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Original Articles

Estimating error bounds for tensor product binary subdivision volumetric model

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Pages 879-903 | Received 10 Dec 2005, Accepted 30 Oct 2006, Published online: 26 Mar 2007

References

  • MacCracken , R. and Joy , K. Free-form deformations of solid primitives with constraints . Computer Graphics Proceedings, Annual Conference Series . Proceedings of SIGGRAPH 1996 , pp. 181 – 188 . New York : ACM Press/ACM SIGGRAPH/Addison-Wesley Longman .
  • Bajaj , C. , Warren , J. and Xu , G. 2002 . A subdivision scheme for hexahedral meshes . The Visual Computer , 18 : 343 – 356 .
  • Mustafa , G. and Liu , X. 2005 . A new solid subdivision scheme . Journal of University of Science and Technology of China , 35 : 285 – 300 .
  • Chang , Y. S. , McDonnell , K. T. and Qin , H. A new solid subdivision scheme based on box splines . Proceedings of Solid Modeling 2002 . pp. 226 – 233 .
  • Chang , Y. S. , McDonnell , K. T. and Qin , H. An interpolatory subdivision for volumetric models over simplicial complexes . Proceedings of Shape Modeling International 2003 . pp. 143 – 152 .
  • Nairn , D. , Peters , J. and Lutterkort , D. 1999 . Sharp quantitative bounds on the distance between a polynomial piece and its Bézier control polygon . Computer Aided Geometric Design , 16 : 613 – 631 .
  • Lutterkort , D. and Peters , J. 2001 . Tight linear envelopes for splines . Numerische Mathematik , 89 : 735 – 748 .
  • Karavelas , M. , Notre Dame , I. , Kaklis , P. D. , Kostas , K. and Athens , V. 2004 . Bounding the distance between 2D parametric Bézier curves and their control polygon . Computing , 72 : 117 – 128 .
  • Reif , U. 2000 . Best bounds on the approximation of polynomials and splines by their control structure . Computer Aided Geometric Design , 17 : 579 – 589 .
  • Cheng , F. 1992 . Estimating subdivision depths for rational curves and surfaces . ACM Transactions on Graphics , 11 : 140 – 151 .
  • Wang , H. W. and Qin , K. H. 2004 . Estimating subdivision depth of Catmull–Clark surfaces . Journal of Computer Science and Technology , 19 : 657 – 664 .
  • Zeng , X.-M. and Chen , X. J. 2006 . Computational formula of depth for Catmull–Clark subdivion surfaces . Journal of Computational and Applied Mathematics , 195 : 252 – 262 .
  • Catmull , E. and Clark , J. 1978 . Recursively generated B-spline surfaces on arbitrary topological meshes . Computer Aided Design , 10 : 350 – 355 .
  • Mustafa , G. , Falai , C. and Deng , J. 2006 . Estimating error bounds for binary subdivision curves/surfaces . Journal of Computational and Applied Mathematics , 193 : 596 – 613 .
  • Chaikin , G. 1974 . An algorithm for high speed curve generation . Computer Graphics and Image Processing , 3 : 346 – 349 .
  • Dyn , N. , Levin , D. and Micchelli , C. A. 1990 . Using parameters to increase smoothness of curves and surfaces generated by subdivision . Computer Aided Geometric Design , 7 : 129 – 140 .
  • Dyn , N. , Levin , D. and Gregory , J. A. 1987 . A 4-point interpolatory subdivision scheme for curve design . Computer Aided Geometric Design , 4 : 257 – 268 .
  • Dyn , N. , Gregory , A. and Levin , D. 1991 . Analysis of uniform binary subdivision schemes for curve design . Constructive Approximation , 7 : 127 – 147 .

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