circleGraphLayout: Find an arrangement of circles satisfying a graph of...

In packcircles: Circle Packing

Find an arrangement of circles satisfying a graph of adjacencies

Description

Attempts to derive an arrangement of circles satisfying prior conditions for size and adjacency. Unlike the circleRepelLayout function, this is a deterministic algorithm. Circles are classified as either internal or external. Viewing the pattern of adjacencies as a triangulated mesh, external circles are those on the boundary. In the version of the algorithm implemented here, the radii of external circles are provided as inputs, while the radii of internal circles are derived as part of the output arrangement.

Usage

circleGraphLayout(internal, external)

Arguments

internal	A list of vectors of circle ID values where, in each vector, the first element is the ID of an internal circle and the remaining elements are the IDs of that circle's neighbours arranged as a cycle. The cycle may be clockwise or anti-clockwise but the same ordering must be used for all vectors.
external	A data.frame or matrix of external circle radii, with circle IDs in the first column and radii in the second column.

Details

The internal argument specifies circle adjacencies (ie. tangencies). The format is an concise representation of graph edges, and consists of a list of vectors: one per internal circle. In each vector the first element is the ID value of the internal circle and the remaining values are IDs of neighbouring circles, which may be either internal or external.

The external argument is a data.frame which specifies the radii of external circles. Internal circle radii should not be specified as they are derived as part of the fitting algorithm. The function will issue an error if any internal circle IDs are present in the external data.

Value

A data.frame with columns for circle ID, centre X and Y ordinate, and radius.

The output arrangement as a data.frame with columns for circle ID, centre X and Y ordinates, and radius. For external circles the radius will equal input values.

Note

Please treat this function as experimental.

References

C.R. Collins & K. Stephenson (2003) An algorithm for circle packing. Computational Geometry Theory and Applications 25:233-256.

Examples

## Simple example with two internal circles surrounded by
## four external circles. Internal circle IDs are 1 and 2.
internal <- list( c(1, 3, 4, 5), c(2, 3, 4, 6) )

## Uniform radius for external circles
external <- data.frame(id=3:6, radius=1.0)

## Generate the circle packing
packing <- circleGraphLayout(internal, external)

packcircles documentation built on Sept. 8, 2023, 5:55 p.m.