ddg.geometry.lie_models module
Lie geometry module.
- class ddg.geometry.lie_models.ProjectiveModel(dimension)[source]
Bases:
CayleyKleinGeometryLie 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:
- Quadric
- 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:
- centerPoint or numpy.ndarray of shape (n+1,)
- radiusfloat
Cayley-Klein radius
- subspaceSubspace or list of numpy.ndarray of shape (k,) (default=None)
- Returns:
- CayleyKleinSphere
- generalized_cayley_klein_sphere(center, radius, subspace=None, atol=None, rtol=None)
Create a generalized Cayley-Klein sphere.
- Parameters:
- centerPoint or numpy.ndarray of shape (n+1,)
- radiusfloat
Generalized radius
- subspaceSubspace or list of numpy.ndarray of shape (k,) (default=None)
- Returns:
- GeneralizedCayleyKleinSphere
- inner_product(v, w)
Alias for self.absolute.inner_product.