Greedy Geometric Algorithms for Collection of Balls, with Applications to Geometric Approximation and Molecular Coarse‐Graining. (13th March 2014) - Cazals, F.; Dreyfus, T.; Sachdeva, S.; Shah, N.
<x xml:space="preserve">Abstract</x> Choosing balls which best approximate a 3D object is a nontrivial problem. To answer it, we first address the inner approximation problem, which consists of approximating an object <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1f92mq7m" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />FO</alternatives> defined by a union of n balls with <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1f92mq85" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />k<n</alternatives> balls defining a region <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1f92mq2v" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />FS⊂FO</alternatives>. This solution is further used to construct an outer approximation enclosing the initial shape, and an interpolated approximation sandwiched between the inner and outer approximations. <boxed-text content-type="graphic" position="anchor" orientation="portrait"> </boxed-text>