Entities

class diofant.geometry.entity.GeometryEntity[source]

The base class for all geometrical entities.

This class doesn’t represent any particular geometric entity, it only provides the implementation of some methods common to all subclasses.

ambient_dimension

What is the dimension of the space that the object is contained in?

encloses(o)[source]

Return True if o is inside (not on or outside) the boundaries of self.

The object will be decomposed into Points and individual Entities need only define an encloses_point method for their class.

Examples

>>> t  = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices)
>>> t2 = Polygon(*RegularPolygon(Point(0, 0), 2, 3).vertices)
>>> t2.encloses(t)
True
>>> t.encloses(t2)
False
intersection(o)[source]

Returns a list of all of the intersections of self with o.

Notes

An entity is not required to implement this method.

is_similar(other)[source]

Is this geometrical entity similar to another geometrical entity?

Two entities are similar if a uniform scaling (enlarging or shrinking) of one of the entities will allow one to obtain the other.

Notes

This method is not intended to be used directly but rather through the \(are_similar\) function found in util.py. An entity is not required to implement this method. If two different types of entities can be similar, it is only required that one of them be able to determine this.

See also

scale()

rotate(angle, pt=None)[source]

Rotate angle radians counterclockwise about Point pt.

The default pt is the origin, Point(0, 0)

See also

scale(), translate()

Examples

>>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices)
>>> t # vertex on x axis
Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2))
>>> t.rotate(pi/2) # vertex on y axis now
Triangle(Point2D(0, 1), Point2D(-sqrt(3)/2, -1/2), Point2D(sqrt(3)/2, -1/2))
scale(x=1, y=1, pt=None)[source]

Scale the object by multiplying the x,y-coordinates by x and y.

If pt is given, the scaling is done relative to that point; the object is shifted by -pt, scaled, and shifted by pt.

See also

rotate(), translate()

Examples

>>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices)
>>> t
Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2))
>>> t.scale(2)
Triangle(Point2D(2, 0), Point2D(-1, sqrt(3)/2), Point2D(-1, -sqrt(3)/2))
>>> t.scale(2, 2)
Triangle(Point2D(2, 0), Point2D(-1, sqrt(3)), Point2D(-1, -sqrt(3)))
translate(x=0, y=0)[source]

Shift the object by adding to the x,y-coordinates the values x and y.

See also

rotate(), scale()

Examples

>>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices)
>>> t
Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2))
>>> t.translate(2)
Triangle(Point2D(3, 0), Point2D(3/2, sqrt(3)/2), Point2D(3/2, -sqrt(3)/2))
>>> t.translate(2, 2)
Triangle(Point2D(3, 2), Point2D(3/2, sqrt(3)/2 + 2),
    Point2D(3/2, -sqrt(3)/2 + 2))