Skip to main content
SpringerLink
Log in

The sharp upper bound on the distance between a parametric patch and its interpolated triangle

  • Published:
Science in China Series F: Information Sciences Aims and scope Submit manuscript

Abstract

In computer aided geometric design (CAGD) and computer graphics, it is a general manipulation to approximate a surface by triangulation mesh. Thus a key problem is to estimate the error of the approximation. So far, many papers have given various estimate bounds of the distance between a parametric patch of a C 2 surface and an arbitrary triangle whose vertices are on the patch, but these estimates are all imperfect, some of them have large error, some of them have complicated representation formulae. By using a succinct new method, a sharp upper estimate of the maximum distance between a patch and a triangle is obtained and a strict proof is given. This is very valuable for CAGD.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lane J M, Carpenter L. A generalized scan line algorithm for the computer display of parametrically defined surface. Comput Vision Graph Image Proc, 1979, 11: 290–297

    Article  Google Scholar 

  2. Filip D, Magedson R, Markot R. Surface algorithm using bounds on derivatives. Comput Aided Geom Des, 1986, 3: 295–311

    Article  MATH  MathSciNet  Google Scholar 

  3. Sheng X, Hirsh B E. Triangulation of trimmed surface in parametric space. Comput-Aided Des, 1992, 24: 437–444

    Article  MATH  Google Scholar 

  4. Piegl L, Richard A. Tessellating trimmed NURBS surfaces, Comput-Aided Des, 1995, 27: 16–26

    Article  MATH  Google Scholar 

  5. Brunet P, Vigo M. Piecewise linear approximation of trimmed surfaces. In: Farin G, Hagen H, Noltemeier H, eds. Geometric Modelling, 1995, Computing Suppl. 10. Berlin: Springer, 1995. 341–356

    Google Scholar 

  6. Marc V A, Núria P G, Pere B C. Directional adaptive surface triangulation. Comput Aided Geom Des, 1999, 16: 107–126

    Article  MATH  Google Scholar 

  7. Sun W, Bradley C, Zhang Y F, et al. Cloud data medelling employing a unified, non-redundant triangular mesh, Comput-Aided Des, 2001, 33: 83–193

    Google Scholar 

  8. Zhang R J, Wang G J. The error estimates for approximating parametric surface by interpolated plane triangular patch. Math Num Sin (in Chinese), 2004, 26(2): 169–178

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, China Jiliang University, Hangzhou, 310018, China

    Zhang RenJiang

  2. State Key Laboratory of CAD and CG, Zhejiang University, Hangzhou, 310027, China

    Zhang RenJiang & Wang GuoJin

Authors
  1. Zhang RenJiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wang GuoJin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhang RenJiang.

Additional information

Supported by the National Basic Research Program of China (Grant No. 2004CB719400), the National Natural Science Foundation of China (Grant Nos. 60673031 and 60503057) and the Natural Science Foundation of Zhejiang Province (Grant No. Y607034)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, R., Wang, G. The sharp upper bound on the distance between a parametric patch and its interpolated triangle. Sci. China Ser. F-Inf. Sci. 51, 113–119 (2008). https://doi.org/10.1007/s11432-008-0018-0

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-008-0018-0

Keywords

Search

Navigation