles at vertices

arclength

paths.JuliaPath.arclength()

Compute the total arc length of the path.

Returns

Name	Type	Description
	float	Total arc length of all curves in the path

arg

paths.JuliaPath.arg(z)

Find the parameter value corresponding to point z on the path.

Parameters

Name	Type	Description	Default
z	complex	Point to locate on the path	required

Returns

Name	Type	Description
	float or None	Parameter value if z is on the path, None otherwise

closest

paths.JuliaPath.closest(z)

Find the closest point on the path to z.

Parameters

Name	Type	Description	Default
z	complex	Reference point	required

Returns

Name	Type	Description
	complex	Closest point on the path to z

conj

paths.JuliaPath.conj()

Return the complex conjugate of the path.

Returns

Name	Type	Description
	JuliaPath	Complex conjugate of this path

curve

paths.JuliaPath.curve(k)

Get the k-th curve in the path.

Parameters

Name	Type	Description	Default
k	int	Index of the curve (0-based)	required

Returns

Name	Type	Description
	JuliaCurve	The k-th curve in the path

curves

paths.JuliaPath.curves()

Get all curves that make up the path.

Returns

Name	Type	Description
	list of JuliaCurve	List of curve objects that form the path

dist

paths.JuliaPath.dist(z)

Compute the distance from point z to the path.

Parameters

Name	Type	Description	Default
z	complex	Reference point	required

Returns

Name	Type	Description
	float	Distance from z to the closest point on the path

get

paths.JuliaPath.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

intersect

paths.JuliaPath.intersect(other)

Find intersection points with another path.

Parameters

Name	Type	Description	Default
other	JuliaPath	Another path to intersect with	required

Returns

Name	Type	Description
	numpy.ndarray or other	Array of intersection points or other result

inv

paths.JuliaPath.inv()

Compute the inversion of the path with respect to the unit circle.

Returns

Name	Type	Description
	JuliaPath	Inverted path

isapprox

paths.JuliaPath.isapprox(other)

Check if this path is approximately equal to another.

Parameters

Name	Type	Description	Default
other	JuliaPath	Another path to compare with	required

Returns

Name	Type	Description
	bool	True if paths are approximately equal, False otherwise

isfinite

paths.JuliaPath.isfinite()

Check if the path has finite length.

Returns

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

ispositive

paths.JuliaPath.ispositive()

Check if the path has positive orientation.

Returns

Name	Type	Description
	bool	True if positively oriented, False otherwise

isreal

paths.JuliaPath.isreal()

Check if the path lies on the real axis.

Returns

Name	Type	Description
	bool	True if the path is real, False otherwise

length

paths.JuliaPath.length()

Get the number of curves in the path.

Returns

Name	Type	Description
	int	Number of curves in the path

normal

paths.JuliaPath.normal(t=0.0)

Compute the normal vector at parameter t.

Parameters

Name	Type	Description	Default
t	float	Parameter value, default is 0	0.0

Returns

Name	Type	Description
	complex	Normal vector at parameter t

point

paths.JuliaPath.point(t)

Evaluate the path at parameter value t.

Parameters

Name	Type	Description	Default
t	float	Parameter value, typically in [0, 1]	required

Returns

Name	Type	Description
	complex	Point on the path at parameter t

reflect

paths.JuliaPath.reflect(z)

Reflect point z across the path.

Parameters

Name	Type	Description	Default
z	complex	Point to reflect	required

Returns

Name	Type	Description
	complex	Reflected point

reverse

paths.JuliaPath.reverse()

Return the path with reversed orientation.

Returns

Name	Type	Description
	JuliaPath	Path with reversed orientation

tangent

paths.JuliaPath.tangent(t=0.0)

Compute the tangent vector at parameter t.

Parameters

Name	Type	Description	Default
t	float	Parameter value, default is 0	0.0

Returns

Name	Type	Description
	complex	Tangent vector at parameter t

unittangent

paths.JuliaPath.unittangent(t=0.0)

Compute the unit tangent vector at parameter t.

Parameters

Name	Type	Description	Default
t	float	Parameter value, default is 0	0.0

Returns

Name	Type	Description
	complex	Unit tangent vector at parameter t

vertex

paths.JuliaPath.vertex(k)

Get the k-th vertex of the path.

Parameters

Name	Type	Description	Default
k	int	Index of the vertex	required

Returns

Name	Type	Description
	complex	Coordinates of the k-th vertex

vertices

paths.JuliaPath.vertices()

Get all vertices of the path.

Returns

Name	Type	Description
	numpy.ndarray	Array of vertex coordinates

Path

paths.Path(curves)

A path composed of connected curves.

This class represents a sequence of curves that form a continuous path.

Parameters

Name	Type	Description	Default
curves	list of JuliaCurve or juliacall.AnyValue	List of curves that form the path, or Julia Path object to wrap	required

Examples

>>> from cxregions.curves import Segment
>>> seg1 = Segment(0, 1)
>>> seg2 = Segment(1, 1+1j)
>>> path = Path([seg1, seg2])

Polygon

paths.Polygon(arg)

A polygon with straight sides.

This class represents a polygon where all sides are straight line segments.

Parameters

Name	Type	Description	Default
arg	list of complex or juliacall.AnyValue	List of vertex coordinates or Julia Polygon object to wrap	required

Attributes

Name	Type	Description
path	ClosedPath	The underlying closed path

Examples

>>> # Unit square
>>> poly = Polygon([0, 1, 1+1j, 1j])
>>> # More complex polygon
>>> poly2 = Polygon([4, 4 + 3j, 3j, -2j, 6 - 2j, 6])

Methods

Name	Description
side	Get the k-th side of the polygon.
sides	Get all sides of the polygon.

side

paths.Polygon.side(k)

Get the k-th side of the polygon.

Parameters

Name	Type	Description	Default
k	int	Index of the side	required

Returns

Name	Type	Description
	JuliaCurve	The k-th side of the polygon

sides

paths.Polygon.sides()

Get all sides of the polygon.

Returns

Name	Type	Description
	list of JuliaCurve	List of line segments that form the polygon sides

Rectangle

paths.Rectangle(a, b=None)

A rectangular polygon.

This class represents a rectangle, which is a special case of a polygon with four sides at right angles.

Parameters

Name	Type	Description	Default
a	complex, list, or juliacall.AnyValue	Center point, list of vertices, or Julia Rectangle object to wrap	required
b	array - like or complex	Radii array (if a is center) or opposite corner (if a is corner)	None

Attributes

Name	Type	Description
center	complex	Center of the rectangle
radii	array - like	Half-widths in x and y directions
rotation	float	Rotation angle of the rectangle
polygon	Polygon	The underlying polygon representation

Examples

>>> # Rectangle from center and radii
>>> rect1 = Rectangle(0+0j, np.array([1.0, 0.5]))
>>> # Rectangle from opposite corners
>>> rect2 = Rectangle(-1-1j, 1+1j)

Functions

Name	Description
get_julia	Extract the Julia object from a Python wrapper.
n_gon	Construct a regular n-gon as a Polygon object.
quad	Construct a quadrilateral region from a Rectangle.
wrap_jl_path	Wrap a Julia path object in the appropriate Python class.

get_julia

paths.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

n_gon

paths.n_gon(n)

Construct a regular n-gon as a Polygon object.

Parameters

Name	Type	Description	Default
n	int	Number of sides	required

Returns

Name	Type	Description
	Polygon	Regular n-sided polygon centered at origin with unit circumradius

Examples

>>> # Regular hexagon
>>> hex_poly = n_gon(6)
>>> # Regular triangle
>>> triangle = n_gon(3)

quad

paths.quad(rect)

Construct a quadrilateral region from a Rectangle.

Parameters

Name	Type	Description	Default
rect	Rectangle	Rectangle to convert to a region	required

Returns

Name	Type	Description
	Interior1CRegion	Interior region of the rectangle

Examples

>>> rect = Rectangle(0+0j, np.array([1.0, 0.5]))
>>> region = quad(rect)

wrap_jl_path

paths.wrap_jl_path(jul)

Wrap a Julia path object in the appropriate Python class.

Parameters

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

Returns

Name	Type	Description
	Path	The appropriate Python path wrapper

Raises

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