Geopy - python geometry library

With this library you can create primitives and shapes, show it with matplotlib, get intersections and transform. Here is: Vector, Segment, Line, Ray and Point primitives; Polygons and Circle shapes.

Primitives

Polygons are made from primitives. Firstly they have a common parent empty class Primitive, so you can do:

>>> from geopy import Primitive
>>> a = "123"
>>> isinstance(a, Primitive)
False

Point primitive

Point costructed from X and Y, also you can name it:

>>> from geopy import Point
>>> Point(1,1, name="Maybe it is a point")
Point(1.0, 1.0, name="Maybe it is a point")
>>>
>>> Point([777,228], name="It is point too")
Point(777.0, 228.0, name="It is point too")
>>> Point[0,0]
Point(0.0, 0.0, name="Point")

You can get X and Y from Point:

>>> a = Point(1,1, name="a")
>>> a.x; a.y
1.0
1.0
>>> a.pos
[1.0, 1.0]

You can calculate points mathematically:

>>> a = Point[0,0]
>>> b = Point[10,5]
>>>
>>> a + b
Point(10.0, 5.0, name="Point")
>>> a - b
Point(-10.0, -5.0, name="Point")
>>> a * b
Point(0.0, 0.0, name="Point")
>>> a / b
Point(0.0, 0.0, name="Point")
>>> b / a
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "...", line 105, in __truediv__
    return Point(self.x / object.x, self.y / object.y)
                 ~~~~~~~^~~~~~~~~~
ZeroDivisionError: float division by zero
>>> b ** a
Point(1.0, 1.0, name="Point")

You can get random point in rect from pos1 to pos2:

>>> Point.random([0,0], [10,10])
Point(8.085890440593959, 4.454630028598453, name="Point")
>>> Point.random([0,0], [10,10], uniform=False)
Point(4.0, 5.0, name="Point")

Also you can get height to primitive object, like Line or Segment:

>>> from geopy import Point, Segment
>>>
>>> seg = Segment([1,0], [-1,0])
>>> p = Point[0,1]
>>> p.height_to(seg)
Line(Point[0.0, 1.0], Point[0.0, 2.0], name="Line")

linear primitives

They are a Line, Segment, Ray and Vector, Line is a Ray and Segment parent, Segment is a Vector parent. Linear primitives is defined by 2 points ( or list/tuple, then it will be converted to Point ):

>>> from geopy import Line, Segment, Ray, Vector
>>> Line([1,0], [0,0], name='abrakadabra')
Line(Point[1.0, 0.0], Point[0.0, 0.0], name="abrakadabra")
>>> Segment([1,0], [0,0], name='123')
Segment(Point[1.0, 0.0], Point[0.0, 0.0], name="123")

Line and its children has a linear function, you can get it as string or call methods to get X from Y and Y from X:

>>> line = Line([1,0], [0,0], name='abrakadabra')
>>> line.as_geometry
'y = 0.0'
>>> line = Line([1,1], [0,0])
>>> line.as_geometry
'y = x'
>>> line = Line([1,1], [2,3], name='123')
>>> line.as_geometry
'y = 2.0x - 1.0'
>>> line.x_from_y(1)
1.0
>>> line.y_from_x(1)
1.0
>>> line.y_from_x(2)
3.0
>>> line(2)
3.0
>>> line(2) == line.y_from_x(2) # Line and its children __call__ method returns line.y_from_x result
True

Line and its children also save start pos and end pos from constructor:

>>> line.pos1
Point(1.0, 1.0, name="Point")
>>> line.pos2
Point(2.0, 3.0, name="Point")
>>> line.pos2.x
2.0

You can get their angle:

Line(Point[1.0, -1.0], Point[2.0, -2.0], name="Line")
>>> Line([1,1], [0,0]).angle
Angle(Point[0.0, 0.0] -> Point[1.0, 1.0] -> Point[2.0, 1.0], name="Angle")
>>> Line([1,1], [0,0]).angle.degrees
135.0

Linear primitives can get each other`s intersection points:

>>> a = Line([1,1], [0,0])
>>> b = Vector([0,1], [1,0])
>>> a.intersects(b)
[Point(0.5, 0.5, name="Point")]
>>> b.intersects(a)
[Point(0.5, 0.5, name="Point")]
>>> a in b; b in a # returns True if a intersects b
True
True

You can move it to any position:

>>> Segment([1,0], [2,0]).at_pos([0,1])
Segment(Point[0.0, 1.0], Point[1.0, 1.0], name="Segment")

And can calculate linear primitives mathematically:

>>> Segment([1,0], [2,1]) + [2,2]
Segment(Point[3.0, 2.0], Point[4.0, 3.0], name="Segment")
>>> Segment([1,0], [2,1]) - [2,2]
Segment(Point[-1.0, -2.0], Point[0.0, -1.0], name="Segment")

Line primitive

Line and Segment has the same direction options, you can get its directions:

>>> Line([1,0], [0,0]).direction
'horizontal'
>>> Line([1,1], [0,0]).direction
'normal'
>>> Line([0,1], [0,0]).direction
'vertical'

You can get perpendicular:

>>> Line([1,1], [0,0]).perpendicular
Line(Point[1.0, -1.0], Point[2.0, -2.0], name="Line")

Also you can get line by point and degree and by linear function:

>>> from geopy import line_by_angle, line_by_function
>>> line_by_angle([0,0], 45)
Line(Point[1.0, 0.9999999999999999], Point[2.0, 1.9999999999999998], name="Line")
>>>
>>> line_by_function( lambda x: 2 * x + 10 )
Line(Point[1.0, 12.0], Point[2.0, 14.0], name="Line")
>>> line_by_function( lambda x: 2 * x + 10 ).as_geometry
'y = 2.0x + 10.0'

Segment primitive

It is a Line child. Line and Segment has the same direction options, you can get its directions:

>>> Segment([1,0], [0,0]).direction
'horizontal'
>>> Segment([1,1], [0,0]).direction
'normal'
>>> Segment([0,1], [0,0]).direction
'vertical'

You can get perpendicular:

>>> Segment([1,1], [0,0]).perpendicular
Line(Point[1.0, 0.0], Point[2.0, -1.0], name="Line")

Segment has a length:

>>> Segment([1,0], [2,3]).length
3.1622776601683795

And center point:

>>> Segment([1,0], [2,3]).center
Point(1.5, 1.5, name="Point")

Vector primitive

It is a Segment child. It may be created by one point:

>>> Vector[1,1]
Vector(Point[0.0, 0.0], Point[1.0, 1.0], name="Vector")

Vector has a detailed direction:

>>> Vector[1,1].direction
'right-up'
>>> Vector[1,0].direction
'right'
>>> Vector[1,-1].direction
'right-down'
>>> Vector[0,-1].direction
'down'
>>> Vector[-1,-1].direction
'left-down'
>>> Vector[-1,0].direction
'left'
>>> Vector[-1,1].direction
'left-up'
>>> Vector[0,1].direction
'up'

You can normalize and move Vector to (0,0) point:

>>> Vector([1,1], [2,2]).to_zero
Vector(Point[0.0, 0.0], Point[1.0, 1.0], name="Vector")
>>> Vector([1,1], [2,2]).normalize
Vector(Point[1.0, 1.0], Point[1.7071067811865475, 1.7071067811865475], name="Vector")

Also you can calculate vectors mathematically:

>>> Vector[1,1] + Vector[0,1]
Vector(Point[0.0, 0.0], Point[1.0, 2.0], name="Vector")
>>> Vector[1,1] * Vector[0,1]
Vector(Point[0.0, 0.0], Point[0.0, 1.0], name="Vector")
>>> Vector[1,1] - Vector[0,1]
Vector(Point[0.0, 0.0], Point[0.0, 1.0], name="Vector")

Ray primitive

Ray has a detailed direction like a Vector:

>>> Vector[1,1].direction
'right-up'
>>> Vector[1,0].direction
'right'
>>> Vector[1,-1].direction
'right-down'
>>> Vector[0,-1].direction
'down'
>>> Vector[-1,-1].direction
'left-down'
>>> Vector[-1,0].direction
'left'
>>> Vector[-1,1].direction
'left-up'
>>> Vector[0,1].direction
'up'

But it is all.

Angle

Angle is not a Primitive. It defined by 3 points, second point is a midpoint. You can type tuple or list to Angle constructor, then it will be converted to the Point objects:

>>> Angle([1,0], [0,0], [0,1], name="angle ABC")
Angle(Point[1.0, 0.0] -> Point[0.0, 0.0] -> Point[0.0, 1.0], name="angle ABC")

You can get its type:

>>> Angle([1,0], [0,0], [0,1]).type
'right'
>>> Angle([1,0], [0,0], [1,1]).type
'acute'
>>> Angle([1,0], [0,0], [-1,1]).type
'obtuse'

And its bisector ray:

>>> Angle([1,0], [0,0], [0,1]).bisector.as_geometry
'y = x'

Angle has a 3 points, so there is 2 vectors between them:

>>> a = Angle([1,0], [0,0], [0,1])
>>> a.vec1; a.vec2
Vector(Point[0.0, 0.0], Point[1.0, 0.0], name="Vector")
Vector(Point[0.0, 0.0], Point[0.0, 1.0], name="Vector")

Also you can calculate cosinus, sinus and tangens:

>>> a = Angle([1,0], [0,0], [0,1])
>>> a.cos; a.sin; a.tan
0.0
1.0
0.0

And get angle degrees, minutes and radians:

>>> a = Angle([1,0], [0,0], [0,1])
>>> a.degrees; a.minutes; a.radians
90.0
5400.0
1.5707963267948966

Shapes

They are Circle and Polygon, they have a common parent empty class Shape, so you can do:

>>> from geopy import Shape
>>> a = "123"
>>> isinstance(a, Shape)
False

Also they have an intersects method that returns list of Point objects ( you can set check_inside kwarg to False, by default it is True ):

>>> from geopy import Polygon, Circle, Vector
>>>
>>> polygon = Polygon([0,0], [1,1], [1,-1], [0,-1])
>>> vec = Vector[10,10]
>>> polygon.intersects(vec, check_inside=True)
[Point(0.0, 0.0, name="Point"), Point(1.0, 1.0, name="Point")]
>>> vec.intersects(polygon)
[Point(0.0, 0.0, name="Point"), Point(1.0, 1.0, name="Point")]
>>> vec in polygon; polygon in vec
True
True

You can move created Shape to position or get a new Shape at position:

>>> polygon = Polygon([0,0], [1,1], [1,-1], [0,-1])
>>> polygon.at_pos([1,0])
Polygon([Point(0.5, 0.25, name="Point"), Point(1.5, 1.25, name="Point"), Point(1.5, -0.75, name="Point"), Point(0.5, -0.75, name="Point")], name="Polygon", pos=Point[1.5, -0.25])
>>> polygon.to_pos([1,0])
>>> polygon
Polygon([Point(0.5, 0.25, name="Point"), Point(1.5, 1.25, name="Point"), Point(1.5, -0.75, name="Point"), Point(0.5, -0.75, name="Point")], name="Polygon", pos=Point[1.0, 0.0])

You can show your Shape in matplotlib:

Polygon([0,0], [1,1], [1,-1], [0,-1]).plot()
Circle([0,0], 10).plot()

And in simply tkinter:

Circle([0,0], 1).view()

Also you can scale it:

>>> Polygon([0,0], [1,1], [1,-1], [0,-1]).scale(2)
Polygon([Point(-0.5, 0.25, name="Point"), Point(1.5, 2.25, name="Point"), Point(1.5, -1.75, name="Point"), Point(-0.5, -1.75, name="Point")], name="Polygon", pos=Point[0.5, -0.25])

And calculate center point mathematically

>>> Polygon([0,0], [1,1], [1,-1], [0,-1]) + [1,0]
Polygon([Point(1.0, 0.0, name="Point"), Point(2.0, 1.0, name="Point"), Point(2.0, -1.0, name="Point"), Point(1.0, -1.0, name="Point")], name="Polygon", pos=Point[1.5, -0.25])

Polygon

It is defined by Point list:

>>> from geopy import Polygon
>>>
>>> Polygon([0,0], [1,1], [1,-1], [0,-1])
Polygon([Point(0.0, 0.0, name="Point"), Point(1.0, 1.0, name="Point"), Point(1.0, -1.0, name="Point"), Point(0.0, -1.0, name="Point")], name="Polygon", pos=Polygon center[0.5, -0.25])

Polygon automaticly initialize segments and angles between the points:

>>> polygon = Polygon([0,0], [1,1], [1,-1], [0,-1])
>>> polygon.vertices
[Point(0.0, 0.0, name="Point"), Point(1.0, 1.0, name="Point"), Point(1.0, -1.0, name="Point"), Point(0.0, -1.0, name="Point")]
>>> polygon.segments
[Segment(Point[0.0, -1.0], Point[0.0, 0.0], name="sPolygon0"), Segment(Point[0.0, 0.0], Point[1.0, 1.0], name="sPolygon1"), Segment(Point[1.0, 1.0], Point[1.0, -1.0], name="sPolygon2"), Segment(Point[1.0, -1.0], Point[0.0, -1.0], name="sPolygon3")]
>>> polygon.angles
[Angle(Point[1.0, -1.0] <- Point[0.0, -1.0] -> Point[0.0, 0.0], name="aPolygon0"), Angle(Point[0.0, -1.0] <- Point[0.0, 0.0] -> Point[1.0, 1.0], name="aPolygon1"), Angle(Point[0.0, 0.0] <- Point[1.0, 1.0] -> Point[1.0, -1.0], name="aPolygon2"), Angle(Point[1.0, 1.0] <- Point[1.0, -1.0] -> Point[0.0, -1.0], name="aPolygon3")]

You can change type of segments to Vector or your custom:

>>> from geopy import Polygon, Vector
>>> polygon = Polygon([0,0], [1,1], [1,-1], [0,-1], segment_object=Vector)
>>> polygon.segments
[Vector(Point[0.0, -1.0], Point[0.0, 0.0], name="sPolygon0"), Vector(Point[0.0, 0.0], Point[1.0, 1.0], name="sPolygon1"), Vector(Point[1.0, 1.0], Point[1.0, -1.0], name="sPolygon2"), Vector(Point[1.0, -1.0], Point[0.0, -1.0], name="sPolygon3")]

And rotate it by degree:

>>> Polygon([0,0], [1,1], [1,-1], [0,-1]).rotate(45)
Polygon([Point(0.02461312445760555, -0.5441212650626268, name="Point"), Point(-0.30096841125878315, 0.8321042482892214, name="Point"), Point(1.4008386378094537, -0.21853972934623805, name="Point"), Point(0.8755166489917239, -1.0694432538803564, name="Point")], name="Polygon", pos=Polygon center[0.5, -0.25])

Polygon has a property to get random point inside and center of mass:

>>> polygon = Polygon([0,0], [1,1], [1,-1], [0,-1])
>>> polygon.random_point
Point(0.4057370412021215, 0.07220382319695706, name="Point")
>>> polygon.center_of_mass
Point(0.5, -0.25, name="Polygon center")

And property to get perimeter and area:

>>> polygon.perimeter
5.414213562373095
>>> polygon.area
1.5

You can get polygon objects by position:

polygon.segments_by_point(self, point: Point) -> List[Segment]
polygon.segments_by_fromto_point(self, point: Point) -> List[Segment]
polygon.segments_by_from_point(self, point: Point) -> List[Segment]
polygon.segments_by_to_point(self, point: Point) -> List[Segment]
polygon.angle_by_pos(self, point: Point) -> Angle

And get a Box on top of the Polygon:

>>> Polygon([0,0], [1,1], [1,-1], [0,-1]).box
Box([Point(-1.0, 0.0, name="Polygon_min"), Point(-1.0, 1.0, name="Point"), Point(1.0, 1.0, name="Polygon_min"), Point(1.0, 0.0, name="Point")], name="Box", pos=Box center[0.0, 0.5])

Box

It is a Polygon child and defined by 2 points:

>>> from geopy import Box
>>> Box([0,0], [1,1])
Box([Point(0.0, 0.0, name="Point"), Point(0.0, 1.0, name="Point"), Point(1.0, 1.0, name="Point"), Point(1.0, 0.0, name="Point")], name="Box", pos=Box center[0.5, 0.5])

Rhombus

It is a Polygon child and defined by center point and 2 diagonals:

>>> from geopy import Rhombus
>>> Rhombus([0,0], 1, 2)
Rhombus([Point(0.0, 1.0, name="Point"), Point(-0.5, 0.0, name="Point"), Point(0.0, -1.0, name="Point"), Point(0.5, 0.0, name="Point")], name="Rhombus", pos=Rhombus center[0.0, 0.0])

Triangle

It is a Polygon child and defined by 3 points:

>>> Triangle([1,0], [0,0], [0,1])
Triangle([Point(1.0, 0.0, name="Point"), Point(0.0, 0.0, name="Point"), Point(0.0, 1.0, name="Point")], name="Triangle", pos=Triangle center[0.3333333333333333, 0.3333333333333333])

It has type by angle and by side:

>>> tr = Triangle([1,0], [0,0], [0,1])
>>> tr.angle_type
'right'
>>> tr.side_type
'isosceles'
>>> tr.type
'right isosceles'

You can get legs and hypotenuse if it is right triangle:

>>> tr = Triangle([1,0], [0,0], [0,1])
>>> tr.hypotenuse
Segment(Point[0.0, 1.0], Point[1.0, 0.0], name="sTriangle0")
>>> tr.legs
[Segment(Point[1.0, 0.0], Point[0.0, 0.0], name="sTriangle1"), Segment(Point[0.0, 0.0], Point[0.0, 1.0], name="sTriangle2")]

And orthocenter, the center by sides perpendiculars:

>>> tr.orthocenter
Point(0.5, 0.5, name="Point")

Circle

It is defined by center point and radius

>>> from geopy import Circle
>>> Circle([0,0], 2)
Circle(Point[0.0, 0.0], 2)

Or by 2 points:

>>> from geopy import circle_by_points
>>> circle_by_points([0,0], [1,1])
Circle(Point[0.0, 0.0], 1.4142135623730951)
>>> circle_by_points([0,0], [1,0])
Circle(Point[0.0, 0.0], 1.0)

It has property to get perimeter and area:

>>> circle = Circle([0,0], 1)
>>> circle.perimeter
6.283185307179586
>>> circle.area
3.141592653589793

And as_geometry property to get circle equation:

>>> circle.as_geometry
'(x - 0.0)**2 + (y - 0.0)**2 = 1**2'

You can solve this equation manually using circle.radius and circle.center or use functions to get X from Y and Y from X:

>>> circle.y_from_x(0)
[-1.0, 1.0]
>>> [ Point(0, y) for y in circle.y_from_x(0) ]
[Point(0.0, -1.0, name="Point"), Point(0.0, 1.0, name="Point")]

You can get circle center fast:

>>> circle.x; circle.y; circle.center
0.0
0.0
Point(0.0, 0.0, name="Point")

Object groups

Geopy has a group for primitives and shapes, that you can use as default shape. You can get intersections inside of PrimitiveGroup or Composite:

>>> from geopy import Composite, Triangle, Box, Circle
>>> p1 = Triangle([1,0],[0,0],[0,1])
>>> p2 = Box([0,0], [5,5])
>>> c1 = Circle([1,1], 2)
>>> c2 = Circle([-1,1], 0.5)
>>> Composite(p1, p2, c1, c2)
Composite([Triangle([Point(1.0, 0.0, name="Point"), Point(0.0, 0.0, name="Point"), Point(0.0, 1.0, name="Point")], name="Triangle", pos=Triangle center[0.3333333333333333, 0.3333333333333333]), Box([Point(0.0, 0.0, name="Point"), Point(0.0, 5.0, name="Point"), Point(5.0, 5.0, name="Point"), Point(5.0, 0.0, name="Point")], name="Box", pos=Box center[2.5, 2.5]), Circle(Point[1.0, 1.0], 2), Circle(Point[-1.0, 1.0], 0.5)], name="Composite", pos=Point[0.0, 0.0])
>>> composite = Composite(p1, p2, c1, c2)
>>> composite.intersections
[Point(0.0, 2.732050807568877, name="Point"), Point(2.732050807568877, 0.0, name="Point"), Point(-0.9375, 0.5039216291753892, name="Point"), Point(1.0, 0.0, name="Point"), Point(-0.9375, 1.4960783708246108, name="Point"), Point(-0.9375, 0.5039216291753892, name="Point"), Point(0.0, 1.0, name="Point"), Point(-0.9375, 1.4960783708246108, name="Point"), Point(0.0, 1.0, name="Point"), Point(0.0, 2.732050807568877, name="Point"), Point(0.0, 0.0, name="Point"), Segment(Point[1.0, 0.0], Point[0.0, 0.0], name="Segment"), Segment(Point[0.0, 1.0], Point[0.0, 0.0], name="Segment"), Point(0.0, 0.0, name="Point"), Segment(Point[1.0, 0.0], Point[0.0, 0.0], name="Segment"), Point(0.0, 0.0, name="Point"), Segment(Point[0.0, 0.0], Point[0.0, 1.0], name="Segment"), Point(0.0, 0.0, name="Point"), Point(2.732050807568877, 0.0, name="Point"), Point(1.0, 0.0, name="Point")]

Or get intersections with another object ( you can set check_inside kwarg to False if it is a Composite method, by default it is True ):

>>> c3 = Circle([0,0], 2)
>>> composite.intersects(c3)
[Point(2.0, 0.0, name="Point"), Point(0.0, 2.0, name="Point"), Point(-0.8228756555322952, 1.822875655532295, name="Point"), Point(1.822875655532295, -0.8228756555322952, name="Point"), Point(-2.782339674459376, 0.09266032554062398, name="Point"), Point(-0.09266032554062398, 2.782339674459376, name="Point")]

You can show PrimitiveGroup and Composite in matplotlib:

composite.plot()
PrimitiveGroup(Segment([1,0],[0,1])).plot()

Composite

It is a group of shapes:

>>> from geopy import Composite, Triangle, Box, Circle
>>> p1 = Triangle([1,0],[0,0],[0,1])
>>> p2 = Box([0,0], [5,5])
>>> c1 = Circle([1,1], 2)
>>> c2 = Circle([-1,1], 0.5)
>>> Composite(p1, p2, c1, c2)
Composite([Triangle([Point(1.0, 0.0, name="Point"), Point(0.0, 0.0, name="Point"), Point(0.0, 1.0, name="Point")], name="Triangle", pos=Triangle center[0.3333333333333333, 0.3333333333333333]), Box([Point(0.0, 0.0, name="Point"), Point(0.0, 5.0, name="Point"), Point(5.0, 5.0, name="Point"), Point(5.0, 0.0, name="Point")], name="Box", pos=Box center[2.5, 2.5]), Circle(Point[1.0, 1.0], 2), Circle(Point[-1.0, 1.0], 0.5)], name="Composite", pos=Point[0.0, 0.0])

It has a center of mass:

>>> composite.center_of_mass
Point(0.7083333333333334, 1.2083333333333335, name="Composite center")

It also has a perimeter and area:

>>> composite.perimeter
39.12217683032206
>>> composite.area
38.85176877775662

PrimitiveGroup

It is a group of primitives and can not contain shapes:

>>> l1 = Line([1,0], [0,1])
>>> v1 = Vector[1,1]
>>> s1 = Segment([11,88], [0,1])
>>> PrimitiveGroup(l1, v1, s1)
PrimitiveGroup([Line(Point[1.0, 0.0], Point[0.0, 1.0], name="Line"), Vector(Point[0.0, 0.0], Point[1.0, 1.0], name="Vector"), Segment(Point[11.0, 88.0], Point[0.0, 1.0], name="Segment")], name="PrimitiveGroup")

Scene

You can show your shapes, primitives or groups in matplotlib. To do it you must create Scene with objects or add it after:

>>> from geopy import *
>>> l1 = Line([1,0], [0,1])
>>> v1 = Vector[1,1]
>>> s1 = Segment([11,88], [0,1])
>>> group1 = PrimitiveGroup(l1, v1, s1)
>>>
>>> sh1 = Triangle([0,11], [2,3], [5,5])
>>> sh2 = Box([-1,-1],[-4,-4])
>>> group2 = Composite(sh1, sh2)
>>>
>>> sh3 = Circle([0,0], 2)
>>> sh4 = Circle([5,5], 4)
>>>
>>> scene = Scene(group1, *group1.intersections)
>>> scene.add(group2)
>>> scene.add(sh3)
>>> scene.add(sh4)

It has show method:

scene.show()