Creating Geometries¶
Creating Point¶
Creating a Point using three cordinates:
>>> from Geometry3D import *
>>> pa = Point(1,2,3)
>>> pa
Point(1, 2, 3)
Creating a Point using a list of coordinates:
>>> pb = Point([2,4,3])
>>> pb
Point(2, 4, 3)
Specifically, special Point can be created using class function:
>>> o = origin()
>>> o
Point(0, 0, 0)
Creating Vector¶
Creating a Vector using three cordinates:
>>> from Geometry3D import *
>>> va = Vector(1,2,3)
>>> va
Vector(1, 2, 3)
Creating a Vector using two Points:
>>> pa = Point(1,2,3)
>>> pb = Point(2,3,1)
>>> vb = Vector(pa,pb)
>>> vb
Vector(1, 1, -2)
Creating a Vector using a list of coordinates:
>>> vc = Vector([1,2,4])
>>> vc
Vector(1, 2, 4)
Specifically, special Vectors can be created using class functions:
>>> x_unit_vector()
Vector(1, 0, 0)
>>> y_unit_vector()
Vector(0, 1, 0)
>>> z_unit_vector()
Vector(0, 0, 1)
Creating Line¶
Creating Line using two Points:
>>> from Geometry3D import *
>>> pa = Point(1,2,3)
>>> pb = Point(2,3,1)
>>> l = Line(pa,pb)
>>> l
Line(sv=Vector(1, 2, 3),dv=Vector(1, 1, -2))
Creating Line using two Vectors:
>>> va = Vector(1,2,3)
>>> vb = Vector(-1,-2,-1)
>>> l = Line(va,vb)
>>> l
Line(sv=Vector(1, 2, 3),dv=Vector(-1, -2, -1))
Creating Line using a Point and a Vector:
Line(sv=Vector(1, 2, 3),dv=Vector(-1, -2, -1))
>>> pa = Point(2,6,-2)
>>> v = Vector(2,0,4)
>>> l = Line(pa,v)
>>> l
Line(sv=Vector(2, 6, -2),dv=Vector(2, 0, 4))
Specifically, special Lines can be created using class functions:
>>> x_axis()
Line(sv=Vector(0, 0, 0),dv=Vector(1, 0, 0))
>>> y_axis()
Line(sv=Vector(0, 0, 0),dv=Vector(0, 1, 0))
>>> z_axis()
Line(sv=Vector(0, 0, 0),dv=Vector(0, 0, 1))
Creating Plane¶
Creating Plane using three Points:
>>> from Geometry3D import *
>>> p1 = origin()
>>> p2 = Point(1,0,0)
>>> p3 = Point(0,1,0)
>>> p = Plane(p1,p2,p3)
>>> p
Plane(Point(0, 0, 0), Vector(0, 0, 1))
Creating Plane using a Point and two Vectors:
>>> p1 = origin()
>>> v1 = x_unit_vector()
>>> v2 = z_unit_vector()
>>> p = Plane(p1,v1,v2)
>>> p
Plane(Point(0, 0, 0), Vector(0, -1, 0))
Creating Plane using a Point and a Vector:
>>> p1 = origin()
>>> p = Plane(p1,Vector(1,1,1))
>>> p
Plane(Point(0, 0, 0), Vector(1, 1, 1))
Creating Plane using four parameters:
# Plane(a, b, c, d):
# Initialise a plane given by the equation
# ax1 + bx2 + cx3 = d (general form).
>>> p = Plane(1,2,3,4)
>>> p
Plane(Point(-1.0, 1.0, 1.0), Vector(1, 2, 3))
Specifically, special Planes can be created using class functions:
>>> xy_plane()
Plane(Point(0, 0, 0), Vector(0, 0, 1))
>>> yz_plane()
Plane(Point(0, 0, 0), Vector(1, 0, 0))
>>> xz_plane()
Plane(Point(0, 0, 0), Vector(0, 1, 0))
Creating Segment¶
Creating Segment using two Points:
>>> from Geometry3D import *
>>> p1 = Point(0,0,2)
>>> p2 = Point(-1,2,0)
>>> s = Segment(p1,p2)
>>> s
Segment(Point(0, 0, 2), Point(-1, 2, 0))
Creating Segment using a Point and a Vector:
>>> s = Segment(origin(),x_unit_vector())
>>> s
Segment(Point(0, 0, 0), Point(1, 0, 0))
Creating ConvexPolygon¶
Creating ConvexPolygon using a tuple of points:
>>> from Geometry3D import *
>>> pa = origin()
>>> pb = Point(1,1,0)
>>> pc = Point(1,0,0)
>>> pd = Point(0,1,0)
>>> cpg = ConvexPolygon((pa,pb,pc,pd))
>>> cpg
ConvexPolygon((Point(0, 0, 0), Point(0, 1, 0), Point(1, 1, 0), Point(1, 0, 0)))
Specifically, Parallelogram can be created using one Point and two Vectors:
>>> pa = origin()
>>> cpg = Parallelogram(pa,x_unit_vector(),y_unit_vector())
>>> cpg
ConvexPolygon((Point(0, 0, 0), Point(1, 0, 0), Point(1, 1, 0), Point(0, 1, 0)))
Creating ConvexPolyhedron¶
Creating ConvexPolyhedron using a tuple of ConvexPolygons:
>>> 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)
>>> cpg0 = ConvexPolygon((a,d,h,e))
>>> cpg1 = ConvexPolygon((a,e,f,b))
>>> cpg2 = ConvexPolygon((c,b,f,g))
>>> cpg3 = ConvexPolygon((c,g,h,d))
>>> cpg4 = ConvexPolygon((a,b,c,d))
>>> cpg5 = ConvexPolygon((e,h,g,f))
>>> cph0 = ConvexPolyhedron((cpg0,cpg1,cpg2,cpg3,cpg4,cpg5))
>>> cph0
ConvexPolyhedron
pyramid set:{Pyramid(ConvexPolygon((Point(1, 1, -1), Point(1, -1, -1), Point(-1, -1, -1), Point(-1, 1, -1))), Point(0.0, 0.0, 0.0)), Pyramid(ConvexPolygon((Point(1, 1, 1), Point(1, 1, -1), Point(-1, 1, -1), Point(-1, 1, 1))), Point(0.0, 0.0, 0.0)), Pyramid(ConvexPolygon((Point(-1, -1, 1), Point(-1, 1, 1), Point(-1, 1, -1), Point(-1, -1, -1))), Point(0.0, 0.0, 0.0)), Pyramid(ConvexPolygon((Point(-1, -1, 1), Point(-1, -1, -1), Point(1, -1, -1), Point(1, -1, 1))), Point(0.0, 0.0, 0.0)), Pyramid(ConvexPolygon((Point(1, 1, 1), Point(1, -1, 1), Point(1, -1, -1), Point(1, 1, -1))), Point(0.0, 0.0, 0.0)), Pyramid(ConvexPolygon((Point(1, 1, 1), Point(-1, 1, 1), Point(-1, -1, 1), Point(1, -1, 1))), Point(0.0, 0.0, 0.0))}
point set:{Point(1, 1, -1), Point(-1, -1, -1), Point(1, -1, 1), Point(-1, 1, 1), Point(1, 1, 1), Point(-1, -1, 1), Point(-1, 1, -1), Point(1, -1, -1)}
Specifically, Parallelepiped can be created using a Point and Three Vectors:
>>> cph = Parallelepiped(origin(),x_unit_vector(),y_unit_vector(),z_unit_vector())
>>> cph
ConvexPolyhedron
pyramid set:{Pyramid(ConvexPolygon((Point(1, 1, 1), Point(0, 1, 1), Point(0, 1, 0), Point(1, 1, 0))), Point(0.5, 0.5, 0.5)), Pyramid(ConvexPolygon((Point(0, 0, 0), Point(0, 1, 0), Point(0, 1, 1), Point(0, 0, 1))), Point(0.5, 0.5, 0.5)), Pyramid(ConvexPolygon((Point(0, 0, 0), Point(1, 0, 0), Point(1, 0, 1), Point(0, 0, 1))), Point(0.5, 0.5, 0.5)), Pyramid(ConvexPolygon((Point(1, 1, 1), Point(1, 0, 1), Point(1, 0, 0), Point(1, 1, 0))), Point(0.5, 0.5, 0.5)), Pyramid(ConvexPolygon((Point(0, 0, 0), Point(1, 0, 0), Point(1, 1, 0), Point(0, 1, 0))), Point(0.5, 0.5, 0.5)), Pyramid(ConvexPolygon((Point(1, 1, 1), Point(0, 1, 1), Point(0, 0, 1), Point(1, 0, 1))), Point(0.5, 0.5, 0.5))}
point set:{Point(0, 0, 1), Point(1, 1, 1), Point(1, 1, 0), Point(0, 1, 1), Point(1, 0, 1), Point(0, 0, 0), Point(1, 0, 0), Point(0, 1, 0)}
Creating HalfLine¶
Creating HalfLine using two Points or a Point and a Vector:
>>> from Geometry3D import *
>>> HalfLine(origin(),Point(1,0,0))
HalfLine(Point(0, 0, 0), Vector(1, 0, 0))
>>> HalfLine(origin(),y_unit_vector())
HalfLine(Point(0, 0, 0), Vector(0, 1, 0))
Other Geometries¶
Inscribed convex polygon and convex polyhedron of circle, cylinder, sphere, cone are also available:
>>> from Geometry3D import *
>>> import copy
>>>
>>> b = Circle(origin(),y_unit_vector(),10,20)
>>> a = Circle(origin(),x_unit_vector(),10,20)
>>> c = Circle(origin(),z_unit_vector(),10,20)
>>> r = Renderer()
>>> r.add((a,'g',3))
>>> r.add((b,'b',3))
>>> r.add((c,'r',3))
>>>
>>> s1 = Sphere(Point(20,0,0),10,n1=12,n2=5)
>>> s2 = copy.deepcopy(s1).move(Vector(10,2,-3.9))
>>> s3 = intersection(s1,s2)
>>>
>>> r.add((s1,'r',1))
>>> r.add((s2,'b',1))
>>> r.add((s3,'y',3))
>>>
>>> cone = Cone(origin(),3,20 * z_unit_vector(),n=20)
>>> r.add((cone,'y',1),normal_length=0)
>>>
>>> cylinder = Cylinder(Point(0,0,20),2,5 * z_unit_vector(),n=15)
>>> r.add((cylinder,'g',1),normal_length=1)
>>>
>>> r.show()
