lumen-geometry

Mathematical models for tubular anatomical structures.

What is this?

This crate provides pure math for generating and querying the geometry of hollow organs like the colon, bronchi, and intestines. No game engine required - just math you can use anywhere.

"Lumen" is the medical term for the interior space of a tubular organ (from Latin lumen, meaning "light" or "opening").

Who is this for?

• Medical students learning GI tract anatomy
• Simulation developers building surgical trainers
• Researchers needing procedural anatomical models
• Game developers creating medical environments

Quick Start

use lumen_geometry::colon::{ColonConfig, ColonCurve};
use lumen_geometry::TubularCurve;

// Create a colon with default anatomical parameters
let config = ColonConfig::default();
let colon = ColonCurve::new(&config);

// Query positions along the centerline (t: 0.0 = rectum, 1.0 = cecum)
let rectum_pos = colon.position_at(0.0);
let transverse_pos = colon.position_at(0.5);
let cecum_pos = colon.position_at(1.0);

// Get the direction the tube is heading at any point
let forward = colon.tangent_at(0.3);

// Query wall position including haustra (pouches)
let wall_point = colon.wall_position_at(0.3, std::f32::consts::PI);

Colon Anatomy

The human colon is approximately 1.5 meters long and consists of anatomically distinct regions:

t=0.0                                                    t=1.0
  │                                                        │
  ▼                                                        ▼
Rectum → Sigmoid → Descending → Splenic → Transverse → Hepatic → Ascending → Cecum
                                Flexure                 Flexure

Segments

Haustra

The colon wall has characteristic sac-like pouches called haustra, formed by:

1. Taeniae coli: Three longitudinal muscle bands running the length of the colon, spaced 120° apart
2. Circular muscle contractions: Create individual pouch boundaries

    Taenia 1 (0°)
         │
   ╭─────┴─────╮
  ╱             ╲
 │   Haustrum    │
  ╲             ╱
   ╰─────┬─────╯
         │
    Taenia 2 (120°)

Procedural Variation

Different seeds produce anatomically plausible variations:

use lumen_geometry::colon::{ColonConfig, ColonCurve};

// Same anatomy every time
let standard = ColonCurve::new(&ColonConfig::default());

// Procedurally varied
let patient_a = ColonCurve::new(&ColonConfig::with_seed(42));
let patient_b = ColonCurve::new(&ColonConfig::with_seed(123));

Seeds affect:

• Segment length ratios (within anatomical bounds)
• Flexure angles
• Radius variations
• Secondary curve wobble

Key Concepts

t-parameter

Position along the curve is expressed as t ∈ [0.0, 1.0]:

• t = 0.0 → Rectum (entry point)
• t = 1.0 → Cecum (end)

Arc Length

Physical distance along the curve (in world units). Convert between t and arc length:

use lumen_geometry::TubularCurve;

// Travel 10 units forward from t=0.3
let new_t = colon.advance_by_arc(0.3, 10.0);

// Get arc length to a specific t
let distance = colon.t_to_arc(0.5);

Local Coordinate Frame

At any point, you can get a local coordinate system:

• Tangent: Forward direction (along the curve)
• Normal: Up direction
• Binormal: Right direction

use lumen_geometry::TubularCurve;

let tangent = colon.tangent_at(0.5);
let normal = colon.normal_at(0.5);
let binormal = colon.binormal_at(0.5);
let frame = colon.frame_at(0.5); // As a quaternion

No Dependencies on Game Engines

This crate only depends on:

• glam - Standard 3D math (Vec3, Quat)
• rand / rand_chacha - Deterministic random number generation

Use it with Bevy, Godot, Unity (via FFI), or plain Rust.

License

Licensed under either of:

• Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.