Abstract
This paper introduces a new family of C4-continuous interpolatory variable-degree polynomial splines and investigates their interpolation and asymptotic properties as the segment degrees increase. The basic outcome of this investigation is an iterative algorithm for constructing C4 interpolants, which conform with the discrete convexity and torsion information contained in the associated polygonal interpolant. The performance of the algorithm, in particular the fairness effect of the achieved high parametric continuity, is tested and discussed for a planar and a spatial data set.
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References
Asaturyan, S., Costantini, P., Manni, C.: Shape-preserving interpolating curves in n3: A local approach. In: Creating fair and shape-preserving curves and surfaces (Nowacki, H., Kaklis, P. D., eds.), pp. 99–108. Stuttgart: B.G. Teubner, 1998.
Costantini, P.: Shape-preserving interpolation with variable degree polynomial splines. In: Advanced course on FAIRSHAPE (Hoschek, J., Kaklis, P. D., eds.), pp. 87–114. Stuttgart: B.G. Teubner, 1996.
Costantini, P.: Variable degree polynomial splines. In: Curves and surfaces with applications in CAGD (Le Méhauté, A., Rabut, C., Schumaker, L. L., eds.), pp. 85–94. Nashville: Vanderbilt University Press, 1997.
Costantini, P.: Curve and surface construction using variable degree polynomial splines. CAGD 17, 419–446 (2000).
Eckhaus, W.: Asymptotic analysis of singular perturbations. Amsterdam- North-Holland, 1979.
Ginnis, A. I., Kaklis, P. D., Gabrielides, N. C.: Sectional-curvature preserving skinning surfaces with a 3D spine curve. In: Advanced topics in multivariate approximation (Fontanella, F., Jetter,K., Laurent, P.-J., eds.), pp. 113–123. Singapore: World Scientific, 1996.
Goodman, T. N. T., Ong, B. H.: Shape preserving interpolation by G2 curves in three dimensions. In: Curves and surfaces with applications in CAGD (Le Méhauté, A., Rabut, C., Schumaker, L.L., eds.), pp. 151–158. Nashville: Vanderbilt University Press, 1997.
Goodman, T. N. T., Ong, B. H.: Shape preserving interpolation by space curves. CAGD 15, 1–17 (1997).
Hoschek, J., Lasser, D.: Fundamentals of computer aided geometric design. Wellesley: AK Peters, 1993.
Kaklis, P. D., Ginnis, A. I.: Sectional-curvature preserving skinning surfaces. CAGD 13, 583–671 (1996).
Kaklis, P. D., Karavelas, M. I.: Shape-preserving interpolation in 083. IMA J. Numer. Anal. 17, 373–419 (1997).
Kaklis, P. D., Pandelis, D. G.: Convexity-preserving polynomial splines of non-uniform degree. IMA J. Numer. Anal. 10, 223–234 (1990).
Kaklis, P. D., Sapidis, N. S.: Convexity-preserving interpolatory parametric splines of nonuniform polynomial degree. CAGD 12, 1–26 (1995).
Messac, A., Sivanandan, A.: A new family of convex splines for data interpolation. CAGD 15, 39–59 (1997).
Sapidis, N. S., Kaklis, P. D.: A hybrid method for shape-preserving interpolation with curvature-continuous quintic splines. Computing [Suppl.] 10, 285–301 (1995).
Späth, H.: Exponential spline interpolation. Computing 4, 225–233 (1969).
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© 2001 Springer-Verlag Wien
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Gabrielides, N.C., Kaklis, P.D. (2001). C4 Interpolatory Shape-Preserving Polynomial Splines of Variable Degree. In: Brunnett, G., Bieri, H., Farin, G. (eds) Geometric Modelling. Computing, vol 14. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6270-5_8
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DOI: https://doi.org/10.1007/978-3-7091-6270-5_8
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83603-3
Online ISBN: 978-3-7091-6270-5
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