cxregions

This package provides classes and methods that are useful for working with curves and regions in the (extended) complex plane. It presents a Pythonic interface to the functionality provided by the Julia package ComplexRegions.jl, which is the computational engine. Julia and the necessary dependencies are installed automatically when you first use cxregions.

Core classes

These are three core classes in the package. Each is in a submodule of the same name, but are also imported into the top-level namespace for convenience. In general, names follow Julian conventions rather than Python conventions.

curves

A curve is a smooth curve in the extended complex plane. Implicitly, curves are expected to be non-self-intersecting, but that condition is not enforced. The generic Curve type requires you to specify explicit parameterizations for the point and tangent that are not checked for smoothness. Particular predefined subtypes are Circle, Arc, Line, Ray, and Segment.

paths

A path is a piecewise-continuous complex-valued path. In practice, a Path can be specified as a vector of curves. The path is checked for continuity at creation time. The most important provided specific path subtypes are Polygon and CircularPolygon.

Both curves and paths have closed subtypes. These are additionally checked at creation to ensure that the initial and final points are the same.

One atypical aspect of curves and paths, even “closed” ones, is that they lie in the extended or compactified complex plane and thus may be unbounded. For instance, a line in the plane may be interpreted as a circle on the Riemann sphere, and is thus a closed curve passing through infinity.

regions

A region is an open region in the extended plane bounded by closed curves or paths. These include the simply connected Interior1CRegion and Exterior1CRegion types, which are bounded by a single closed curve or path, as well as more complicated multiply connected regions bounded by several such objects.

Tolerance

Boundaries and endpoints are not well-posed ideas in floating-point, since an arbitrarily small perturbation to a value can move a point on or off of them. Thus, many concepts in the package such as intersection or continuity are checked only up to a small tolerance. This value defaults to a modest multiple of machine precision and can be overridden on a per-call basis.