Finding feasible mold parting directions using graphics hardware
Proceedings of the 2005 ACM symposium on Solid and physical modeling
A new global accessibility algorithm for a polyhedral model with convex polygonal facets
Computer-Aided Design
Critical point analysis using domain lifting for fast geometry queries
Computer-Aided Design
Global curve analysis via a dimensionality lifting scheme
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Computer-Aided Design
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In manufacturing processes like injection molding ordie casting, a 2-piece mold is required to be separable, thatis, having both pieces of the molds removed in oppositedirections while interfering neither with the mold nor witheach other.The fundamental problem is to find a viewing (i.e. separating)direction, from which a valid partition line (i.e.the contact curves of the two mold pieces) exists. Whileprevious research work on this problem exists for polyhedralmodels, verifying and finding such a partition line forgeneral freeform shapes, represented by NURBS surfaces,is still an open question.This paper shows that such a valid partition exists fora compact surface of genus g, , if and only if there is a viewingg + 1 non-singular disjoint loops. Hence, the 2-piece moldseparability problem is essentially reduced to the topologicalanalysis of silhouettes.It follows that the aspect graph, which gives all topologicallydistinct silhouettes, allows one to determine theexistence of a valid partition as well as to find such apartition when it exists. In this paper, we present an aspectgraph computation technique for compact free-formobjects represented as NURBS surfaces. All the visionevent curves (parabolic curves, flecnodal curves, and bitangencycurves) relevant to mold separability are computedby symbolic techniques based on the NURBS representation,combined with numerical processing. An imagedilation technique is then used for robust aspect graph celldecomposition on the sphere of viewing directions. Thus,an exact solution to the 2-piece mold separability problemis given for such models.