Use Domain to Check Points Containment

import minterpy as mp
import numpy as np

Once a Domain instance is constructed, it can be used to verify whether a given set of points lies within the domain.

This guide demonstrates how to carry out such a check.

Example: Three-dimensional rectangular domain

Create a three-dimensional rectangular domain that corresponds to:

\[ \Omega = [0.0, 5.0] \times [10.0, 15.0] \times [0.5, 3.0] \]

Domain instance

The rectangular domain is defined by three pairs of bounds (each forms an interval) one for each dimension. We can specify them in a single two-dimensional array of three rows:

bounds = np.array([
    [0.0, 5.0],
    [10.0, 15.0],
    [0.5, 3.0],
])

An instance of Domain given an array of bounds can be constructed using the default constructor:

dom = mp.Domain(bounds)

We can verify that the domain is three dimensional:

print(dom.spatial_dimension)

3

and with the appropriate bounds:

print(dom.bounds)

[[ 0.   5. ]
 [10.  15. ]
 [ 0.5  3. ]]

Check containment with respect to the user domain

A set of points can be verified to lie within the user domain using the contains() method. For instance, to check if the following set of points

xx = np.array([
    [0.1, 11.0, 1.75],  # True
    [0.4, 13, 2.75],    # True
    [-1, 11, 0.5],      # False
    [0.2, 16.0, 2.0],   # False
])

lie within the domain:

dom.contains(xx)

array([ True,  True, False, False])

Notice that the check is carried for each point.

Check containment with respect to the internal domain

Alternatively, a set of points can also be verified to lie within the internal domain using the same method and passing internal=True argument. For instance, to check if the following set of points

xx = np.array([
    [0.0, 0.0, 0.0],     # True
    [-1, -1, -1],        # True
    [-0.75, 0.75, 0.5],  # True
    [-2, -2, 2],         # False
])

lie within the internal domain:

dom.contains(xx, internal=True)

array([ True,  True,  True, False])

Once again, notice that the check is carried for each point.