Module spherical 

Spherical Geometry

Operations on the n-sphere S^n = {x ∈ R^{n+1} : ||x|| = 1}

Use Cases in Vector Search

• Cyclical patterns: Time-of-day, day-of-week, seasonal data
• Directional data: Wind directions, compass bearings
• Normalized embeddings: Common in NLP (unit-normalized word vectors)
• Angular similarity: Natural for cosine similarity

Key Operations

• Geodesic distance: d(x, y) = arccos(⟨x, y⟩)
• Exponential map: Move from x in direction v
• Logarithmic map: Find direction from x to y
• Fréchet mean: Spherical centroid

Structs

SphericalConfig

Configuration for spherical operations

SphericalSpace

Spherical space operations