Operations Examples
===================

move
----

Move a Point::

    >>> a = Point(1,2,1)
    >>> print('a before move:{}'.format(a))
    a before move:Point(1, 2, 1)
    >>> a.move(x_unit_vector())
    Point(2, 2, 1)
    >>> print('a after move:{}'.format(a))
    a after move:Point(2, 2, 1)

Move a Segment::

    >>> b = origin()
    >>> c = Point(1,2,3)
    >>> s = Segment(b,c)
    >>> s
    Segment(Point(0, 0, 0), Point(1, 2, 3))
    >>> s.move(Vector(-1,-2,-3))
    Segment(Point(-1, -2, -3), Point(0, 0, 0))
    >>> s
    Segment(Point(-1, -2, -3), Point(0, 0, 0))

Move a ConvexPolygon **Without** Changing the Original Object::

    >>> import copy
    >>> cpg0 = Parallelogram(origin(),x_unit_vector(),y_unit_vector())
    >>> cpg0
    ConvexPolygon((Point(0, 0, 0), Point(1, 0, 0), Point(1, 1, 0), Point(0, 1, 0)))
    >>> cpg1 = copy.deepcopy(cpg0).move(Vector(0,0,1))
    >>> cpg0
    ConvexPolygon((Point(0, 0, 0), Point(1, 0, 0), Point(1, 1, 0), Point(0, 1, 0)))
    >>> cpg1
    ConvexPolygon((Point(0, 0, 1), Point(1, 0, 1), Point(1, 1, 1), Point(0, 1, 1)))

Intersection
------------

The operation of intersection is very complex. There are a total of 21 situations.

+-----------------+-----------------+--------------------------------------+
|obj1             |obj2             | output obj                           |
+=================+=================+======================================+
|Point            |Point            | None, Point                          |
+-----------------+-----------------+--------------------------------------+
|Point            |Line             | None, Point                          |
+-----------------+-----------------+--------------------------------------+
|Point            |Plane            | None, Point                          |
+-----------------+-----------------+--------------------------------------+
|Point            |Segment          | None, Point                          |
+-----------------+-----------------+--------------------------------------+
|Point            |ConvexPolygon    | None, Point                          |
+-----------------+-----------------+--------------------------------------+
|Point            |ConvexPolyhedron | None, Point                          |
+-----------------+-----------------+--------------------------------------+
|Point            |HalfLine         | None, Point                          |
+-----------------+-----------------+--------------------------------------+
|Line             |Line             | None, Point, Line                    |
+-----------------+-----------------+--------------------------------------+
|Line             |Plane            | None, Point, Line                    |
+-----------------+-----------------+--------------------------------------+
|Line             |Segment          | None, Point, Segment                 |
+-----------------+-----------------+--------------------------------------+
|Line             |ConvexPolygon    | None, Point, Segment                 |
+-----------------+-----------------+--------------------------------------+
|Line             |ConvexPolyhedron | None, Point, Segment                 |
+-----------------+-----------------+--------------------------------------+
|Line             |HalfLine         | None, Point, HalfLine                |
+-----------------+-----------------+--------------------------------------+
|Plane            |Plane            | None, Line, Plane                    |
+-----------------+-----------------+--------------------------------------+
|Plane            |Segment          | None, Point, Segment                 |
+-----------------+-----------------+--------------------------------------+
|Plane            |ConvexPolygon    | None, Point, Segment, ConvexPolygon  |
+-----------------+-----------------+--------------------------------------+
|Plane            |ConvexPolyhedron | None, Point, Segment, ConvexPolygon  |
+-----------------+-----------------+--------------------------------------+
|Plane            |HalfLine         | None, Point, HalfLine                |
+-----------------+-----------------+--------------------------------------+
|Segment          |Segment          | None, Point, Segment                 |
+-----------------+-----------------+--------------------------------------+
|Segment          |ConvexPolygon    | None, Point, Segment                 |
+-----------------+-----------------+--------------------------------------+
|Segment          |ConvexPolyhedron | None, Point, Segment                 |
+-----------------+-----------------+--------------------------------------+
|Segment          |HalfLine         | None, Point, Segment                 |
+-----------------+-----------------+--------------------------------------+
|ConvexPolygon    |ConvexPolygon    | None, Point, Segment, ConvexPolygon  |
+-----------------+-----------------+--------------------------------------+
|ConvexPolygon    |ConvexPolyhedron | None, Point, Segment, ConvexPolygon  |
+-----------------+-----------------+--------------------------------------+
|ConvexPolygon    |HalfLine         | None, Point, Segment                 |
+-----------------+-----------------+--------------------------------------+
|ConvexPolyhedron |ConvexPolyhedron | None, Point, Segment, ConvexPolygon, |
|                 |                 | ConvexPolyhedron                     |
+-----------------+-----------------+--------------------------------------+
|ConvexPolyhedron |HalfLine         | None, Point, Segment                 |
+-----------------+-----------------+--------------------------------------+
|HalfLine         |HalfLine         | None, Point, Segment, HalfLine       |
+-----------------+-----------------+--------------------------------------+


All of the situations above are implemented. The documentation shows some examples. 

Example 1::

    >>> po = origin()
    >>> l1 = x_axis()
    >>> l2 = y_axis()
    >>> intersection(po,l1)
    Point(0, 0, 0)
    >>> intersection(l1,l2)
    Point(0.0, 0.0, 0.0)
    >>> s1 = Segment(Point(1,0,1),Point(0,1,1))
    >>> s2 = Segment(Point(0,0,1),Point(1,1,1))
    >>> s3 = Segment(Point(0.5,0.5,1),Point(-0.5,1.5,1))
    >>> intersection(s1,s2)
    Point(0.5, 0.5, 1.0)
    >>> intersection(s1,s3)
    Segment(Point(0.5, 0.5, 1.0), Point(0, 1, 1))
    >>> intersection(l1,s1) is None
    True
    >>> cph0 = Parallelepiped(origin(),x_unit_vector(),y_unit_vector(),z_unit_vector())
    >>> p = Plane(Point(0.5,0.5,0.5),Vector(1,1,1))
    >>> cpg = intersection(cph0,p)
    >>> r = Visualizer()
    >>> r.add((cph0,'r',1),normal_length = 0)
    >>> r.add((cpg,'b',1),normal_length=0)
    >>> r.show()

.. image:: _static/p4.png

Example 2::

    >>> from Geometry3D import *
    >>> import copy
    >>> r = Visualizer()
    >>> cph0 = Parallelepiped(origin(),x_unit_vector(),y_unit_vector(),z_unit_vector())
    >>> cph6 = Parallelepiped(origin(),2 * x_unit_vector(),2 * y_unit_vector(),2 * z_unit_vector())
    >>> r.add((cph0,'b',1),normal_length = 0.5)
    >>> r.add((cph6,'r',1),normal_length = 0.5)
    >>> r.add((intersection(cph6,cph0),'g',2))
    >>> print(intersection(cph0,cph6))
    ConvexPolyhedron
    pyramid set:{Pyramid(ConvexPolygon((Point(1, 1, 1), Point(0, 1, 1), Point(0.0, 0.0, 1.0), Point(1, 0, 1))), Point(0.5, 0.5, 0.5)), Pyramid(ConvexPolygon((Point(1.0, 0.0, 0.0), Point(1, 0, 1), Point(1, 1, 1), Point(1, 1, 0))), Point(0.5, 0.5, 0.5)), Pyramid(ConvexPolygon((Point(1, 1, 0), Point(1, 1, 1), Point(0, 1, 1), Point(0.0, 1.0, 0.0))), Point(0.5, 0.5, 0.5)), Pyramid(ConvexPolygon((Point(0, 0, 1), Point(0, 0, 0), Point(0, 1, 0), Point(0, 1, 1))), Point(0.5, 0.5, 0.5)), Pyramid(ConvexPolygon((Point(1, 0, 0), Point(1, 0, 1), Point(0, 0, 1), Point(0, 0, 0))), Point(0.5, 0.5, 0.5)), Pyramid(ConvexPolygon((Point(1, 1, 0), Point(1, 0, 0), Point(0, 0, 0), Point(0, 1, 0))), Point(0.5, 0.5, 0.5))}
    point set:{Point(1, 1, 0), Point(1, 1, 1), Point(0, 0, 1), Point(0, 1, 0), Point(0, 1, 1), Point(1.0, 0.0, 0.0), Point(0, 0, 0), Point(1, 0, 1)}
    >>> r.show()

.. image:: _static/p2.png

Example 3::

    >>> from Geometry3D import *
    >>> 
    >>> a = Point(1,1,1)
    >>> b = Point(-1,1,1)
    >>> c = Point(-1,-1,1)
    >>> d = Point(1,-1,1)
    >>> e = Point(1,1,-1)
    >>> f = Point(-1,1,-1)
    >>> g = Point(-1,-1,-1)
    >>> h = Point(1,-1,-1)
    >>> cph0 = Parallelepiped(Point(-1,-1,-1),Vector(2,0,0),Vector(0,2,0),Vector(0,0,2))
    >>> cpg12 = ConvexPolygon((e,c,h))
    >>> cpg13 = ConvexPolygon((e,f,c))
    >>> cpg14 = ConvexPolygon((c,f,g))
    >>> cpg15 = ConvexPolygon((h,c,g))
    >>> cpg16 = ConvexPolygon((h,g,f,e))
    >>> cph1 = ConvexPolyhedron((cpg12,cpg13,cpg14,cpg15,cpg16))
    >>> a1 = Point(1.5,1.5,1.5)
    >>> b1 = Point(-0.5,1.5,1.5)
    >>> c1 = Point(-0.5,-0.5,1.5)
    >>> d1 = Point(1.5,-0.5,1.5)
    >>> e1 = Point(1.5,1.5,-0.5)
    >>> f1 = Point(-0.2,1.5,-0.5)
    >>> g1 = Point(-0.2,-0.5,-0.5)
    >>> h1 = Point(1.5,-0.5,-0.5)
    >>> 
    >>> cpg6 = ConvexPolygon((a1,d1,h1,e1))
    >>> cpg7 = ConvexPolygon((a1,e1,f1,b1))
    >>> cpg8 = ConvexPolygon((c1,b1,f1,g1))
    >>> cpg9 = ConvexPolygon((c1,g1,h1,d1))
    >>> cpg10 = ConvexPolygon((a1,b1,c1,d1))
    >>> cpg11 = ConvexPolygon((e1,h1,g1,f1))
    >>> cph2 = ConvexPolyhedron((cpg6,cpg7,cpg8,cpg9,cpg10,cpg11))
    >>> cph3 = intersection(cph0,cph2)
    >>> 
    >>> cph4 = intersection(cph1,cph2)
    >>> r = Visualizer()
    >>> r.add((cph0,'r',1),normal_length = 0)
    >>> r.add((cph1,'r',1),normal_length = 0)
    >>> r.add((cph2,'g',1),normal_length = 0)
    >>> r.add((cph3,'b',3),normal_length = 0.5)
    >>> r.add((cph4,'y',3),normal_length = 0.5)
    >>> r.show()

.. image:: _static/p3.png