A 2D Delaunay triangulation of a set of vertices.

An error type indicating that the two given vertices have the same position.

All the details about a particular face of a Delaunay triangulation:

• The three input vertices it is formed from
• The Triangle2d defining its shape
• The circumcircle of that triangle

An empty Delaunay triangulation with no vertices or faces.

Construct a Delaunay triangulation from an array of points. The points must all be distinct; if any two points are equal, you will get an Err CoincidentVertices.

Note that if all points are collinear, then the resulting triangulation will be empty (have no faces).

Construct a Delaunay triangulation from an array of vertices of arbitrary type, by supplying a function that returns the position of each vertex as a Point2d. For example, if you had

types alias Vertex =
    { position = Point2d Meters WorldCoordinates
    , color = String
    }

and

vertices : Array Vertex
vertices =
    ...

then you would use

DelaunayTriangulation2d.fromVerticesBy .position
    vertices

The vertices must all be distinct; if any two have the same position, you will get an Err CoincidentVertices.

Note that if all vertices are collinear, then the resulting triangulation will be empty (have no faces).

Add a new point into an existing Delaunay triangulation. It must not be equal to any existing point; if it is, you will get an Err CoincidentVertices.

Add a new vertex into an existing Delaunay triangulation, by supplying a function to get the position of the vertex. The vertex must not have the same position as any existing vertex; if it is, you will get an Err CoincidentVertices.

Get the vertices of a Delaunay triangulation. If the triangulation was constructed by calling fromPoints or fromVerticesBy, then the returned vertex array will simply be the array that was passed in. If any vertices were added using insertPoint or insertVertexBy, then they will be appended to the end of the array. This is a simple accessor, so complexity is O(1).

Get all triangles in a given Delaunay triangulation;

DelaunayTriangulation2d.triangles triangulation

is equivalent to

DelaunayTriangulation2d.faces triangulation
    |> List.map .triangle

but somewhat more efficient. Complexity: O(n).

Get all circumcircles in a given Delaunay triangulation;

DelaunayTriangulation2d.circumcircles triangulation

is equivalent to

DelaunayTriangulation2d.faces triangulation
    |> List.map .circumcircle

but somewhat more efficient. Complexity: O(n).

Get a list of all Faces in a given Delaunay triangulation. Complexity: O(n).

Convert a Delaunay triangulation to a TriangularMesh. Complexity: O(n).