pyntegrals 1.0.0

A tool for calculating definite integrals over a 2D polygonal domain

Pyntegrals

Pyntegrals is a simple library for computing a definite integral over a 2D polygonal domain.
At the moment the only function of the library is integrate_over_polygon, which perform the calculation.
It is possible that in the future other functions will be added.

pyntegrals.integrals

pyntegrals.integrals.integrate_over_polygon

pyntegrals.integrals.integrate_over_polygon(function: Union[Callable, float], polygon: list[tuple]) -> float

Computes the integral of a two-variables function over a polygonal domain in R².

Returns the definite integral of function(x, y) = f(x, y) over polygon = Σ, that is:

∫_Σ f(x, y) dΣ

Parameters

function : Union[Callable, float]

A scalar or a Python function with two arguments: the first one is x and the second one is y in R² space.

polygon: list[tuple]

A polygon defined by a list of its vertices. Each vertex is described by a tuple containing its coordinated in the form (x, y). The vertices in the list must be in clockwise or counter-clockwise order (it makes no difference)

Returns

r : float

The definite integral of function(x, y) over polygon.

Example

Compute the integral of x² + y over a 50 x 40 rectangle Σ with a vertex in (0, 0) and another in (50, 40)

∫_Σ (x² + y) dΣ

from pyntegrals.integrals import integrate_over_polygon
polygon = [(0, 0), (50, 0), (50, 40), (0, 40)]
rho = lambda x, y: x**2 + y
mass = integrate_over_polygon(function=rho, polygon=polygon)
>>> 1706666.666666667

For more example see examples/example.py