Module hyperbolic_geometry 

hyperbolic_geometry.rs - Poincaré Disk Model Implementation for horon-engine

Hyperbolic Geometry Implementation

This module implements the Poincaré disk model of hyperbolic geometry, providing the mathematical foundation for Hyperbolic Tree Tensors (HTT).

Key Features:

• Poincaré Disk Model: Represents hyperbolic space within a unit disk
• Fixed-Point Arithmetic: Ensures deterministic results across platforms
• Möbius Transformations: Efficient operations for manipulating points
• Hyperbolic Distance Calculations: Accurate measurement in hyperbolic space

The Poincaré disk is ideal for representing hierarchical tree structures because it visually emphasizes the exponential growth characteristic of hyperbolic space, making it perfect for HTT’s hierarchical representations.

Structs

HyperbolicPoint

A point in the Poincaré disk model of hyperbolic space.

PoincareDisk

The Poincaré disk model of hyperbolic space.

Functions

distance_to_ratio

Convert a hyperbolic distance to its corresponding ratio threshold.

ratio_to_distance

Convert a Möbius ratio back to its hyperbolic distance.