.. _geometry_intersection:

Intersections and Joins
=======================

To handle intersecting and joining an arbitrary number of geometric objects of varying type, we have the module :py:mod:`ddg.geometry.intersection`. The most important functions are :py:func:`~ddg.geometry.intersection.intersect` (also available as :py:func:`~ddg.geometry.intersection.meet`) and :py:func:`~ddg.geometry.intersection.join`:

.. doctest::

   >>> import numpy as np
   >>> from ddg.geometry.quadrics import Quadric
   >>> from ddg.geometry.subspaces import Subspace, Point
   >>> from ddg.geometry.intersection import intersect, join

   >>> Q = Quadric(np.diag([1, 1, 1, -1]))
   >>> S1 = Subspace([0, 1, 0, 0]).dualize()
   >>> S2 = Subspace([0, 0, 1, 0]).dualize()
   >>> intsct = intersect(Q, S1, S2)
   >>> isinstance(intsct, Quadric)
   True
   >>> intsct.dimension
   0
   >>> Point([1, 0, 0, 1]) in intsct and Point([-1, 0, 0, 1]) in intsct
   True

.. image:: intersection.png
    :scale: 50 %
    :align: center

In this example, the function ``intersect`` automatically applied the functions :py:func:`ddg.geometry.subspaces.intersect_subspaces` and :py:func:`ddg.geometry.quadrics.intersect_quadric_subspace` to reduce the intersection as much as possible. In this case, it could be fully resolved to a single ``Quadric`` object.

If the intersection or join can not be fully resolved due to lack of implemented intersection functions for the given types, we instead get an :py:class:`ddg.geometry.intersection.Intersection` or :py:class:`ddg.geometry.intersection.Join` object. ``Intersection`` supports the ``in`` keyword.