Metrics

Metrics define distances on base/total spaces used in cover construction, analysis and visualization.

circle_bundles.EuclideanMetric	Standard Euclidean metric on \(\mathbb{R}^d\).
circle_bundles.S1AngleMetric	Geodesic distance on the circle \(\mathbb{S}^1\) using angles.
circle_bundles.RP1AngleMetric	Geodesic distance on the real projective line \(\mathbb{RP}^1\) using angular coordinates.
circle_bundles.S1UnitVectorMetric	Geodesic distance on \(\mathbb{S}^1\) using unit vectors in \(\mathbb{R}^2\).
circle_bundles.RP1UnitVectorMetric	Geodesic distance on \(\mathbb{RP}^1\) using unit vectors in \(\mathbb{R}^2\).
circle_bundles.RP2UnitVectorMetric	Metric on \(\mathbb{RP}^2\) using antipodal unit vectors in \(\mathbb{R}^3\).
circle_bundles.T2FlatMetric	Flat metric on the 2-torus \(\mathbb{T}^2\).
circle_bundles.Torus_DiagQuotientMetric_R4	Z2 quotient metric on R^4 C^2-torus embedding for the diagonal pi-shift:
circle_bundles.Torus_KleinQuotientMetric_R4	Z2 quotient metric on R^4 C^2-torus embedding that implements the Klein identification (base,fiber) ~ (base+pi, -fiber) with an explicit base-factor choice.
circle_bundles.RP2_TrivialMetric	Trivial circle bundle over RP^2: (v,z)~(-v,z).
circle_bundles.RP2_TwistMetric	Orientable nontrivial (monodromy -1): (v,z)~(-v,-z).
circle_bundles.RP2_FlipMetric	Non-orientable (reflection on fiber): (v,z)~(-v,conj z).
circle_bundles.S3QuotientMetric