Continuous skeletons of discrete objects
Atul Sudhalkar, Levent Gürsöz, Fritz B. Prinz · 1993
The Medial Axis Tra@brm (hiAT) wtM&~by Ilium in the sixties as an alternate description of the shape of an object, Since then, its potential qoplicability in 4 wide range of ertgi-@ering domains ha? been acbwwledged.Howevec this p&entid has never qttite been mdised, acept recently in two dimensions.One reason is thedi)jicdty in defining algorithms for $nding the MAT,especiallyin threedinte?uiom.Anotkr rea$onis the lack @incentive for modeling&?signrdin?ctiy in MAPs.Given this impasse, sctne latzrd thinking appears to be in order.Perhaps the MT per se is not the cmly skeleton which can be ttsed.Are them otk~mow easily derived skdetom, whichsharethcase propertiesof tk MATwhichareof interest in engineeringdesign?In this work, we i&ntifi a set of pnyerties @ tk MAT which, we argue, are r#prhrtary interest.Bri4@y, tkse pmpertks are dimensbnal reduction (in thesenseof having no interwr), homc%cpicequivalence, and invertibiiity.For tk restricted class @discrete objects, we dejine an algorithmfor identi~ing .nobtset, called a skele~which shams theseproperties withthe MAT Furthermom,thikske&tonis to the box-mwm (LW norm) what tk MAT is to the euclidean norm, and hence Ihe akviotwn of thir skekton/iwn the MIT is tightiybountkd.Thealgorithm wiil be developedfor bothtwo andthme-dirnenswnd ccaw.r.Pnwfs c#some aspectsof tk algorithmhaveken worked out, and shall be indicated.Tk use of thk skleton in automated numerical analysis of iy"ection molded parts shall be &non@rat& on industrial-sised parts.The we of the3D skeleton in aiding automatic mesh &u?raIiOn fo? @e-ekment analysisis alswc$intemst,andstil be discwsed.Permissmn 10 copy wIfhoutfee all or parl of this material M granted provided [hat [he copies are noi made or distributed for direct commercial advanrdge, Ihe ACM copymght notice and the title of the puhlicatimr and its datr appear.and notice IS given that copying is by permission of the Aiw>ciation Inr Computing Mach] nery.To copy o[hcrw,we, or to repuhllsh, requires ir fee mwfhr specifi' perrnissinn.?nd ACM Solid Modeling '93-5 /93 fMonlreal, Canada {) 1993 ACM ().S979 I .584-4/93/()()05/()()85. ..$ I .50