{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T17:14:42Z","timestamp":1764782082966,"version":"3.41.2"},"reference-count":30,"publisher":"ASME International","issue":"2","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2016,6,1]]},"abstract":"<jats:p>For the purposes of automating the assignment of tolerances during design, a math model, called the Tolerance-Map (T-Map), has been produced for most of the tolerance classes that are used by designers. Each T-Map is a hypothetical point-space that represents the geometric variations of a feature in its tolerance-zone. Of the six tolerance classes defined in the ASME\/ANSI\/ISO Standards, profile tolerances have received the least attention for representation in computer models. The objective of this paper is to provide a comprehensive treatment of T-Map construction for any line-profile by using primitive T-Map elements and their Boolean intersection. The method requires (a) decomposing a profile into segments, each of constant curvature; (b) creating a solid-model T-Map primitive for each in a common global reference frame; and (c) combining these by Boolean intersection to generate the T-Map for a complete line-profile of any shape. Freeform portions of a profile are modeled as a series of closely spaced points and subsequent formation of short circular arc-segments, each formed from the circle that osculates to three adjacent points.<\/jats:p>","DOI":"10.1115\/1.4033236","type":"journal-article","created":{"date-parts":[[2016,4,4]],"date-time":"2016-04-04T22:30:50Z","timestamp":1459809050000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":8,"title":["Tolerance-Maps for Line-Profiles Formed by Intersecting Kinematically Transformed Primitive Tolerance-Map Elements"],"prefix":"10.1115","volume":"16","author":[{"given":"Y.","family":"He","sequence":"first","affiliation":[{"name":"Siemens PLM Software, Inc., 2000 Eastman Drive, Milford, OH 45150 e-mail:"}]},{"given":"J. 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