IntroductionGiven a fixed set of identical or different-sized circular items, the problem consists on finding the smallest object within which the items can be packed. As smallest object, we consider the object which has the smallest area, perimeter, volume or surface area, depending on the object and the problem dimension. This page shows numerical results and visual solutions for the problems considered in: E. G. Birgin and F. N. C. Sobral, Minimizing the object dimensions in circle and sphere packing problems, Computers & Operations Research 35, pp. 2357-2375, 2008. [Abstract] [pdf] [ps] Unitary-radius circlesThe objects considered here are: circle, square, strip, equilateral triangle and rectangle.
mp desired-file.mp A file named desired-file.1 (an EPS file) will be created. Rename it to figure.1. Now you have to include this recently created file into a Tex file. Download the file figures.tex. Then type latex figures.tex dvips figures.dvi -o figures.ps Now type gv figures.ps to see the desired solution. Unitary-radius spheresThe objects considered here are: cube, cuboid, cylinder, pyramid, regular tetrahedron, sphere and 3D strip.
play desired-file.vmd |