#Pack circles in rectangle code#

The 257 × 157 rectangle has area 40349, but at most a 2 3 fraction of that area can be used: at most area 40349 2 3 36592.5.

#Pack circles in rectangle code#

The implementation is based on a Python version by David Eppstein (see CirclePack.py in the PADS library. But you can estimate the number of circles that will fit by knowing that the limiting density of the triangular packing is 2 3. Functions for packing N circles into a rectangle of width W and height H, together with a function for plotting solution and some example code fitting 13. The function circleGraphLayout is an initial Rcpp port of an algorithm described by Collins and Stephenson (2003) to find an arrangement of circles which corresponds to a graph of desired circle tangencies. For the latter, package lpSolve must be installed. It provides several fast heuristic algorithms to choose from, as well as two based on linear programming. The function circleRemoveOverlaps takes an initial set of overlapping circles and attempts to find a non-overlapping subset or, optionally, a subset with some specified degree of overlap. The underlying algorithm is described in the paper: Visualization of large hierarchical data by circle packing by Weixin Wang et al. (2006). Packing problems for regular shapes (circles and rectangles) of objects and/or. It was adapted from a version written in C by Peter Menzel. Keywords: circle packing, integer programming, large scale optimization. The function circleProgressiveLayout arranges a set of circles, which are denoted by their sizes, by consecutively placing each circle externally tangent to two previously placed circles while avoiding overlaps. Each circle’s centre is constrained to lie within the rectangle but its edges are allowed to extend outside. To avoid edge effects, the bounding rectangle is treated as a toroid. This process is repeated iteratively until no more movement takes place (acceptable layout) or a maximum number of iterations is reached (layout failure). There is a mn rectangular matrix whose top-left(start) location is (1, 1) and bottom-right(end) location is (mn). The distance moved by each circle is proportional to the radius of the other to approximate inertia (very loosely), so that when a small circle is overlapped by a large circle, the small circle moves furthest. It involves iterative pair-repulsion, in which overlapping circles move away from each other. The algorithm is adapted from an example written in Processing by Sean McCullough (which no longer seems to be available online). The function circleRepelLayout attempts to arrange a set of circles of specified radii within a rectangle such that there is no-overlap between circles. This package provides functions to find non-overlapping arrangements of circles. Algorithms to find arrangements of non-overlapping circles