What I came away with though was an appreciation for how sometimes the simplest option is a much better option that you might care to admit. So here I am several weeks later, still not quite finished texture packing my fonts after having explored several algorithms and learned a great deal about something probably not that important. Turns out though, this is not such a trivial problem, and there’s a huge wealth of literature on the topic. I figured it would be easy, I’d just search around for an algorithm to do this, implement it and move on. Recently, while working on my engine, I decided I should pack all my rasterized font bitmaps into one big texture rather than uploading all these individual characters bitmaps to the GPU. Also, balls should be a minimum diameter of 70mm to prevent choking and ball pool surfaces should have continuous level bases.Exploring rectangle packing algorithms Posted | Share: Moreover, ball pools should not be entered directly from a slide. ROSPA recommend that ball pools should have a maximum depth of 450mm in a toddler area and 600mm in a junior area to minimise the danger of accidents from concealment. Whilst the best possible packing density is about 74%, the theoretical worst is about 60% before you stop filling the space or start ignoring gravity, and randomly-poured sphere packing efficiency is around 64% which is traditionally used for playpen balls.Īs per the 2D Circle Packing calculation above, it is relatively easy to divide the volume of a sphere into the volume you want to fill multiplied by the efficiency of 64% and get a very accurate idea of how many balls you will need. ![]() Carl Friedrich Gauss proved in 1831 that Hexagonal packing is the densest possible amongst all possible lattice packings using the following formula: Density=π/(3√2)=74.048% In three-dimensional space, there are three packing types for identical spheres: cubic lattice, face-centred cubic lattice, and hexagonal lattice. Sphere packing is an arrangement of non-overlapping spheres within a containing space. Note this does not allow for the part balls around the edges or disruption of the hexagonal packing but larger areas contribute to far less than a 1% error. Then, apply the packing density to get a very accurate calculation of how many balls you will need. ![]() ![]() Therefore, by using this density percentage of 90.7%, it is relatively easy to divide the area of a circle into the area of a surface you want to cover. ![]() The density of this arrangement is Density=(π√3)/6=90.690% In two-dimensional space, Joseph Louis Lagrange proved in 1773 that the highest-density lattice arrangement of circles is the hexagonal packing arrangement in which the centres of the circles are arranged in a hexagonal lattice (staggered rows like a honeycomb), and each circle is surrounded by 6 other circles. The associated packing density is the proportion of the surface covered by the circles. In geometry, circle packing is an arrangement of non-overlapping circles within a containing space and would apply to any balls sitting on a flat surface such as tanks, pools and reservoirs. Circle Packing Surfaces – 2D Calculations
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