NURBS approximation of surface/surface intersection curves
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We use a combination of both symbolic and numerical techniques to construct degree boundedC k -continuous, rational B-spline ε-approximations of real algebraic surface-surface intersection curves. The algebraic surfaces could be either in implicit or rational parametric form. At singular points, we use the classical Newton power series factorizations to determine the distinct branches of the space intersection curve. In addition to singular points, we obtain an adaptive selection of regular points about which the curve approximation yields a small number of curve segments yet achievesC k continuity between segments. Details of the implementation of these algorithms and approximation error bounds are also provided.
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- C. Bajaj, Geometric modeling with algebraic surfaces,The Mathematics of Surfaces III, ed. D. Handscomb (Oxford University Press, 1990) pp. 3–48.Google Scholar
- C. Bajaj, The emergence of algebraic curves and surfaces in geometric design,Directions in Geometric Computing, ed. R. Martin (Information Geometers Press, UK, 1993) pp. 1–29.Google Scholar
- C. Bajaj and A. Royappa, The GANITH algebraic geometry toolkit, in:Proc. 1 st Int. Symp. on the Design and Implementation of Symbolic Computation Systems, Lecture Notes in Computer Science No. 429 (Springer, 1990) pp. 268–269.Google Scholar
- C.L. Bajaj and G. Xu, Piecewise rational approximation of real algebraic curves, CAPO Technical Report 92-19, Computer Science Department, Purdue University (1992).Google Scholar
- C.L. Bajaj and G. Xu, Converting a rational curve to a standard rational Bézier representation, to appear inGRAPHICS GEMS IV ed. P. Heckbert (Academic Press, New York, 1994).Google Scholar
- K. Cheng, Using plane vector fields to obtain all the intersection curves of two general surfaces,Theory and Practice of Geometric Modeling, ed. W. Strasser and H.-P. Seidel (Springer, Berlin, 1989) pp. 187–204.Google Scholar
- G. Farin,Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide (Academic Press, Boston, 1988).Google Scholar
- A. Geisow, Surface interrogations, Ph.D. Thesis, University of East Anglia (1983).Google Scholar
- R. Goldman and C. Micchelli, Algebraic aspects of geometric continuity, in:Mathematical Methods in Computer Aided Geometric Design, ed. T. Lyche and L. Schumaker (Academic Press, Boston, 1989) pp. 313–332.Google Scholar
- M. Pratt and A. Geisow, Surface/surface intersection problems,The Mathematics of Surfaces, ed. J. Gregory (Oxford University Press, 1986) pp. 117–142.Google Scholar
- M.A. Sabin, Contouring—the state of the art, NATO ASI Series,Fundamental Algorithms for Computer Graphics, F17(1985) pp. 411–482.Google Scholar
- T. Sederberg, J. Zhao and A. Zundel, Rational approximation of algebraic curves, in:Theory and Practice of Geometric Modeling, ed. W. Strasser and H.-P. Seidel (Springer) pp. 33–54.Google Scholar