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 = Renderer()
>>> r.add((cph0,'r',1),normal_length = 0)
>>> r.add((cpg,'b',1),normal_length=0)
>>> r.show()

Example 2:

>>> from Geometry3D import *
>>> import copy
>>> r = Renderer()
>>> 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()

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 = Renderer()
>>> 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()