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Keywords:
tensor product surface; bilinear form; B-spline; NURBS
Summary:
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.
References:
[1] Boor, C. De: A Practical Guide to Splines. Springer Berlin (1978). MR 0507062 | Zbl 0406.41003
[2] De, U. C., Sengupta, J., Shaikh, A. A.: Tensor Calculus. Alpha Science International Oxford (2005).
[3] Goldman, R.: The ambient spaces of computer graphics and geometric modeling. IEEE Computer Graphics and Applications, Vol. 20 IEEE Computer Society Press Los Alamitos (2000), 76-84. DOI 10.1109/38.824547
[4] Hewitt, W. T., Ma, Ying Liang: Point inversion and projection for NURBS curve: control polygon approach. Proc. Conf. Theory and Practice of Computer Graphics IEEE Las Vegas (2003), 113-120. MR 1982049
[5] Hwang, Chang-Soon, Sasaki, K.: Evaluation of robotic fingers based on kinematic analysis. Proc. Conf. Intelligent Robots and Systems (IROS 2003) IEEE/RSJ (2003), 3318-3324.
[6] Kay, D. C.: Schaumm's Outline of Tensor Calculus. McGraw-Hill New York (1998).
[7] Li, Chong-Jun, Wang, Ren-Hong: Bivariate cubic spline space and bivariate cubic NURBS surface. Proc. Geometric Modeling and Processing 2004 (GHP 04) IEEE Beijing (2004), 115-123.
[8] Piegl, L.: Modifying the shape of rational B-splines. Part 1: Curves. Computer Aided Design 21 (1989), 509-518. DOI 10.1016/0010-4485(89)90059-6
[9] Piegl, L., Tiller, W.: NURBS Book. Springer Berlin (1995). Zbl 0828.68118
[10] Procházková, J., Sedlák, J.: Direct B-spline interpolation from clouds of points. Engineering Technology, Brno 12 (2007), 24-28.
[11] Qin, H., Terzopoulos, D.: D-NURBS: A physics-based framework for geometric design. IEEE Transaction of Visualisation and Computer Graphics 2 (1996), 85-96. DOI 10.1109/2945.489389
[12] Sederberg, T., Parry, S.: Free-form deformation of solid geometric models. ACM SIGGRAPH Computer Graphics 20 (1986), 151-160. DOI 10.1145/15886.15903
[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.
[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.
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