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Complex polyhedralobjectsare often constructedfrom simpler polyhedralobjectsusingCSG,booleansandvariousblendoperationsthatproducefillets andchamfers.Skinningandshrinkwrapping techniquesprovide alternati ves to generatinga smoothcompositeobjectfrom individual objectparts. This paperpresentsan effectiveandgeneraltechniquefor incrementallybuilding complex polyhedralobjectsfrom simpler parts. We provide a procedural implicit functiondefinition for a region of a polyhedralobjectthat is star-shapedwith respectto a skeletalpoint, calleda blendcenter. We extendthis definition to provide a singleimplicit function definition for anarbitrarypolyhedralobject,whereevery region is star-shapedwith respecto aproximalblendcenter , chosenfrom an arbitrarysetof blendcenters.Thisallowstheapplicationof implicit functionbasedmodelingtechniquesin constructingtransitionsurfacesbetweenarbitrarypolyhedralobjectparts.Generalizationsof our approachallow thealgebraiccombinationof arbitrarily shaped andpositioned,disjointobjectparts,andis thusasignificantsuper setof CSG,booleans,andotherblendingtechniques.At thesame timeoriginaldetailandcharacterof objectpartsarepreservedin regionswherethey arenotinvolvedin constructingtransitionsurfaces or donotinteractwith otherobjectparts.A completeimplemetation of thepresentedconceptsshow polyhedralimplicit primitivesto be a generalandefficient techniquefor building complex polyhedral objectsfrom a modularsetof polyhedralobjectparts.

Joining polyhedral objects using implicitly defined surfaces