Relation between algebraic and geometric view on NURBS tensor product surfaces

Dalibor Martišek; Jana Procházková

Applications of Mathematics (2010)

  • Volume: 55, Issue: 5, page 419-430
  • ISSN: 0862-7940

Abstract

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NURBS (Non-Uniform Rational B-Splines) belong to special approximation curves and surfaces which are described by control points with weights and B-spline basis functions. They are often used in modern areas of computer graphics as free-form modelling, modelling of processes. In literature, NURBS surfaces are often called tensor product surfaces. In this article we try to explain the relationship between the classic algebraic point of view and the practical geometrical application on NURBS.

How to cite

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Martišek, Dalibor, and Procházková, Jana. "Relation between algebraic and geometric view on NURBS tensor product surfaces." Applications of Mathematics 55.5 (2010): 419-430. <http://eudml.org/doc/116471>.

@article{Martišek2010,
abstract = {NURBS (Non-Uniform Rational B-Splines) belong to special approximation curves and surfaces which are described by control points with weights and B-spline basis functions. They are often used in modern areas of computer graphics as free-form modelling, modelling of processes. In literature, NURBS surfaces are often called tensor product surfaces. In this article we try to explain the relationship between the classic algebraic point of view and the practical geometrical application on NURBS.},
author = {Martišek, Dalibor, Procházková, Jana},
journal = {Applications of Mathematics},
keywords = {tensor product surface; bilinear form; B-spline; NURBS; tensor product surface; bilinear form; B-spline; NURBS},
language = {eng},
number = {5},
pages = {419-430},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Relation between algebraic and geometric view on NURBS tensor product surfaces},
url = {http://eudml.org/doc/116471},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Martišek, Dalibor
AU - Procházková, Jana
TI - Relation between algebraic and geometric view on NURBS tensor product surfaces
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 5
SP - 419
EP - 430
AB - NURBS (Non-Uniform Rational B-Splines) belong to special approximation curves and surfaces which are described by control points with weights and B-spline basis functions. They are often used in modern areas of computer graphics as free-form modelling, modelling of processes. In literature, NURBS surfaces are often called tensor product surfaces. In this article we try to explain the relationship between the classic algebraic point of view and the practical geometrical application on NURBS.
LA - eng
KW - tensor product surface; bilinear form; B-spline; NURBS; tensor product surface; bilinear form; B-spline; NURBS
UR - http://eudml.org/doc/116471
ER -

References

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  9. Piegl, L., Tiller, W., NURBS Book, Springer Berlin (1995). (1995) Zbl0828.68118
  10. Procházková, J., Sedlák, J., Direct B-spline interpolation from clouds of points, Engineering Technology, Brno 12 (2007), 24-28. (2007) 
  11. Qin, H., Terzopoulos, D., 10.1109/2945.489389, IEEE Transaction of Visualisation and Computer Graphics 2 (1996), 85-96. (1996) DOI10.1109/2945.489389
  12. Sederberg, T., Parry, S., 10.1145/15886.15903, ACM SIGGRAPH Computer Graphics 20 (1986), 151-160. (1986) DOI10.1145/15886.15903
  13. Tang, Sy-sen, Yan, Hong, Liew, Alan Wee-Chung, A NURBS-based vector muscle model for generating human facial expressions, Proc. 4th Conf. Information, Communications and Signal Processing and 4th Pacific Rim Conf. on Multimedia ICICS-PCM Singapore (2003), 15-18. (2003) 
  14. Zheng, J., Wang, Y., Seah, H. S., Adaptive T-spline surface fitting to Z-map models, Proc. 3rd Conf. Computer Graphics and Interactive Techniques in Australasia and South East Asia ACM New York (2005), 405-411. (2005) 

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