ddg.geometry.lie_models module

Lie geometry module.

class ddg.geometry.lie_models.ProjectiveModel(dimension)

Bases: CayleyKleinGeometry

Lie geometry.

Model space

The model space is the quadric with matrix diag([1,...,1, -1, -1]) in RP^{n+2}.

Points in this quadric correspond to oriented hyperspheres and hyperplanes in R^n.

Parameters:

dimensionint

Attributes:

dimensionint

property absolute

The absolute quadric with matrix diag([1,...,1, -1, -1]).

Returns:

ddg.geometry.Quadric

property moebius_point

property moebius_subspace

moebius()

Corresponding projective model of Moebius geometry.

from_moebius(object_, embedded=False)

to_moebius(object_, embedded=False)

property laguerre_point

property laguerre_subspace

laguerre()

Corresponding projective model (Blaschke cylinder) of Laguerre geometry.

from_laguerre(object_, embedded=False)

to_laguerre(object_, embedded=False)

property ambient_dimension

cayley_klein_distance(v, w)

Alias for self.absolute.cayley_klein_distance.

cayley_klein_sphere(center, radius, subspace=None, atol=None, rtol=None)

Create a Cayley-Klein sphere.

Parameters:

centerddg.geometry.Point or numpy.ndarray of shape (n+1,)

radiusfloat

Cayley-Klein radius

subspaceddg.geometry.Subspace or list of numpy.ndarray of shape (k,)

(default=None)

Returns:

ddg.geometry.spheres.CayleyKleinSphere

generalized_cayley_klein_sphere(center, radius, subspace=None, atol=None, rtol=None)

Create a generalized Cayley-Klein sphere.

Parameters:

centerddg.geometry.Point or numpy.ndarray of shape (n+1,)

radiusfloat

Generalized radius

subspaceddg.geometry.Subspace or list of numpy.ndarray of shape (k,)

(default=None)

Returns:

ddg.geometry.spheres.GeneralizedCayleyKleinSphere

inner_product(v, w)

Alias for self.absolute.inner_product.