{"id":13162,"date":"2021-12-06T19:21:34","date_gmt":"2021-12-07T00:21:34","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=13162"},"modified":"2021-12-06T19:21:42","modified_gmt":"2021-12-07T00:21:42","slug":"tr-06-04-rotational-clamshell-casting-in-three-dimensions","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2006\/tr-06-04-rotational-clamshell-casting-in-three-dimensions\/","title":{"rendered":"TR-06-04: Rotational Clamshell Casting In Three Dimensions"},"content":{"rendered":"

Carleton University
\nTechnical Report<\/a> TR-06-04
\nFebruary 17, 2006<\/p>\n

Rotational Clamshell Casting In Three Dimensions<\/h2>\n
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P. Bose, P. Morin, M. Smid, S. Wuhrer<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

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Abstract<\/h3>\n

A popular manufacturing technique is clamshell casting, where liquid is poured into a cast and the cast is removed once the liquid has hardened. We consider the case where the object to be manufactured is modeled by a polyhedron with combinatorial complexity n of arbitrary genus. The cast consists of exactly two parts and is removed by a rotation around a line in space. The following two problems are addressed: (1) Given a line of rotation l in space, we determine in O(n log n) time whether there exists a partitioning of the cast into exactly two parts, such that one part can be rotated clockwise around l and the other part can be rotated counterclockwise around l without colliding with the interior of P or the cast. If the problem is restricted further, such a partitioning is only valid when no reflex edge or face of P is perpendicular to l, the algorithm runs in O(n) time. (2) An algorithm running in O(n4 log n) time is presented to find all the lines in space that allow a cast partitioning as described above. If we restrict the problem further and find all the lines in space that allow a cast partitioning as described above, such that no reflex edge or face of P is perpendicular to l, the algorithm\u0092s running time becomes O(n4(n)).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

TR-06-04.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Carleton University Technical Report TR-06-04 February 17, 2006 Rotational Clamshell Casting In Three Dimensions P. Bose, P. Morin, M. Smid, S. Wuhrer Abstract A popular manufacturing technique is clamshell casting, where liquid is poured into a cast and the cast is removed once the liquid has hardened. We consider the case where the object to […]<\/p>\n","protected":false},"author":49,"featured_media":0,"parent":12352,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":"","_links_to":"","_links_to_target":""},"yoast_head":"\nTR-06-04: Rotational Clamshell Casting In Three Dimensions - School of Computer Science<\/title>\n<meta name=\"description\" content=\"Carleton University Technical Report TR-06-04 February 17, 2006 Rotational Clamshell Casting In Three Dimensions P. 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