ddg.conversion.nets.geometry.spheres module
- ddg.conversion.nets.geometry.spheres.euclidean_sphere_to_smooth_net(s, affine_component=-1)[source]
Converts a two-dimensional sphere in three-dimensional ambient space to a smooth net.
- Parameters:
- sddg.Sphere
A two-dimensional sphere in three-dimensional projective space.
- Returns:
- ddg.datastructures.nets.SmoothNet
A parameter-dependent smooth net.
- Raises:
- ValueError
If the given sphere is not a two-dimensional sphere in three-dimensional projective space.
- NotImplementedError
If center of the sphere is a point at infinity.
Notes
The resulting SmoothNet object depends the radius and the center of the sphere as parameters.
- ddg.conversion.nets.geometry.spheres.euclidean_circle_to_smooth_net(c, affine_component=-1)[source]
Converts a circle in n-dimensional space to a smooth curve.
- Parameters:
- cddg.Sphere
A one-dimensional sphere in n-dimensional projective space.
- Returns:
- ddg.datastructures.nets.SmoothCurve
A parameter-dependent smooth curve.
- Raises:
- ValueError
If the given sphere is not a circle in n-dimensional projective space.
- NotImplementedError
If center of the circle is a point at infinity.
Notes
The resulting SmoothCurve object depends on the following parameters: the radius of the circle, the center of the circle and optionally (if the ambient dimension is greater than 2) the normals of its defining plane.
- ddg.conversion.nets.geometry.spheres.cayley_klein_sphere_to_smooth_net(sphere, affine_component=-1)[source]
Convert Cayley-Klein sphere to smooth net.
This function works by first converting the sphere to a quadric and then using quadric_to_smooth_net. For this to work, the sphere’s geometry must implement metric_to_cayley_klein_distance and the resulting quadric type must be convertible to a smooth net.
- Parameters:
- sphereSphere
- affine_component: int (default=-1)
- Returns:
- SmoothNet