{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T20:12:29Z","timestamp":1672431149512},"reference-count":27,"publisher":"ASME International","issue":"1","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2006,3,1]]},"abstract":"<jats:p>We consider the problem of whether a given geometry can be molded in a two-part, rigid, reusable mold with opposite removal directions. We describe an efficient algorithm for solving the opposite direction moldability problem for a 2D \u201cpolygon\u201d bounded by edges that may be either straight or curved. We introduce a structure, the normal graph of the polygon, that represents the range of normals of the polygon\u2019s edges, along with their connectivity. We prove that the normal graph captures the directions of all lines corresponding to feasible parting directions. Rather than building the full normal graph, which could take time O(nlogn) for a polygon bounded by n possibly curved edges, we build a summary structure in O(n) time and space, from which we can determine all feasible parting directions in time O(n).<\/jats:p>","DOI":"10.1115\/1.2164450","type":"journal-article","created":{"date-parts":[[2006,2,23]],"date-time":"2006-02-23T23:03:30Z","timestamp":1140735810000},"page":"60-68","update-policy":"http:\/\/dx.doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":9,"title":["Finding Undercut-Free Parting Directions for Polygons with Curved Edges"],"prefix":"10.1115","volume":"6","author":[{"given":"Sara","family":"McMains","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of California, Berkeley, CA, Berkeley"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaorui","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of California, Berkeley, CA, Berkeley"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2005,10,12]]},"reference":[{"issue":"4","key":"2019100519260007000_c1","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1007\/BF01201764","article-title":"Parting Line Formation by Slicing a 3D CAD Model","volume":"14","author":"Wong","journal-title":"Eng. Comput.","ISSN":"http:\/\/id.crossref.org\/issn\/0264-4401","issn-type":"print"},{"key":"2019100519260007000_c2","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/0010-4485(90)90024-7","article-title":"Decision Criteria for Computer Aided Parting Surface Design","volume":"22","author":"Ravi","journal-title":"Comput.-Aided Des.","ISSN":"http:\/\/id.crossref.org\/issn\/0010-4485","issn-type":"print"},{"issue":"9","key":"2019100519260007000_c3","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1016\/S0890-6955(97)00007-2","article-title":"Determining Parting Direction Based on Minimum Bounding Box and Fuzzy Logics","volume":"37","author":"Chen","journal-title":"Int. J. Mach. Tool Des. Res.","ISSN":"http:\/\/id.crossref.org\/issn\/0020-7357","issn-type":"print"},{"issue":"2","key":"2019100519260007000_c4","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/0010-4485(92)90002-R","article-title":"Mould Design with Sweep Operations-A Heuristic Search Approach","volume":"24","author":"Hui","journal-title":"Comput.-Aided Des.","ISSN":"http:\/\/id.crossref.org\/issn\/0010-4485","issn-type":"print"},{"issue":"3","key":"2019100519260007000_c5","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/S0010-4485(96)00064-4","article-title":"Geometric Aspects of the Mouldability of Parts","volume":"29","author":"Hui","journal-title":"Comput.-Aided Des.","ISSN":"http:\/\/id.crossref.org\/issn\/0010-4485","issn-type":"print"},{"issue":"4","key":"2019100519260007000_c6","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1177\/1063293X9700500403","article-title":"Virtual Prototyping of Die Design Part One: Theory and Formulation","volume":"5","author":"Wuerger","journal-title":"Concurr. Eng. Res. Appl.","ISSN":"http:\/\/id.crossref.org\/issn\/1063-293X","issn-type":"print"},{"issue":"4","key":"2019100519260007000_c7","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1177\/1063293X9700500404","article-title":"Virtual Prototyping of Die Design Part Two: Algorithmic, Computational, and Practical Considerations","volume":"5","author":"Wuerger","journal-title":"Concurr. Eng. Res. Appl.","ISSN":"http:\/\/id.crossref.org\/issn\/1063-293X","issn-type":"print"},{"key":"2019100519260007000_c8","doi-asserted-by":"crossref","unstructured":"Ganter, M. A., and Skoglund, P. A., 1991. \u201cFeature Extraction for Casting Core Development,\u201d in 17th Design Automation Conference presented at the 1991 ASME Design Technical Conferences, American Society of Mechanical Engineers, pp. 93\u2013100.","DOI":"10.1115\/DETC1991-0074"},{"key":"2019100519260007000_c9","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1080\/07408179908969895","article-title":"Generation of Optimal Parting Direction Based on Undercut Features in Injection Molded Parts","volume":"31","author":"Fu","journal-title":"IIE Trans.","ISSN":"http:\/\/id.crossref.org\/issn\/0740-817X","issn-type":"print"},{"issue":"12","key":"2019100519260007000_c10","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1016\/S0010-4485(99)00070-6","article-title":"Undercut Feature Recognition in an Injection Mould Design System","volume":"31","author":"Fu","journal-title":"Comput.-Aided Des.","ISSN":"http:\/\/id.crossref.org\/issn\/0010-4485","issn-type":"print"},{"key":"2019100519260007000_c11","doi-asserted-by":"publisher","first-page":"1023","DOI":"10.1016\/S0010-4485(00)00138-X","article-title":"A Hybrid Method for Recognition of Undercut Features from Moulded Parts","volume":"33","author":"Ye","journal-title":"Comput.-Aided Des.","ISSN":"http:\/\/id.crossref.org\/issn\/0010-4485","issn-type":"print"},{"key":"2019100519260007000_c12","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/S0010-4485(00)00084-1","article-title":"Virtual Prototyping of Mold Design: Geometric Mouldability Analysis for Near-Net-Shape Manufactured Parts by Feature Recognition and Geometric Reasoning","volume":"33","author":"Yin","journal-title":"Comput.-Aided Des.","ISSN":"http:\/\/id.crossref.org\/issn\/0010-4485","issn-type":"print"},{"issue":"12","key":"2019100519260007000_c13","doi-asserted-by":"publisher","first-page":"762","DOI":"10.1016\/0010-4485(93)90103-U","article-title":"Parting Directions for Mold and Die Design","volume":"25","author":"Chen","journal-title":"Comput.-Aided Des.","ISSN":"http:\/\/id.crossref.org\/issn\/0010-4485","issn-type":"print"},{"issue":"5","key":"2019100519260007000_c14","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/0278-6125(95)98869-8","article-title":"Partial Visibility for Selecting a Parting Direction in Mold and Die Design","volume":"14","author":"Chen","journal-title":"J. Manuf. Syst.","ISSN":"http:\/\/id.crossref.org\/issn\/0278-6125","issn-type":"print"},{"issue":"3","key":"2019100519260007000_c15","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1115\/1.1603308","article-title":"A Reverse Glue Approach to Automated Construction of Multi-Piece Molds","volume":"3","author":"Chen","journal-title":"J. Comput. Inf. Sci. Eng.","ISSN":"http:\/\/id.crossref.org\/issn\/1530-9827","issn-type":"print"},{"issue":"3","key":"2019100519260007000_c16","first-page":"225","article-title":"A Feature Based Approach to Automated Design of Multi-Piece Sacrificial Molds","volume":"1","author":"Dhaliwal","journal-title":"Comp. Biochem. Physiol., Part C: Pharmacol., Toxicol. Endocrinol.","ISSN":"http:\/\/id.crossref.org\/issn\/0742-8413","issn-type":"print"},{"issue":"13","key":"2019100519260007000_c17","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1016\/S0010-4485(03)00008-3","article-title":"Generating Sacrificial Multi-Piece Molds Using Accessibility Driven Spatial Partitioning","volume":"35","author":"Huang","journal-title":"Comput.-Aided Des.","ISSN":"http:\/\/id.crossref.org\/issn\/0010-4485","issn-type":"print"},{"issue":"3","key":"2019100519260007000_c18","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1115\/1.1485741","article-title":"Automated Design of Multi-Stage Molds for Manufacturing Multi-Material Objects","volume":"124","author":"Kumar","journal-title":"ASME J. Mech. Des.","ISSN":"http:\/\/id.crossref.org\/issn\/1050-0472","issn-type":"print"},{"issue":"1\u20132","key":"2019100519260007000_c19","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/S0921-5093(01)01800-7","article-title":"Rapid Prototyping and Manufacturing by Gelcasting of Metallic and Ceramic Slurries","volume":"334","author":"Stampfl","journal-title":"Mater. Sci. Eng., A","ISSN":"http:\/\/id.crossref.org\/issn\/0921-5093","issn-type":"print"},{"issue":"3","key":"2019100519260007000_c20","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0010-4485(03)00107-6","article-title":"Geometric Algorithms for Automated Design of Multi-Piece Permanent Molds","volume":"36","author":"Priyadarshi","journal-title":"Comput.-Aided Des.","ISSN":"http:\/\/id.crossref.org\/issn\/0010-4485","issn-type":"print"},{"key":"2019100519260007000_c21","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/PL00014422","article-title":"Determining the Castability of Simple Polyhedra","volume":"19","author":"Bose","journal-title":"Algorithmica","ISSN":"http:\/\/id.crossref.org\/issn\/0178-4617","issn-type":"print"},{"issue":"15","key":"2019100519260007000_c22","doi-asserted-by":"crossref","first-page":"3529","DOI":"10.1080\/0020754031000098939","article-title":"Automatic Parting Surface Determination for Plastic Injection Mold","volume":"41","author":"Li","journal-title":"Int. J. Prod. Res.","ISSN":"http:\/\/id.crossref.org\/issn\/0020-7543","issn-type":"print"},{"key":"2019100519260007000_c23","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/0925-7721(94)90020-5","article-title":"Moldable and Castable Polygons","volume":"4","author":"Rappaport","journal-title":"Computational Geometry: Theory and Applications"},{"key":"2019100519260007000_c24","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1016\/S0010-4485(01)00119-1","article-title":"Separating an Object from its Cast","volume":"34","author":"Ahn","journal-title":"Comput.-Aided Des.","ISSN":"http:\/\/id.crossref.org\/issn\/0010-4485","issn-type":"print"},{"key":"2019100519260007000_c25","first-page":"263","article-title":"Mold Accessibility via Gauss Map Analysis","author":"Elber"},{"key":"2019100519260007000_c26","volume-title":"Modern Differential Geometry of Curves and Surfaces","author":"Gray"},{"key":"2019100519260007000_c27","doi-asserted-by":"crossref","unstructured":"McMains, S., and Chen, X., 2004. \u201cDetermining Moldability and Parting Directions for Polygons with Curved Edges,\u201d In International Mechanical Engineering Congress and Exposition, ASME, pp. 359\u2013368.","DOI":"10.1115\/IMECE2004-62227"}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/6\/1\/60\/5687725\/60_1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/6\/1\/60\/5687725\/60_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,24]],"date-time":"2021-07-24T07:42:06Z","timestamp":1627112526000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/6\/1\/60\/460157\/Finding-UndercutFree-Parting-Directions-for"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,10,12]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,3,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.2164450","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"value":"1530-9827","type":"print"},{"value":"1944-7078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,10,12]]}}}