Greedy Geometric Algorithms for Collection of Balls, with Applications to Geometric Approximation and Molecular Coarse‐Graining. (13th March 2014)

• Record Type: Journal Article
• Authors: Cazals, F.; Dreyfus, T.; Sachdeva, S.; Shah, N.
• Is Part Of: Computer graphics forum. Volume 33:Number 6(2014)
• Page Start: 1
• Page End: 17
• Publication Date: 2014-03-13
• Subjects: Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.12270
• Languages: English
• ISSNs: 0167-7055

Abstract

<abstract abstract-type="graphical" xml:lang="en" id="cgf12270-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p>Choosing balls which best approximate a 3D object is a nontrivial problem. To answer it, we first address the <italic>inner approximation</italic> problem, which consists of approximating an object <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1f92mq7m" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:01677055:cgf12270:equation:cgf12270-math-0400" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="script">F</mml:mi><mml:mi mathvariant="script">O</mml:mi></mml:msub></mml:math></alternatives></inline-formula> defined by a union of <italic>n</italic> balls with <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1f92mq85" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:01677055:cgf12270:equation:cgf12270-math-0401" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>k</mml:mi><mml:mo><</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula> balls defining a region <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1f92mq2v" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:01677055:cgf12270:equation:cgf12270-math-0402" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="script">F</mml:mi><mml:mi mathvariant="script">S</mml:mi></mml:msub><mml:mo>⊂</mml:mo><mml:msub><mml:mi mathvariant="script">F</mml:mi><mml:mi mathvariant="script">O</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>. This solution is further used to construct an <italic>outer approximation</italic> enclosing the initial shape, and an <italic>interpolated approximation</italic> sandwiched between the inner and outer approximations. <boxed-text content-type="graphic" position="anchor" orientation="portrait"><graphic position="anchor" mimetype="image" xlink:href="ark:/27927/pgh1f92qppq" orientation="portrait" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /></boxed-text></p> </abstract>