![]() Circles Outside a Circle - Calculate the numbers of circles on the outside of an inner circle - like the geometry of rollers on a shaft.Circles - Circumferences and Areas - Circumferences and areas of circles with diameters in inches.Area Units Converter - Convert between units of area.Area Survey App - Online app that can be used to make an exact plot of a surveyed area - like a room, a property or any 2D shape.Area of Intersecting Circles - Calculate area of intersecting circles.Electrical - Electrical units, amps and electrical wiring, wire gauge and AWG, electrical formulas and motors.Mathematics - Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.Greedy Best Long Side Fit - the same as Best Long Side Fit, but if an item fits perfectly along any side of free space (no side length wasted), this placement is preferred.Update: another heuristics is added to solve the edge case from the comments In case of a tie, the Best Short Side Fit rule is used. Best Area Fit - the free space area should be the smallest in the area to place the next rectangle into.Best Long Side Fit - the free space area should have the minimum length of the longer leftover side.Best Short Side Fit - the free space area should have the minimum length of the shorter leftover side.In the case of a tie, the one with the smallest x-coordinate value is used. Bottom-Left - the y-coordinate of the top side of the rectangle should be the smallest.As for particular placement rule, this implementation actually checks four of them and then picks the rule which produces the best result (i.e., uses a minimum amount of bins). Here we use the global approach, which means that on each step, we compute 'score' for each remaining rectangle and each remaining free space and choose the combination which gives us the best score. There are also different rules for choosing which rectangle to place into which bin. The idea of the Maximal Rectangles heuristic is to keep track of all maximal free rectangular spaces, which are still available after placing an object into the container (see picture below) This heuristic is an extension of the Guillotine Split heuristic and shows excellent results for offline packing 1 This particular implementation of 2D bin packing problem solver relies on Maximal Rectangles Algorithms. So, we can only approximate the optimal solution with heuristic algorithms. This is one of the classical problems in combinatorial optimization and is proven to be NP-hard. So, here we need to deal with the offline 2D rectangle bin packing problem. If the set of objects to be packed is known beforehand, the problem is called 'offline' as opposed to the 'online' problem, where objects appear one by one. The goal usually is to pack all objects using as few containers as possible. ![]() ![]() A set of objects (again, in our case, these are smaller rectangles) should be packed into one or more containers. In any bin packing problem, you are given some containers (in our case, the container is a 2D rectangular region). Ok, so here we deal with the Two-Dimensional Rectangle Bin Packing problem.
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