Efficient offset trimming for deformable planar curves using a dynamic hierarchy of bounding circular arcs. (January 2015)

• Record Type: Journal Article
• Authors: Lee, Jaewook; Kim, Yong-Joon; Kim, Myung-Soo; Elber, Gershon
• Is Part Of: Computer aided design. Volume 58(2015)
• Page Start: 248
• Page End: 255
• Publication Date: 2015-01
• Subjects: Planar freeform curve -- Offset curve trimming -- Monotone spiral curve -- Bounding circular arcs -- Dynamic BVH -- Self-intersection; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2014.08.031
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: We present an efficient algorithm for computing a family of trimmed offsets for planar freeform curves under deformation. The algorithm is based on a dynamic bounding volume hierarchy (BVH) for the untrimmed offsets of a given planar curve, which can be generated efficiently using a hierarchy of recursive bisections of the given curve. The proposed algorithm is effective for deformable planar curves. At each time frame, we segment the input curve into monotone spiral pieces (Barton and Elber, 2011), which is the only pre-processing needed for the dynamic BVH construction. To speed up the on-line generation of dynamic BVH, we employ the bounding circular arcs (BCA) of Meek and Walton (1995) that can be computed very efficiently using the position and tangent information at the endpoints of each monotone spiral curve segment. Using several experimental results, we demonstrate the performance improvement of our algorithm over the previous biarc-based algorithm of Kim et al. (2012). Highlights: Offset trimming for planar freeform curves under deformation. Dynamic BVH generation using a hierarchy of recursive bisections. BV generation using the bounding circular arcs (BCA) of Meek and Walton (1995). Performance improvement over the biarc-based algorithm of Kim et al. (2012).