Matpic
mathematics, in pictures
Generator

voronoi

A generator in the geometry library, called 7 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.

voronoi is one function. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and if the generator changes, this page changes with it.

At its defaults

The plane divided by nearest neighbour10 sites, and every point of the rectangle shaded by which site is closest to it. The boundaries are the places where two sites tie.

show: "bisector"

Where two sites tieTwo sites, and the line of points equally far from both. Every point on one side is nearer to one site; the boundary between two cells is always a piece of this line.one sitethe otherequally far from both

show: "delaunay"

The Delaunay triangulationThe 11 triangles dual to the cells: two sites are joined exactly when their cells share an edge. No triangle's circumcircle contains any other site.

What it checks while it draws

Collected by running the family and listening to lib/verify.js, not written here. The count is how many separate times this build put that claim to the test.

Where it is called

Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.

Geometry

The plane, divided by whoever is nearest

Scatter some points and colour every other point of the plane by which one is closest. The result is a tiling nobody designed, and its dual triangulation has a property that no part of the construction mentions.

The whole library · What the figures prove