{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T00:44:55Z","timestamp":1755218695856,"version":"3.43.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2003,4,1]],"date-time":"2003-04-01T00:00:00Z","timestamp":1049155200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2003,4,1]],"date-time":"2003-04-01T00:00:00Z","timestamp":1049155200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Reliable Computing"],"published-print":{"date-parts":[[2003,4]]},"DOI":"10.1023\/a:1023046502854","type":"journal-article","created":{"date-parts":[[2003,4,7]],"date-time":"2003-04-07T18:17:24Z","timestamp":1049739444000},"page":"161-175","source":"Crossref","is-referenced-by-count":8,"title":["Robust Approximation of Offsets, Bisectors, and Medial Axes of Plane Curves"],"prefix":"10.1007","volume":"9","author":[{"given":"Jo\u00e3o Batista","family":"Oliveira","sequence":"first","affiliation":[]},{"given":"Luiz Henrique","family":"De Figueiredo","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"7","key":"5122360_CR1","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/BF01900662","volume":"10","author":"W. Barth","year":"1994","unstructured":"Barth, W., Lieger, R., and Schindler, M.: Ray Tracing General Parametric Surfaces Using Interval Arithmetic, The Visual Computer\n10(7) (1994), pp. 363-371.","journal-title":"The Visual Computer"},{"key":"5122360_CR2","unstructured":"Chiang, C.-S., Hoffmann, C. M., and Lynch, R. E.: How to Compute Offsets without Self-Intersection, Technical Report CSD-TR-91-072, Department of Computer Sciences, Purdue University, 1991."},{"key":"5122360_CR3","unstructured":"Comba, J. L. D. and Stolfi, J.: Affine Arithmetic and Its Applications to Computer Graphics, in: Proceedings of SIBGRAPI'93, 1993, pp. 9-18."},{"key":"5122360_CR4","doi-asserted-by":"crossref","unstructured":"de Cusatis Jr., A., de Figueiredo, L. H., and Gattass, M.: Interval Methods for Ray Casting Implicit Surfaces with Affine Arithmetic, in: Proceedings of SIBGRAPI'99, 1999, pp. 65-71.","DOI":"10.1109\/SIBGRA.1999.805711"},{"key":"5122360_CR5","unstructured":"de Figueiredo, L. H.: Surface Intersection Using Affine Arithmetic, in: Proceedings of Graphics Interface'96, 1996, pp. 168-175."},{"issue":"5","key":"5122360_CR6","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1111\/1467-8659.1550287","volume":"15","author":"L. H. de Figueiredo","year":"1996","unstructured":"de Figueiredo, L. H. and Stolfi, J.: Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic, Computer Graphics Forum\n15(5) (1996), pp. 287-296.","journal-title":"Computer Graphics Forum"},{"issue":"4","key":"5122360_CR7","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/S0925-7721(99)00051-6","volume":"15","author":"T. K. Dey","year":"2000","unstructured":"Dey, T. K., Mehlhorn, K., and Ramos, E. A.: Curve Reconstruction: Connecting Dots with Good Reason, Computational Geometry: Theory and Applications\n15(4) (2000), pp. 229-244.","journal-title":"Computational Geometry: Theory and Applications"},{"issue":"2","key":"5122360_CR8","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1145\/142920.134027","volume":"26","author":"T. Duff","year":"1992","unstructured":"Duff, T.: Interval Arithmetic and Recursive Subdivision for Implicit Functions and Constructive Solid Geometry, Computer Graphics\n26(2) (1992), pp. 131-138 (SIGGRAPH'92 Proceedings).","journal-title":"Computer Graphics"},{"issue":"3","key":"5122360_CR9","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1109\/38.586019","volume":"17","author":"G. Elber","year":"1997","unstructured":"Elber, G., Lee, I.-K., and Kim, M.-S.: Comparing Offset Curve Approximation Methods, IEEE Computer Graphics & Applications\n17(3) (1997), pp. 62-71.","journal-title":"IEEE Computer Graphics & Applications"},{"issue":"2","key":"5122360_CR10","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0167-8396(94)90029-9","volume":"11","author":"R. T. Farouki","year":"1994","unstructured":"Farouki, R. T. and Johnstone, J. K.: The Bisector of a Point and a Plane Parametric Curve, Computer Aided Geometric Design\n11(2) (1994), pp. 117-151.","journal-title":"Computer Aided Geometric Design"},{"issue":"1-4","key":"5122360_CR11","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/0167-8396(90)90024-L","volume":"7","author":"R. T. Farouki","year":"1990","unstructured":"Farouki, R. T. and Neff, C. A.: Algebraic Properties of Plane Offset Curves, Computer Aided Geometric Design\n7(1-4) (1990), pp. 101-127.","journal-title":"Computer Aided Geometric Design"},{"issue":"1-4","key":"5122360_CR12","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0167-8396(90)90023-K","volume":"7","author":"R. T. Farouki","year":"1990","unstructured":"Farouki, R. T. and Neff, C. A.: Analytic Properties of Plane Offset Curves, Computer Aided Geometric Design\n7(1-4) (1990), pp. 83-99.","journal-title":"Computer Aided Geometric Design"},{"issue":"6","key":"5122360_CR13","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/S0167-8396(98)00007-7","volume":"15","author":"R. T. Farouki","year":"1998","unstructured":"Farouki, R. T. and Ramamurthy, R.: Degenerate Point\/Curve and Curve\/Curve Bisectors Arising in Medial Axis Computations for Planar Domains with Curved Boundaries, Computer Aided Geometric Design\n15(6) (1998), pp. 615-635.","journal-title":"Computer Aided Geometric Design"},{"key":"5122360_CR14","unstructured":"Gleicher, M. and Kass, M.: An Interval Refinement Technique for Surface Intersection, in: Proceedings of Graphics Interface'92, 1992, pp. 242-249."},{"key":"5122360_CR15","volume-title":"Global Optimization Using Interval Analysis","author":"E. Hansen","year":"1992","unstructured":"Hansen, E.: Global Optimization Using Interval Analysis, Marcel Dekker, New York, 1992."},{"key":"5122360_CR16","unstructured":"Heidrich, W. and Seidel, H.-P.: Ray-Tracing Procedural Displacement Shaders, in: Proceedings of Graphics Interface'98, 1998, pp. 8-16."},{"issue":"3","key":"5122360_CR17","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1145\/285857.285859","volume":"17","author":"W. Heidrich","year":"1998","unstructured":"Heidrich, W., Slusallik, P., and Seidel, H.-P.: Sampling Procedural Shaders Using Affine Arithmetic, ACM Transactions on Graphics\n17(3) (1998), pp. 158-176.","journal-title":"ACM Transactions on Graphics"},{"issue":"14","key":"5122360_CR18","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1016\/S0010-4485(98)00063-3","volume":"30","author":"D.-S. Kim","year":"1998","unstructured":"Kim, D.-S.: Polygon Offsetting Using a Voronoi Diagram and Two Stacks, Computer-Aided Design\n30(14) (1998), pp. 1069-1076.","journal-title":"Computer-Aided Design"},{"issue":"5","key":"5122360_CR19","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/0010-4485(93)90040-U","volume":"25","author":"R. Kimmel","year":"1993","unstructured":"Kimmel, R. and Bruckstein, A. M.: Shape Offsets via Level Sets, Computer-Aided Design\n25(5) (1993), pp. 154-162.","journal-title":"Computer-Aided Design"},{"issue":"3","key":"5122360_CR20","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1006\/cviu.1995.1062","volume":"62","author":"R. Kimmel","year":"1995","unstructured":"Kimmel, R., Shaked, D., and Kiryati, N.: Skeletonization via Distance Maps and Level Sets, Computer Vision and Image Understanding\n62(3) (1995), pp. 382-391.","journal-title":"Computer Vision and Image Understanding"},{"key":"5122360_CR21","unstructured":"Kreinovich, V.: Interval Software, http:\/\/www.cs.utep.edu\/interval-comp\/intsoft.html."},{"issue":"2","key":"5122360_CR22","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/S0167-8396(99)00044-8","volume":"17","author":"I.-K. Lee","year":"2000","unstructured":"Lee, I.-K.: Curve Reconstruction from Unorganized Points, Computer Aided Geometric Design\n17(2) (2000), pp. 161-177.","journal-title":"Computer Aided Geometric Design"},{"issue":"3","key":"5122360_CR23","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/S0010-4485(99)00013-5","volume":"31","author":"T. Maekawa","year":"1999","unstructured":"Maekawa, T.: An Overview of Offset Curves and Surfaces, Computer-Aided Design\n31(3) (1999), pp. 165-173.","journal-title":"Computer-Aided Design"},{"key":"5122360_CR24","unstructured":"Mitchell, D. P.: Robust Ray Intersection with Interval Arithmetic, in: Proceedings of Graphics Interface'90, 1990, pp. 68-74."},{"issue":"4","key":"5122360_CR25","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1145\/321479.321486","volume":"15","author":"U. Montanari","year":"1968","unstructured":"Montanari, U.: A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance, Journal of the ACM\n15(4) (1968), pp. 600-624.","journal-title":"Journal of the ACM"},{"issue":"8","key":"5122360_CR26","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1016\/S0167-8396(99)00016-3","volume":"16","author":"H. P. Moon","year":"1999","unstructured":"Moon, H. P.: Minkowski Pythagorean Hodographs, Computer Aided Geometric Design\n16(8) (1999), pp. 739-753.","journal-title":"Computer Aided Geometric Design"},{"key":"5122360_CR27","volume-title":"Interval Analysis","author":"R. E. Moore","year":"1966","unstructured":"Moore, R. E.: Interval Analysis, Prentice Hall, Englewood Cliffs, 1966."},{"issue":"2","key":"5122360_CR28","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1109\/MCG.1984.275931","volume":"4","author":"S. P. Mudur","year":"1984","unstructured":"Mudur, S. P. and Koparkar, P. A.: Interval Methods for Processing Geometric Objects, IEEE Computer Graphics & Applications\n4(2) (1984), pp. 7-17.","journal-title":"IEEE Computer Graphics & Applications"},{"issue":"4","key":"5122360_CR29","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/0010-4485(92)90059-J","volume":"24","author":"B. Pham","year":"1992","unstructured":"Pham, B.: Offset Curves and Surfaces: A Brief Survey, Computer-Aided Design\n24(4) (1992), pp. 223-229.","journal-title":"Computer-Aided Design"},{"issue":"2","key":"5122360_CR30","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/S0167-8396(97)00023-X","volume":"15","author":"H. Pottmann","year":"1998","unstructured":"Pottmann, H. and Peternell, M.: Applications of Laguerre Geometry in CAGD, Computer Aided Geometric Design\n15(2) (1998), 165-186.","journal-title":"Computer Aided Geometric Design"},{"key":"5122360_CR31","doi-asserted-by":"crossref","unstructured":"Ramanathan, M. and Gurumoorthy, B.: Constructing Medial Axis Transform of Planar Domains with Curved Boundaries, Computer-Aided Design (2002), to appear.","DOI":"10.1016\/S0010-4485(02)00085-4"},{"key":"5122360_CR32","unstructured":"Samet, H.: Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS, Addison-Wesley, 1990."},{"key":"5122360_CR33","doi-asserted-by":"crossref","unstructured":"Samet, H.: The Design and Analysis of Spatial Data Structures, Addison-Wesley, 1990.","DOI":"10.1007\/3-540-52208-5_28"},{"issue":"8","key":"5122360_CR34","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1016\/S0010-4485(99)00049-4","volume":"31","author":"E. Saux","year":"1999","unstructured":"Saux, E. and Daniel, M.: Data Reduction of Polygonal Curves Using B-Splines, Computer-Aided Design\n31(8) (1999), pp. 507-515.","journal-title":"Computer-Aided Design"},{"key":"5122360_CR35","doi-asserted-by":"crossref","unstructured":"Snyder, J. M.: Generative Modeling for Computer Graphics and CAD, Academic Press, 1992.","DOI":"10.1145\/142920.134094"},{"issue":"2","key":"5122360_CR36","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1145\/142920.134024","volume":"26","author":"J. M. Snyder","year":"1992","unstructured":"Snyder, J. M.: Interval Analysis for Computer Graphics, Computer Graphics\n26(2) (1992), pp. 121-130 (SIGGRAPH'92 Proceedings).","journal-title":"Computer Graphics"},{"issue":"3","key":"5122360_CR37","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/0097-8493(91)90002-Y","volume":"15","author":"K. G. Suffern","year":"1991","unstructured":"Suffern, K. G. and Fackerell, E. D.: Interval Methods in Computer Graphics, Computers and Graphics\n15(3) (1991), pp. 331-340.","journal-title":"Computers and Graphics"},{"issue":"3","key":"5122360_CR38","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1145\/325165.325233","volume":"19","author":"D. L. Toth","year":"1985","unstructured":"Toth, D. L.: On Ray Tracing Parametric Surfaces, Computer Graphics\n19(3) (1985), pp. 171-179 (SIGGRAPH'85 Proceedings).","journal-title":"Computer Graphics"}],"container-title":["Reliable Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1023046502854.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1023046502854\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1023046502854.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T09:39:50Z","timestamp":1754473190000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1023046502854"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,4]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2003,4]]}},"alternative-id":["5122360"],"URL":"https:\/\/doi.org\/10.1023\/a:1023046502854","relation":{},"ISSN":["1385-3139","1573-1340"],"issn-type":[{"type":"print","value":"1385-3139"},{"type":"electronic","value":"1573-1340"}],"subject":[],"published":{"date-parts":[[2003,4]]}}}