skip to main content
10.1145/1655925.1656108acmotherconferencesArticle/Chapter ViewAbstractPublication PagesicisConference Proceedingsconference-collections
research-article

The approximation of interval Bezier curves by a fuzzy rule-based system

Published: 24 November 2009 Publication History

Abstract

Generally, we are interested in knots and control points as variables for finding a well Bezier model from many measuring data points. In this paper, we have selected good knots from given distributed data points on the basis of geometrical information such as curvature and bending of the curve. We have developed interval Bezier curves by estimating control points as an interval according to the knots which are selected by fuzzy rule basis. We have compared these curves and distributed data with the least squares error. We introduced, to the user the as interval Bezier curve, the one who has the minimum error toleration with variations in order to obtain most appropriate widths of Interval control points.

References

[1]
Anile, A. M., Falcidieno, B., Gollo, G., Spinello, S., Modeling Uncertainty Data with Fuzzy B-spline, Fuzzy Sets and Systems, Vol. 113, pp. 397--410, 2000.
[2]
Bézier, P. E., Mathematical and Practical Possibilities of Unisurf, CAGD, R. E. Barnhill and R. Riesenfield eds., Academic Press, New York, pp. 127--152, 1974.
[3]
Chen, F., Sederberg, T. W., Lou, W., Bounding Interval Rational Bézier Curves with Interval Polynomial Bézier Curves. Proc. Of Geometrik Modeling and Processing, pp. 328--336, 2000
[4]
Gallo, G., Michela, S., Saivatores, Fuzzy B-spline: A Surface Model Encapsulating Uncertainty, Graphical Model, Vol. 62, pp. 40--55, 2000.
[5]
Hu, C. Y., Maekawa, T., Patrikalakis, N. M., Ye, X., Robust interval Algorithm for Surface Intersections, Computer Aided Design (CAD), Vol. 29, No. 9, pp. 617--627, 1997.
[6]
Hu, C. Y., Patrikalakis, N. M., Ye, X., Robust interval Solid Modeling, Part II: Boundary Evaluation, Computer Aided Design (CAD), Vol. 28, No. 5, pp. 819--830, 1996.
[7]
Lin, H., Chen, W., Wang, G., Curve reconstruction based on an interval B-spline curve, Visual Computing, Vol 21, pp. 418--427, 2005.
[8]
Lin, H., Liu, L., Wang, G., Boundary evaluation for interval Bezier curve, CAD, Vol 34, pp. 637--646, 2002.
[9]
Lin, H., Wang, G., Interval B-spline Curve Evaluation Bounding Point Cloud, Proc. of the 10th pasific Conf. On Computer Graphics and Applications, pp. 1--2, 2002.
[10]
Lodwick, W. A., Santos, J., Constructing consistent fuzzy surfaces from fuzzy data, Fuzzy Sets and Systems 135(2): 259--277 (2003).
[11]
Maekawa, T., Patrikalakis, N. M., Computation of Singularities and Intersections of Offsets of Planar Curves, CAGD, Vol. 10, No. 5, pp. 407--429, 1993.
[12]
Maekawa, L., Patrikalakis, N. M., Interrogation of differential Geometry Properties for Design and Manufacture, The Visual Computer, Vol. 10, No. 4, pp. 216--237, 1994.
[13]
Pham, B., Representation of Fuzzy Shapes, Proc. of 4th Int. Workshop on Visual Form, Lecture Notes in Computer Science, Vol. 2059, 239, 2001.
[14]
Sederberg, T. W. Farouki, R. T., Approximation by interval Bezier curves, IEEE Computer Graphics and Applications, Vol. 12, pp. 87--95, 1992.
[15]
Shen, F., Lou, W., Degree Reduction of Interval Bezier Curves, CAD, Vol. 32, No. 10, pp. 571--582, 2000.
[16]
Shen, G., Patrikalakis, N. M., Numerical and Geometric Properties of Interval B-splines, International Journal of Shape Modeling, Vol. (4), pp. 31--62, 1998.
[17]
Su, S. L., Xu, Y.-Q., Shum, H.-Y., Chen, F., Simulating Artistic Brushstrokes Using Interval Splines, 2002.
[18]
Tuohy, S. T., Maekawa, T., Shen, G., Patrikalakis, N. M., Approximation of measured data with interval B-splines, Computer-Aided Design Vol. 29 (11), pp. 791--799, 1997.
[19]
Ülker, E., Arslan, A., Curve fitting in terms N-Control points on 2D using fuzzy set and rough set theory, IJCSNS International Journal of Computer Science and Network Security, Vol 6(11), pp. 139--145, 2006.
[20]
Ülker, E., İşler, V., An Artificial Immune System Approach for B-Spline Surface Approximation Problem, Y. Shi et. al. (Eds.): ICCS2007, Part II, LNCS 4488, pp. 49--56, 2007.
[21]
Wahab, A. F., Ali, J. M., Majid, A. A., Lap, A. O. M., Fuzzy Set in Geometric Modeling. CGIV 2004, 227--232
[22]
Weidon, A. L., Santos, J., Constructing Fuzzy Surface From Fuzzy Data, Fuzzy Sets and Systems, Vol. 135, pp. 259--277, 2003.
[23]
Zadeh, L. A., Fuzzy Sets, Information and Control, 1965, s. 338--353.

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Other conferences
ICIS '09: Proceedings of the 2nd International Conference on Interaction Sciences: Information Technology, Culture and Human
November 2009
1479 pages
ISBN:9781605587103
DOI:10.1145/1655925
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

  • AICIT
  • ETRI
  • KISTI

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 24 November 2009

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. approximation
  2. fuzzy inference
  3. interval Bezier curve
  4. interval control points

Qualifiers

  • Research-article

Conference

ICIS '09
Sponsor:

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 17
    Total Downloads
  • Downloads (Last 12 months)2
  • Downloads (Last 6 weeks)0
Reflects downloads up to 20 Feb 2025

Other Metrics

Citations

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media