ddg.geometry.laguerre_models module
Laguerre geometry module.
Contains model classes and functions for conversion between the models.
- class ddg.geometry.laguerre_models.ProjectiveModel(dimension)[source]
Bases:
CayleyKleinGeometryProjective / Blaschke cylinder model of Laguerre geometry.
Model space
The model space is the quadric with matrix
diag([1,...,1, 0, -1])without the point at infinity [0,…,0, 1 ,0].Representation of objects
Points in this cylinder represent hyperplanes in R^n: In affine coordinates, they have a “direction” v and a “height” h. The point (v, h) corresponds to the hyperplane
<x, v> = h.- Parameters:
- dimensionint
- Attributes:
- dimensionint
- property absolute
The absolute quadric with matrix
diag([1,...,1, 0, -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.
- class ddg.geometry.laguerre_models.EuclideanModel[source]
Bases:
objectEuclidean model of Laguerre geometry.
Model space
The model space is R^n.
Representation of objects
Objects are represented by their Euclidean equivalents, mostly subspaces.