Why is a nudge factor needed when drawing hex lines?

When a line passes exactly over an edge between two hexagons, standard rounding can produce non-deterministic or discontinuous paths. Adding an infinitesimal nudge (epsilon = 1e-6) breaks ties consistently.

Updated: August 2026 • Verified v1.2

Hexagonal Line Drawing & Line of Sight (LOS) Raycaster

Creative & DesignDesign

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dist = max(|dx|, |dy|, |dz|); cube_lerp(a, b, t) = a + (b - a) * t; enforce rx + ry + rz = 0

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Understanding Your Results

Calculates the hex distance between origin `(q1, r1)` and target `(q2, r2)`, executes cube linear interpolation with deterministic tie-breaking nudges, generates the complete step-by-step tile list, and provides copy-ready TypeScript functions.

Practical Guidance & Next Steps

Using cube coordinates $(x, y, z)$ with linear interpolation ($ ext{lerp}$) and cube rounding is the mathematically purest way to draw straight lines on hex grids.

What is this?

A game development geometry utility that calculates the exact ordered sequence of hexagonal tiles traversed by a straight line or projectile.

How does it work?

1. Enter origin hex coordinates (q1, r1) and destination coordinates (q2, r2). 2. View total hex distance and the complete ordered step-by-step tile trajectory. 3. Copy the production-ready TypeScript hex line drawing function.

Why use it?

Eliminates jagged line artifacts and ambiguous edge selection in hex-based game engines.

Technical Scope & Calculation Limitations

Calculates regular planar hexagonal coordinate interpolation.

Frequently Asked Questions

The start and end points are converted to 3D cube coordinates. The algorithm samples $N$ points along the line segment (where $N$ is the hex distance) and rounds each floating point to the nearest discrete hex tile using cube rounding.

Windows Desktop & Widget Options