Multiresolution rendering by sewing trimmed NURBS surfaces

ABSTRACT

Most of the industrial parts are designed as trimmed NURBS. For their efficient rendering multiresolution models are needed. To create such models without artifacts at the trimming curves, one needs to sew parts together along the common boundaries. Due to the problem of determining the geometric places in 3D space along the trimming curves where sewing should be done, current approaches need to have a priori neighbourhood information of the patches and this way they do not provide an automatic solution to create large connected models just from a set of surfaces. In this paper we describe a method, which automatically determines common boundaries of trimmed NURBS surfaces and sews along them. Such a method provides us a non-manifold or manifold structure, which can be handled using standard multi-resolution techniques. Several examples of industrial data demonstrate the efficiency and applicability of our new method. The introduced techniques will also be included into the OpenSG scenegraph API [8] as the basic tool for NURBS rendering.

REFERENCES

• 1: Gill Barequet , Subodh Kumar, Repairing CAD models, Proceedings of the 8th conference on Visualization '97, p.363-ff., October 18-24, 1997, Phoenix, Arizona, United States
• 2: G. Butlin and C. Stops. Cad data repair. In Proceedings of 5th International Meshing Roundtable, pages 7--12, October 1996
• 3: Edwin Earl Catmull, A subdivision algorithm for computer display of curved surfaces., 1974
• 4: James H. Clark, A fast scan-line algorithm for rendering parametric surfaces, ACM SIGGRAPH Computer Graphics, v.13 n.2, p.174, August 1979
• 5: Gerald Farin, Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide, Academic Press Professional, Inc., San Diego, CA, 1993
• 6: Gerald E. Farin , Dianne Hansford, The Essentials of CAGD, A. K. Peters, Ltd., Natick, MA, 2000
• 7: D. R. Forsey , R. V. Klassen, An adaptive subdivision algorithm for crack prevention in the display of parametric surfaces, Proceedings on Graphics interface '90, p.1-8, June 1990, Halifax, Nova Scotia
• 8: OpenSG Forum. The OpenSG Open Source SceneGraph, http://www.opensg.org/, 2000
• 9: André Guéziec , Gabriel Taubin , Francis Lazarus , Bill Horn, Cutting and Stitching: Converting Sets of Polygons to Manifold Surfaces, IEEE Transactions on Visualization and Computer Graphics, v.7 n.2, p.136-151, April 2001 [doi>10.1109/2945.928166]
• 10: James T. Kajiya, Ray tracing parametric patches, ACM SIGGRAPH Computer Graphics, v.16 n.3, p.245-254, July 1982
• 11: Reinhard Klein , Wolfgang Straber, Large mesh generation from boundary models with parametric face representation, Proceedings of the third ACM symposium on Solid modeling and applications, p.431-440, May 17-19, 1995, Salt Lake City, Utah, United States [doi>10.1145/218013.218097]
• 12: Reinhard Klein. Netzgenerierung impliziter und parametrisierter Kurven und Flächen in einem objektorientierten System. PhD thesis, University of Tübingen, 1995
• 13: G. V. V. Ravi Kumar, Prabha Srinivasan, K. G. Shastry, and B. G. Prakash. Geometry based triangulation of multiple trimmed nurbs surfaces. Computer-Aided Design, 33(6):439--454, May 2001. ISSN 0010-4485
• 14: Subodh Kumar , Dinesh Manocha , Hansong Zhang , Kenneth E. Hoff, III, Accelerated walkthrough of large spline models, Proceedings of the 1997 symposium on Interactive 3D graphics, p.91-ff., April 27-30, 1997, Providence, Rhode Island, United States [doi>10.1145/253284.253313]
• 15: Jeffrey M. Lane , Loren C. Carpenter , Turner Whitted , James F. Blinn, Scan line methods for displaying parametrically defined surfaces, Communications of the ACM, v.23 n.1, p.23-34, Jan. 1980 [doi>10.1145/358808.358815]
• 16: T. M. Murali , Thomas A. Funkhouser, Consistent solid and boundary representations from arbitrary polygonal data, Proceedings of the 1997 symposium on Interactive 3D graphics, p.155-ff., April 27-30, 1997, Providence, Rhode Island, United States [doi>10.1145/253284.253326]
• 17: Tomoyuki Nishita , Thomas W. Sederberg , Masanori Kakimoto, Ray tracing trimmed rational surface patches, ACM SIGGRAPH Computer Graphics, v.24 n.4, p.337-345, Aug. 1990
• 18: F. Nooruddin and G. Turk. Simplification and repair of polygonal models using volumetric techniques, 1999
• 19: Les Piegl , Wayne Tiller, The NURBS book, Springer-Verlag, London, 1995
• 20: Franco P. Preparata , Michael I. Shamos, Computational geometry: an introduction, Springer-Verlag New York, Inc., New York, NY, 1985
• 21: Alyn Rockwood , Kurt Heaton , Tom Davis, Real-time rendering of trimmed surfaces, ACM SIGGRAPH Computer Graphics, v.23 n.3, p.107-116, July 1989
• 22: Micheal Shantz , Sheue-Ling Chang, Rendering trimmed NURBS with adaptive forward differencing, ACM SIGGRAPH Computer Graphics, v.22 n.4, p.189-198, Aug. 1988
• 23: Kouki Watanabe and Alexander G. Belyaev. Detection of salient curvature features on polygonal surfaces. Computer Graphics Forum, 20(3):385--392, 2001. ISSN 1067--7055
• 24: Turner Whitted, A scan line algorithm for computer display of curved surfaces, ACM SIGGRAPH Computer Graphics, v.12 n.3, p.26, August 1978

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling

General Terms:
Algorithms

Keywords:
NURBS tessellation, error tolerance, gap closing, sewing