Packing problem circles in rectangle code#

The algorithm works quite poorly on identically-sized circles (it cannot find the famous honeycomb pattern for 20 circles in a square), but pretty well on a wide distribution of random radii. You can safely place about 20 circles, but anything above 100 will make your browser crawl.įor some reason, it is way faster on FireFox than on IE11. The computation time rises pretty steeply.

Packing problem circles in rectangle code#

The code is not optimized, to favor readability (or so I hope :)). Var placement = (this, surface) Ĭonsole.log ('placed',placement.length,'out of','for surface', surface) Surface += Math.PI * Math.pow(this.circles,2) find the smallest rectangle to fit all circlesįor (var i = 0 i != i++) return all placed circles except the four bounding circles match current circle against all possible pairs of placed circles compute all possible placements of the unplaced circlesįor (var i = 0 i != unplaced.length i++) Var w = this.w = Math.sqrt (surface * this.ratio) Var bounding_r = Math.sqrt(surface) * 100 // 'infinite' radius deduce starting dimensions from surface If (in_rect(radius, p2)) res.push(new Circle (radius, p2)) If (in_rect(radius, p1)) res.push(new Circle (radius, p1)) Var p2 = new Point (base.x +u.y * y, base.y - u.x * y) Var p1 = new Point (base.x -u.y * y, base.y + u.x * y) compute c1 and c2 intersection coordinates in (u,v) base Var u = c1.c.vect(c2.c) // c1 to c2 vector

return the corner placements for two circles approximate a segment with an 'infinite' radius circleįunction bounding_circle (x0, y0, x1, y1) check if a circle is inside our rectangle try to fit all circles into a rectangle of a given surface Here is a fiddle var Packer = function (circles, ratio) I have added a simple dichotomic search on top of it to guess the minimal surface (which yields the smallest bounding rectangle for a given aspect ratio). (it simply tries to fit a bunch of circles into a given rectangle). The original algorithm does not produce the smallest rectangle to hold all the circles The algorithm simply starts with the four bounding circles and adds one circle at a time, using the greedy heuristic lambda parameter to pick the 'best' location. This also simplifies the start condition greatly. The 'corner' circles (as the algorithm calls them) are all computed as tangents to a pair of circles, thus eliminating the special circle+segment or segment+segment cases. They are computed to pass through the corners of the bounding box and converge toward the actual sides when the radius grows. The picture shows what the 4 bounding circles look like when the radius is decreased. Instead of segments defining the bounding box, I used circles with 'infinite' radii, that can be considered a good approximation of lines: I used a trick to make the computation more regular. I tweaked it quite a bit, but I think it does basically the same thing. Here is a go at the implementation of your algorithm. Visualization of large multi-criteria result sets.Non-convex QPs on a D-Wave Quantum Computer?.Packing circles in a rectangle: a MIQCP model.The picture at the top of this post represents the optimal solution for the model with the small random data set of just four sensors. For large problems however this thing turns out to be not so easy to solve. We repeat this trick in the second implication.Īs this is a convex MIQCP, we can use some commercial solvers like Cplex and Gurobi. In the model below we try to solve this by maximizing the number of points covered by at least one sensor:īasically we model two implications and an objective:įor points inside circle k we don't impose anything, but leave it to the objective to drive things in the right direction. However if we superimpose over the rectangle a grid with points, and try to minimize the uncovered points we may have a chance. We are dealing with overlapping circles and and circles that cover areas outside the rectangle. It looks very difficult to me to develop a model that minimizes the uncovered (white) area in the above picture. The circles may look more like ellipses as the aspect ratio of the plot is not one (the plot is too wide).

Given a set of circles (with given radius) try to cover as much area of a rectangle.