Precise Hausdorff distance computation for freeform surfaces based on computations with osculating toroidal patches

Alt, 1999 Alt, 2008, Computing the Hausdorff distance between curved objects, Int. J. Comput. Geom. Appl., 18, 307, 10.1142/S0218195908002647 Aspert, 2002, MESH: measuring errors between surfaces using the Hausdorff distance, 705 Bai, 2011, Polyline approach for approximating the Hausdorff distance between two planar free-form curves, Comput. Aided Des., 43, 687, 10.1016/j.cad.2011.02.008 Barton, 2010, Precise Hausdorff distance computation between polygonal meshes, Comput. Aided Geom. Des., 27, 580, 10.1016/j.cagd.2010.04.004 Chen, 2010, Computing the Hausdorff distance between two B-spline curves, Comput. Aided Des., 42, 1197, 10.1016/j.cad.2010.06.009 Cignoni, 1998, Metro: measuring error on simplified surfaces, Comput. Graph. Forum, 17, 167, 10.1111/1467-8659.00236 Elber, 2008, Hausdorff and minimal distances between parametric freeforms in R2 and R3, vol. 4975, 191 Filip, 1986, Surface approximations using bounds on derivatives, Comput. Aided Geom. Des., 3, 295, 10.1016/0167-8396(86)90005-1 Guthe, 2005, Fast and accurate Hausdorff distance calculation between meshes, J. WSCG, 13, 41 Hanniel, 2012, Computing the Hausdorff distance between NURBS surfaces using numerical iteration on the GPU, Graph. Models, 74, 255, 10.1016/j.gmod.2012.05.002 Jüttler, 2000, Bounding the Hausdorff distance of implicitly defined and/or parametric curves, 1 Kang, 2018, Fast and robust Hausdorff distance computation from triangle mesh to quad mesh in near-zero cases, Comput. Aided Geom. Des., 62, 91, 10.1016/j.cagd.2018.03.017 Kang, 2019, Fast and robust computation of the Hausdorff distance between triangle mesh and quad mesh for near-zero cases, Comput. Graph., 81, 61, 10.1016/j.cag.2019.03.014 Kim, 2010, Precise Hausdorff distance computation for planar freeform curves using biarcs and depth buffer, Vis. Comput., 26, 1007, 10.1007/s00371-010-0477-3 Kim, 2013, Efficient Hausdorff distance computation for freeform geometric models in close proximity, Comput. Aided Des., 45, 270, 10.1016/j.cad.2012.10.010 Krishnamurthy, 2011, GPU-accelerated Hausdorff distance computation between dynamically deformable NURBS surfaces, Comput. Aided Des., 43, 1370, 10.1016/j.cad.2011.08.022 Kurnosenko, 2013, Biarcs and bilens, Comput. Aided Geom. Des., 30, 310, 10.1016/j.cagd.2012.12.002 Lee, 2015, Comparison of three bounding regions with cubic convergence to planar freeform curves, Vis. Comput., 31, 809, 10.1007/s00371-015-1093-z Liu, 2009, A torus patch approximation approach for point projection on surfaces, Comput. Aided Geom. Des., 26, 593, 10.1016/j.cagd.2009.01.004 Park, 2020, Surface-surface-intersection computation using a bounding volume hierarchy with osculating toroidal patches in the leaf nodes, Comput. Aided Des., 45, 270 Rucklidge, 1996, Efficient Visual Recognition Using the Hausdorff Distance, vol. 1173 Sir, 2006, Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics, Comput. Aided Des., 38, 608, 10.1016/j.cad.2006.02.003 Son, 2020, Efficient minimum distance computation for solids of revolution, Comput. Graph. Forum, 39, 535, 10.1111/cgf.13950 Tang, 2009, Interactive Hausdorff distance computation for general polygonal models, ACM Trans. Graph., 28, 10.1145/1531326.1531380