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geom2d

The geom2d package implements 2D geometry primitives and operations.

Contents:

Primitives

This geom2d package defines the following two-dimensional geometric primitives:

  • Point: a position in the plane defined by its coordinates xand y.
  • Vector: a direction in the plane defined by its projections u and v.
  • Segment: a straight line segment defined between two points: startand end. The middle points of a segment can be iterated using a parameter t which varies from 0 to 1.
  • Line: an infinite straight line defined by a base point base and a direction vector direction.
  • Size: defined by a width and length.
  • Rect: a rectangle defined by an origin point origin and a Size.
  • Circle: defined by a center point center and a radius.
  • Polygon: defined by a sequence of ordered vertices (instances of the Point class).

Transformations

Apart from these primitives, there's an important algebraic concept defined in this package: AffineTransform. The AffineTransform class defined in the affine_transf.py module represents an affine transformation. This class can be used to apply this type of transformations to the geometric primitives.

To create an affine transformation, use the constructor:

from geom2d import AffineTransform

transf = AffineTransform(sx=1, sy=2, tx=10, ty=20, shx=0.5, shy=0.75)

where the terms correspond to:

  • sx: scale in the x-axis
  • sy: scale in the y-axis
  • tx: translation along the x-axis
  • ty: translation along the y-axis
  • shx: shear in the x-axis
  • shy: shear in the y-axis

You may also create certain types of affine transformations using the factory functions in the affine_transforms.py module:

  • make_scale(sx, sy, center): creates a scale transformation with sx and sy factors and using center as reference
  • make_rotation(radians, center): creates a rotation transformation of radians about the center point

Affine transformations can be applied to almost every primitive in the geom2d package:

  • apply_to_point(point)
  • apply_to_segment(segment)
  • apply_to_polygon(polygon)
  • apply_to_rect(rect): returns the transformed Rect as a Polygon
  • apply_to_circle(circ): returns the transformed Circle as a Polygon

Affine transformations can be concatenated using the then(other) method:

import math
from geom2d import make_scale, make_rotation, Point

center = Point(10, 20)
scale = make_scale(2, 4, center)
rotate = make_rotation(math.pi, center)

scale_and_rotate = scale.then(rotate)

In this case, applying the scale_and_rotate affine transformation is equivalent to first applying the scale transformation, then rotate.

Intersections

There are algorithms defined to compute intersections between:

  • two Segment instances:
from geom2d import Segment, Point

segment_one = Segment(Point(0, 0), Point(100, 100))
segment_two = Segment(Point(0, 100), Point(100, 0))

segment_one.intersection_with(segment_two)

yields:

{ x: 50, y: 50 }

  • two Line instances:
from geom2d import Line, Point, Vector

line_one = Line(Point(0, 0), Vector(1, 1))
line_two = Line(Point(0, 100), Vector(1, -1))

line_one.intersection_with(line_two)

also yields:

{ x: 50, y: 50 }

  • two Rect instances:
from geom2d import Rect, Point, Size

rect_one = Rect(Point(0, 0), Size(50, 50))
rect_two = Rect(Point(10, 10), Size(100, 100))
rect_one.intersection_with(rect_two)

yields the rectangle:

{ origin: { x: 10, y: 10 }, size: { width: 40, height: 40 } }

We can also compute the overlap between two circles in form a penetration vector:

from geom2d import Circle, Point

circ_one = Circle(Point(0, 0), 20)
circ_two = Circle(Point(10, 10), 30)
circ_one.penetration_vector(circ_two)

which yields the vector:

{ u: -25.355339059327374, v: -25.355339059327374 }