Module medial_graph 

The medial axis of any planar face: holes, reflex corners and curved boundaries included, each branch its exact bisector.

The boundary is taken apart into sites: every edge’s open interior, and every reflex corner as a point (a convex corner is where its two edges’ bisector reaches the boundary, not a site of its own). The axis is the set of points with two or more nearest sites, and where two sites meet it is a curve with a closed form: two segments’ bisector is a line, a segment and a point’s a parabola, and a circular arc speaks as a circle, so an arc against a segment is a parabola too and an arc against a point or an arc is a hyperbola or an ellipse. A site on any other curve has no closed form, and its branches are fitted through points solved onto the bisector exactly.

Which sites meet where (the axis’s topology) is read off a sampling: the Delaunay triangulation of points along every site has, inside the region, circumcentres whose three corners name their sites. A centre naming two sites is a point on their branch, one naming three a branch point. Each branch point is then solved exactly (equidistant from its sites, by Newton), and each branch is its exact bisector between the branch points the sampling says it runs between. The result is checked: along every branch no third site may come nearer than the branch’s own two, and every sampled centre must lie on some branch. A result that fails is sampled again, finer.

Structs

MedialBranch

One branch: the curve of points equidistant from two sites.

MedialGraph

The medial axis of a planar face as a graph of exact branches.

MedialVertex

A branch point of the medial axis, or a branch’s end on the boundary.

Enums

MedialSite

A boundary element a medial branch keeps its distance from.

Functions

medial_graph

The medial axis of a planar face: every point with two or more nearest boundary elements, as exact branches between branch points.