More Web Proxy on the site http://driver.im/

research-article

Watertight trimmed NURBS

Authors:

Thomas W. Sederberg,

G. Thomas Finnigan,

Heather IpsonAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 27, Issue 3

Pages 1 - 8

https://doi.org/10.1145/1360612.1360678

Published: 01 August 2008 Publication History

Abstract

This paper addresses the long-standing problem of the unavoidable gaps that arise when expressing the intersection of two NURBS surfaces using conventional trimmed-NURBS representation. The solution converts each trimmed NURBS into an untrimmed T-Spline, and then merges the untrimmed T-Splines into a single, watertight model. The solution enables watertight fillets of NURBS models, as well as arbitrary feature curves that do not have to follow iso-parameter curves. The resulting T-Spline representation can be exported without error as a collection of NURBS surfaces.

Supplementary Material

MOV File (a79-sederberg.mov)

Download
20.90 MB

References

[1]

Bjorck, A. 1996. Numerical Methods for Least squares Problems. SIAM.

[2]

DeRose, T. D., Kass, M., and Truong, T. 1998. Subdivision surfaces in character animation. In Proceedings of SIGGRAPH 1998, Computer Graphics Proceedings, Annual Conference Series, 85--94.

Digital Library

[3]

Farouki, R. T., Han, C. Y., Hass, J., and Sederberg, T. W. 2004. Topologically consistent trimmed surface approximations based on triangular patches. Computer Aided Geometric Design 21, 5, 459--478.

Digital Library

[4]

Farouki, R. T. 1999. Closing the gap between CAD model and downstream application (report on the SIAM Workshop on Integration of CAD and CFD, UC Davis, April 12--13, 1999). SIAM News 32, 5, 1--3.

[5]

Hunter, G. M., and Steiglitz, K. 1979. Operations on images using quad trees. IEEE Transactions on Pattern Analysis and Machine Intelligence 1, 2 (April), 145--153.

[6]

Kasik, D. J., Buxton, W., and Ferguson, D. R. 2005. Ten CAD model challenges. IEEE Computer Graphics and Applications 25, 2, 81--92.

Digital Library

[7]

Katz, S., and Sederberg, T. W. 1988. Genus of the intersection curve of two rational surface patches. Computer Aided Geometric Design 5, 253--258.

Digital Library

[8]

Krishnan, S., and Manocha, D. 1996. Efficient representations and techniques for computing b-rep's of csg models with nurbs primitives. In Proc. of CSG'96, 101--122.

[9]

Krishnan, S., and Manocha, D. 1997. An efficient surface intersection algorithm based on lower-dimensional formulation. ACM Transactions on Graphics 16, 1 (Jan.), 74--106.

Digital Library

[10]

Krishnan, S., Manocha, D., Gopi, M., and Keyser, J. 2001. Boole: A boundary evaluation system for Boolean combinations of sculptured solids. International Journal on Computational Geometry and Applications 11, 1, 105--144.

[11]

Kristjansson, D., Biermann, H., and Zorin, D. 2001. Approximate Boolean operations on free-form solids. In Proceedings of ACM SIGGRAPH 2001, E. Fiume, Ed., Computer Graphics Proceedings, Annual Conference Series, 185--194.

Digital Library

[12]

Kumar, S. 1996. Interactive rendering of parametric spline surfaces. PhD thesis, The University of North Carolina at Chapel Hill.

Digital Library

[13]

Litke, N., Levin, A., and Schröder, P. 2001. Trimming for subdivision surfaces. Computer Aided Geometric Design 18, 5 (June), 463--481.

Digital Library

[14]

Loop, C. 2004. Second order smoothness over extraordinary vertices. In Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, 165--174.

Digital Library

[15]

Moreton, H. 2001. Watertight tessellation using forward differencing. In HWWS '01: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware, ACM, New York, NY, USA, 25--32.

Digital Library

[16]

Müller, K., Reusche, L., and Fellner, D. 2006. Extended subdivision surfaces: Building a bridge between NURBS and Catmull-Clark surfaces. ACM Transactions on Graphics 25, 2 (Apr.), 268--292.

Digital Library

[17]

Müller, K., Reusche, L., and Fellner, D. 1999. Planning Report: Interoperability Cost Analysis of the US Automotive Supply Chain. National Institute of Standards and Technology.

[18]

Patrikalakis, N. M., and Maekawa, T. 2002. Intersection problems. In Handbook of Computer Aided Geometric Design, North-Holland, G. Farin, J. Hoschek, and M.-S. Kim, Eds., 623--649.

[19]

Peters, J. 2000. Patching Catmull-Clark meshes. In Proceedings of ACM SIGGRAPH 2000, Computer Graphics Proceedings, Annual Conference Series, 255--258.

Digital Library

[20]

Samet, H. 1984. The quadtree and related hierarchical data structures. ACM Computing Surveys 16, 2, 187--260.

Digital Library

[21]

Sederberg, T. W., Li, X., Lin, H., and Finnigan, G. T. Nonuniform NURBS. In Preparation.

[22]

Sederberg, T., Anderson, D., and Goldman, R. 1984. Implicit representation of parametric curves and surfaces. Computer Vision, Graphics and Image Processing 28, 72--84.

[23]

Sederberg, T. W., Zheng, J., Sewell, D., and Sabin, M. A. 1998. Non-uniform recursive subdivision surfaces. In Proceedings of SIGGRAPH 1998, Computer Graphics Proceedings, Annual Conference Series, 387--394.

Digital Library

[24]

Sederberg, T. W., Zheng, J., Bakenov, A., and Nasri, A. 2003. T-Splines and T-NURCCs. ACM Transactions on Graphics 22, 3 (July), 477--484.

Digital Library

[25]

Sederberg, T. W., Cardon, D. L., Finnigan, G. T., North, N. S., Zheng, J., and Lyche, T. 2004. T-spline simplification and local refinement. ACM Transactions on Graphics 23, 3 (August).

Digital Library

[26]

Singh, K., and Fiume, E. L. 1998. Wires: A geometric deformation technique. In Proceedings of SIGGRAPH 1998, Computer Graphics Proceedings, Annual Conference Series, 405--414.

Digital Library

[27]

Song, Q., and Wang, J. 2007. Generating g ⁿ parametric blending surfaces based on partial reparameterization of base surfaces. Comput. Aided Des. 39, 11, 953--963.

Digital Library

[28]

Song, X., Sederberg, T. W., Zheng, J., Farouki, R. T., and Hass, J. 2004. Linear perturbation methods for topologically consistent representations of free-form surface intersections. Computer Aided Geometric Design 21, 3, 303--319.

Digital Library

[29]

Stam, J. 1998. Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values. In Proceedings of SIGGRAPH 1998, Computer Graphics Proceedings, Annual Conference Series, 395--404.

Digital Library

[30]

Wang, W., Pottmann, H., and Liu, Y. 2006. Fitting B-spline curves to point clouds by curvature-based squared distance minimization. ACM Transactions on Graphics 25, 2 (Apr.), 214--238.

Digital Library

Cited By

Spainhour JGunderman DWeiss K(2024)Robust Containment Queries over Collections of Rational Parametric Curves via Generalized Winding NumbersACM Transactions on Graphics10.1145/365822843:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658228
Peres MSanches GPaiva APagliosa P(2024)Parallel isogeometric boundary element analysis with T-splines on CUDAComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2024.117296432(117296)Online publication date: Dec-2024
https://doi.org/10.1016/j.cma.2024.117296
Antonelli NAristio RGorgi AZorrilla RRossi RScovazzi GWüchner R(2024)The Shifted Boundary Method in Isogeometric AnalysisComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2024.117228430(117228)Online publication date: Oct-2024
https://doi.org/10.1016/j.cma.2024.117228
Show More Cited By

Index Terms

Watertight trimmed NURBS
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

Recommendations

On increasing the developability of a trimmed NURBS surface

Developable surfaces are desired in designing products manufactured from planar sheets. Trimmed non-uniform rational B-spline (NURBS) surface patches are widely adopted to represent 3D products in CAD/CAM. This paper presents a new method to increase ...
Polynomial splines over hierarchical T-meshes

In this paper, we introduce a new type of splines-polynomial splines over hierarchical T-meshes (called PHT-splines) to model geometric objects. PHT-splines are a generalization of B-splines over hierarchical T-meshes. We present the detailed ...
Degree elevation of NURBS curves by weighted blossom

An algorithmic approach to degree elevation of NURBS curves is presented. The new algorithms are based on the weighted blossoming process and its matrix representation. The elevation method is introduced that consists of the following steps: (a) ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 27, Issue 3

August 2008

844 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1360612

Issue’s Table of Contents

Copyright © 2008 ACM.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 August 2008

Published in TOG Volume 27, Issue 3

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

110
Total Citations
View Citations
2,056
Total Downloads

Downloads (Last 12 months)81
Downloads (Last 6 weeks)16

Reflects downloads up to 19 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

Spainhour JGunderman DWeiss K(2024)Robust Containment Queries over Collections of Rational Parametric Curves via Generalized Winding NumbersACM Transactions on Graphics10.1145/365822843:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658228
Peres MSanches GPaiva APagliosa P(2024)Parallel isogeometric boundary element analysis with T-splines on CUDAComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2024.117296432(117296)Online publication date: Dec-2024
https://doi.org/10.1016/j.cma.2024.117296
Antonelli NAristio RGorgi AZorrilla RRossi RScovazzi GWüchner R(2024)The Shifted Boundary Method in Isogeometric AnalysisComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2024.117228430(117228)Online publication date: Oct-2024
https://doi.org/10.1016/j.cma.2024.117228
Pan QHuang YRabczuk TYang X(2024)The subdivision-based IGA-EIEQ numerical scheme for the Navier–Stokes equations coupled with Cahn–Hilliard phase-field model of two-phase incompressible flow on complex curved surfacesComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2024.116901424(116901)Online publication date: May-2024
https://doi.org/10.1016/j.cma.2024.116901
Yu LHe CTan WXue YZhao GWang A(2024)T-spline Surface Fairing Based on Centripetal Re-parameterizationArtificial Intelligence and Robotics10.1007/978-981-99-9109-9_1(1-8)Online publication date: 4-Jan-2024
https://doi.org/10.1007/978-981-99-9109-9_1
Moulaeifard MBernard SWellmann F(2023)PySubdiv 1.0: open-source geological modeling and reconstruction by non-manifold subdivision surfacesGeoscientific Model Development10.5194/gmd-16-3565-202316:12(3565-3579)Online publication date: 28-Jun-2023
https://doi.org/10.5194/gmd-16-3565-2023
Chi BBai SGuo QZhang YYuan WLi C(2023)A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry DefeaturingMathematics10.3390/math1116347311:16(3473)Online publication date: 11-Aug-2023
https://doi.org/10.3390/math11163473
Jiang XLin Y(2023)Reparameterization of B-spline surface and its application in ship hull modelingOcean Engineering10.1016/j.oceaneng.2023.115535286(115535)Online publication date: Oct-2023
https://doi.org/10.1016/j.oceaneng.2023.115535
Wang ZCao JWei XChen ZCasquero HZhang Y(2023)Kirchhoff–Love shell representation and analysis using triangle configuration B-splinesComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2023.116316416(116316)Online publication date: Nov-2023
https://doi.org/10.1016/j.cma.2023.116316
Hao PWang YJin LMa SWang B(2023)An isogeometric design-analysis-optimization workflow of stiffened thin-walled structures via multilevel NURBS-based free-form deformations (MNFFD)Computer Methods in Applied Mechanics and Engineering10.1016/j.cma.2023.115936408(115936)Online publication date: Apr-2023
https://doi.org/10.1016/j.cma.2023.115936
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents