caa a22 4500 605540934 CHVBK 20210128100914.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00371-015-1093-z doi (NATIONALLICENCE)springer-10.1007/s00371-015-1093-z Comparison of three bounding regions with cubic convergence to planar freeform curves [Elektronische Daten] [Jaewook Lee, Yong-Joon Kim, Myung-Soo Kim, Gershon Elber] We compare the relative performance of bounding regions generated by three different curve-bounding methods with cubic convergence to planar freeform curves: spiral fat arcs (SFA)(Barton and Elber in Graph Models 73(2):50-57, 2011), bilens(Kumosenko in Comput Aided Geom Des 30(3):310-330, 2013), and bounding circular arcs (BCA)(Meek and Walton in J Comput Appl Math 59(2):221-231, 1995). For quantitative comparison, we consider three different criteria: geometric complexity (the number of circular arcs and line segments), construction time, and numerical stability. The BCA construction after one-step refinement (producing four circular arcs) is almost comparable to the other two methods in geometric complexity: the SFA with two circular arcs and two line segments, and the bilens with four circular arcs. In other comparison criteria, the BCA approach is more efficient and stable than the other two methods in producing a hierarchy of bounding regions that approximate a family of freeform planar curves within a given error bound. Springer-Verlag Berlin Heidelberg, 2015 Planar freeform curves nationallicence Monotone spiral curve nationallicence Bounding circular arcs nationallicence Dynamic BVH nationallicence Lee Jaewook Department of Electrical and Computer Engineering, Seoul National University, 151-744, Seoul, Korea aut Kim Yong-Joon Computer Science Department, Technion, 32000, Haifa, Israel aut Kim Myung-Soo Department of Computer Science and Engineering, Seoul National University, 151-744, Seoul, Korea aut Elber Gershon Computer Science Department, Technion, 32000, Haifa, Israel aut The Visual Computer Springer Berlin Heidelberg 31/6-8(2015-06-01), 809-818 0178-2789 31:6-8<809 2015 31 371 https://doi.org/10.1007/s00371-015-1093-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00371-015-1093-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lee Jaewook Department of Electrical and Computer Engineering, Seoul National University, 151-744, Seoul, Korea aut NATIONALLICENCE 700 1- Kim Yong-Joon Computer Science Department, Technion, 32000, Haifa, Israel aut NATIONALLICENCE 700 1- Kim Myung-Soo Department of Computer Science and Engineering, Seoul National University, 151-744, Seoul, Korea aut NATIONALLICENCE 700 1- Elber Gershon Computer Science Department, Technion, 32000, Haifa, Israel aut NATIONALLICENCE 773 0- The Visual Computer Springer Berlin Heidelberg 31/6-8(2015-06-01), 809-818 0178-2789 31:6-8<809 2015 31 371