{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T16:38:30Z","timestamp":1776271110083,"version":"3.50.1"},"reference-count":46,"publisher":"ASME International","issue":"5","license":[{"start":{"date-parts":[[2020,7,9]],"date-time":"2020-07-09T00:00:00Z","timestamp":1594252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.asme.org\/publications-submissions\/publishing-information\/legal-policies"}],"content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2020,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The modern engineering technologies of computer-aided design (CAD), computer-aided engineering (CAE), and computer-aided manufacturing (CAM) are ubiquitous in engineering practice. They are focused on creating, analyzing, and fabricating engineering artifacts represented as geometric models. Historically, these technologies developed independently, with different geometric representations that are customized to the needs of the technology. As a result, the combined use of these technologies has led to differences in data structures, file formats, and user knowledge and practice, requiring translation of representations between systems to support interoperability. Complicating this situation is the approximate nature of modeling operations in CAD systems, which can result in gaps at the boundary curves between mating trimmed surfaces of a model. The research presented here is aimed at removing the gaps between trimmed surfaces, resulting in a \u201cwatertight\u201d model that is suitable for use directly by downstream applications. A three-step algorithm is presented that includes analysis of the parametric space of the trimming curves, reparameterization to create a global parameter space, and reconstruction of the intersecting surfaces to ensure continuity at the trimming curve.<\/jats:p>","DOI":"10.1115\/1.4047427","type":"journal-article","created":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T22:06:20Z","timestamp":1591740380000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":2,"title":["Reconstruction of Trimmed NURBS Surfaces for Gap-Free Intersections"],"prefix":"10.1115","volume":"20","author":[{"given":"Benjamin","family":"Urick","sequence":"first","affiliation":[{"name":"nVariate, Inc., Austin, TX 78705"}]},{"given":"Richard H.","family":"Crawford","sequence":"additional","affiliation":[{"name":"Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712"}]},{"given":"Thomas J. R.","family":"Hughes","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX 78712"}]},{"given":"Elaine","family":"Cohen","sequence":"additional","affiliation":[{"name":"School of Computing, University of Utah, Salt Lake City, UT 84112"}]},{"given":"Richard F.","family":"Riesenfeld","sequence":"additional","affiliation":[{"name":"School of Computing, University of Utah, Salt Lake City, UT 84112"}]}],"member":"33","published-online":{"date-parts":[[2020,7,9]]},"reference":[{"key":"2021022704041507000_CIT0001","doi-asserted-by":"crossref","DOI":"10.21236\/AD0755141","volume-title":"Winged Edge Polyhedron Representation","author":"Baumgart","year":"1972"},{"key":"2021022704041507000_CIT0002","doi-asserted-by":"crossref","DOI":"10.1201\/9781439864203","volume-title":"Geometric Modeling With Splines: An Introduction","author":"Cohen","year":"2001"},{"key":"2021022704041507000_CIT0003","volume-title":"The NURBS Book","author":"Piegl","year":"1977","edition":"2 ed."},{"issue":"1","key":"2021022704041507000_CIT0004","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/0734-189X(84)90140-3","article-title":"Implicit Representation of Parametric Curves and Surfaces","volume":"28","author":"Sederberg","year":"1984","journal-title":"Comput. Vis. Graphics Image Process."},{"issue":"3","key":"2021022704041507000_CIT0005","doi-asserted-by":"crossref","first-page":"79:1","DOI":"10.1145\/1360612.1360678","article-title":"Watertight Trimmed NURBS","volume":"27","author":"Sederberg","year":"2008","journal-title":"ACM Trans. Graphics"},{"key":"2021022704041507000_CIT0006","article-title":"DART System Analysis","author":"Hardwick","year":"2005"},{"issue":"5","key":"2021022704041507000_CIT0007","first-page":"463","article-title":"A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects","volume":"18","author":"Marussig","year":"2018","journal-title":"Arch. Comput. Methods Eng."},{"issue":"8","key":"2021022704041507000_CIT0008","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/0010-4485(92)90011-X","article-title":"Triangulation of Trimmed Surfaces in Parametric Space","volume":"24","author":"Sheng","year":"1992","journal-title":"Comput.-Aided Des."},{"issue":"1","key":"2021022704041507000_CIT0009","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.cad.2010.08.009","article-title":"A Robust Efficient Tracing Scheme for Triangulating Trimmed Parametric Surfaces","volume":"43","author":"Cripps","year":"2011","journal-title":"Comput.-Aided Des."},{"issue":"2","key":"2021022704041507000_CIT0010","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.cad.2012.10.012","article-title":"Direct Rendering of Boolean Combinations of Self-Trimmed Surfaces","volume":"45","author":"Rossignac","year":"2013","journal-title":"Comput.-Aided Des."},{"issue":"2","key":"2021022704041507000_CIT0011","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.cad.2012.10.037","article-title":"Filling Trim Cracks on GPU-Rendered Solid Models","volume":"45","author":"Pavanaskar","year":"2013","journal-title":"Comput.-Aided Des."},{"key":"2021022704041507000_CIT0012","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.cad.2014.08.012","article-title":"Correct Resolution Rendering of Trimmed Spline Surfaces","volume":"58","author":"Wu","year":"2015","journal-title":"Comput.-Aided Des."},{"issue":"4","key":"2021022704041507000_CIT0013","first-page":"1059","article-title":"Trimming for Subdivision Surfaces","volume":"25","author":"Litke","year":"2001","journal-title":"Comput. Aided Geomet. Des."},{"issue":"7\u20138","key":"2021022704041507000_CIT0014","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1016\/j.cagd.2014.06.004","article-title":"Conversion of Trimmed NURBS Surfaces to Catmull\u2013Clark Subdivision Surfaces","volume":"31","author":"Shena","year":"2014","journal-title":"Comput. Aided Geom. Des."},{"key":"2021022704041507000_CIT0015","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/B978-044451104-1\/50026-5","volume-title":"Handbook of Computer Aided Geometric Design","author":"Patrikalakis","year":"2002"},{"issue":"1","key":"2021022704041507000_CIT0016","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/PL00009330","article-title":"The Nature and Meaning of Perturbations in Geometric Computing","volume":"19","author":"Seidel","year":"1998","journal-title":"Discrete Comput. Geom."},{"issue":"6","key":"2021022704041507000_CIT0017","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/S0010-4485(96)00086-3","article-title":"Moving a B-Spline Surface to a Curve\u2013A Trimmed Surface Matching Algorithm","volume":"29","author":"Hu","year":"1997","journal-title":"Comput.-Aided Des."},{"issue":"3","key":"2021022704041507000_CIT0018","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.cagd.2003.11.004","article-title":"Linear Perturbation Methods for Topologically Consistent Representations of Free-Form Surface Intersections","volume":"21","author":"Song","year":"2004","journal-title":"Comput. Aided Geom. Des."},{"issue":"5","key":"2021022704041507000_CIT0019","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.cagd.2004.03.002","article-title":"Topologically Consistent Trimmed Surface Approximations Based on Triangular Patches","volume":"21","author":"Farouki","year":"2004","journal-title":"Comput. Aided Geom. Des."},{"issue":"1","key":"2021022704041507000_CIT0020","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10444-005-7539-5","article-title":"Guaranteed Consistency of Surface Intersections and Trimmed Surfaces Using a Coupled Topology Resolution and Domain Decomposition Scheme","volume":"27","author":"Haas","year":"2007","journal-title":"Adv. Comput. Math."},{"issue":"3","key":"2021022704041507000_CIT0021","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1145\/882262.882295","article-title":"T-Splines and T-NURCCs","volume":"22","author":"Sederberg","year":"2003","journal-title":"ACM Trans. Graphics"},{"key":"2021022704041507000_CIT0022","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1016\/j.cma.2014.12.010","article-title":"A Simple Approach to the Numerical Simulation with Trimmed CAD Surfaces","volume":"285","author":"Beer","year":"2015","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"6\u20137","key":"2021022704041507000_CIT0023","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/0010-4485(95)00043-7","article-title":"A Tessellation Algorithm for the Representation of Trimmed NURBS Surfaces with Arbitrary Trimming Curves","volume":"28","author":"Hamann","year":"1996","journal-title":"Comput.-Aided Des."},{"key":"2021022704041507000_CIT0024","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1137\/1.9781611971644.ch7","volume-title":"Topics in Surface Modeling","author":"Vries-Baayens","year":"1992"},{"issue":"11","key":"2021022704041507000_CIT0025","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1016\/j.cad.2009.04.012","article-title":"On Global Continuity of Coons Mappings in Patching CAD Surfaces","volume":"41","author":"Randrianarivony","year":"2009","journal-title":"Comput.-Aided Des."},{"key":"2021022704041507000_CIT0026","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.cagd.2015.06.001","article-title":"Watertight Conversion of Trimmed CAD Surfaces to Clough\u2013Tocher Splines","volume":"37","author":"Kosinka","year":"2015","journal-title":"Comput. Aided Geom. Des."},{"key":"2021022704041507000_CIT0027","first-page":"229","volume-title":"The Mathematics of Surfaces III","author":"Applegarth","year":"1989"},{"key":"2021022704041507000_CIT0028","unstructured":"Wang, X.\n          , 2001, \u201cGeometric Trimming and Curvature Continuous Surface Blending for Aircraft Fuselage and Wing Shapes,\u201d MS thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA."},{"key":"2021022704041507000_CIT0029","unstructured":"Zhang, X.\n          , 2005, \u201cOptimal Geometric Trimming of B-Spline Surfaces for Aircraft Design,\u201d Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA."},{"key":"2021022704041507000_CIT0030","doi-asserted-by":"crossref","first-page":"101832","DOI":"10.1016\/j.cagd.2020.101832","article-title":"Conversion of B-Rep CAD Models Into Globally G1 Triangular Splines","volume":"77","author":"Hettinga","year":"2020","journal-title":"Comput. Aided Geom. Des."},{"key":"2021022704041507000_CIT0031","doi-asserted-by":"crossref","DOI":"10.1115\/DETC2019-97485","article-title":"Making Trimmed B-Splines Watertight with a Hybrid Representation","author":"Song","year":"2019"},{"issue":"8","key":"2021022704041507000_CIT0032","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1016\/j.cad.2004.09.014","article-title":"Feature-Based Decomposition of Trimmed Surface","volume":"37","author":"Hui","year":"2005","journal-title":"Comput.-Aided Des."},{"key":"2021022704041507000_CIT0033","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.cag.2017.08.009","article-title":"Untrimming: Precise Conversion of Trimmed-Surfaces to Tensor-Product Surfaces","volume":"70","author":"Massarwi","year":"2018","journal-title":"Comput. Graphics"},{"key":"2021022704041507000_CIT0034","article-title":"Reconstruction of Gap-Free Intersections for Trimmed Nurbs Surfaces,\u201d Proceedings of the ASME 2019 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference","volume-title":"ASME","author":"Urick","year":"2019"},{"issue":"3","key":"2021022704041507000_CIT0035","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0167-8396(91)90004-U","article-title":"M\u00f6bius Reparametrizations of Rational B-Splines","volume":"8","author":"Lee","year":"1991","journal-title":"Comput. Aided Geom. Des."},{"issue":"5","key":"2021022704041507000_CIT0036","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/0167-8396(93)90023-V","article-title":"Rational Linear Reparametrization of NURBS and the Blossoming Principle","volume":"10","author":"Alt","year":"1993","journal-title":"Comput. Aided Geom. Des."},{"issue":"6","key":"2021022704041507000_CIT0037","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s003710100110330","article-title":"Reparameterization of Piecewise Rational B\u00e9zier Curves and Its Applications","volume":"17","author":"Tokuyama","year":"2001","journal-title":"Visual Comput."},{"key":"2021022704041507000_CIT0038","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.cma.2015.06.020","article-title":"Weighted T-Splines With Application in Reparameterizing Trimmed NURBS Surfaces","volume":"295","author":"Liu","year":"2015","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2021022704041507000_CIT0039","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.cad.2015.02.006","article-title":"Direct Diffeomorphic Reparameterization for Correspondence Optimization in Statistical Shape Modeling","volume":"64","author":"Li","year":"2015","journal-title":"Comput.-Aided Des."},{"issue":"23\u201324","key":"2021022704041507000_CIT0040","doi-asserted-by":"crossref","first-page":"1296","DOI":"10.1080\/01691864.2017.1396923","article-title":"Kinematically Smoothing Trajectories by NURBS Reparameterization \u2013 An Innovative Approach","volume":"31","author":"Hashemian","year":"2017","journal-title":"Advanced Rob."},{"key":"2021022704041507000_CIT0041","volume-title":"Curves and Surfaces for CAGD: A Practical Guide","author":"Farin","year":"2002","edition":"5 ed."},{"issue":"7","key":"2021022704041507000_CIT0042","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1002\/nme.1006","article-title":"Algebraic Grid Generation on Trimmed Parametric Surface Using Non-Self-Overlapping Planar Coons Patch","volume":"60","author":"Wang","year":"2004","journal-title":"Int. J. Numer. Methods Eng."},{"key":"2021022704041507000_CIT0043","unstructured":"Urick, B.\n          , 2016, \u201cReconstruction of Tensor Product Spline Surfaces to Integrate Surface-Surface Intersection Geometry and Topology While Maintaining Inter-Surface Continuity,\u201d Ph.D. thesis, The University of Texas at Austin, Austin, TX."},{"key":"2021022704041507000_CIT0044","doi-asserted-by":"crossref","DOI":"10.1002\/9780470749081","volume-title":"Isogeometric Analysis: Toward Integration of CAD and FEA","author":"Cottrell","year":"2009"},{"issue":"1","key":"2021022704041507000_CIT0045","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.cad.2019.05.034","article-title":"Watertight Boolean Operations: A Framework for Creating Cad-Compatible Gap-Free Editable Solid Models","volume":"115","author":"Urick","year":"2019","journal-title":"Comput.-Aided Des."},{"issue":"2","key":"2021022704041507000_CIT0046","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1080\/16864360.2014.846085","article-title":"Reconstruction Method of Trimmed Surfaces Maintaining G1-Continuity with Adjacent Surfaces","volume":"11","author":"Muraki","year":"2014","journal-title":"Comput.-Aided Des. Appl."}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4047427\/6647589\/jcise_20_5_051008.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4047427\/6647589\/jcise_20_5_051008.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,27]],"date-time":"2021-02-27T04:05:05Z","timestamp":1614398705000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/doi\/10.1115\/1.4047427\/1084390\/Reconstruction-of-Trimmed-NURBS-Surfaces-for-Gap"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,9]]},"references-count":46,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2020,10,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.4047427","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"value":"1530-9827","type":"print"},{"value":"1944-7078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,9]]},"article-number":"051008"}}