.. _geometry_intersection:

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

The most important functions are :py:func:`~ddg.geometry.intersect` (also available as :py:func:`~ddg.geometry.meet`) and :py:func:`~ddg.geometry.join`:

.. doctest::

   >>> import numpy as np
   >>> import ddg

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

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

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

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