Constructing C3 shape preserving interpolating space curves
Tóm tắt
We present a method for constructing shape-preserving C
3 interpolants in R
3. The resulting curve is obtained by adding a polynomial perturbation of high degree to a curve which is shape-preserving but not sufficiently smooth. The degree of the perturbed curve is selected in order to maintain the shape properties of the basic curve.
Tài liệu tham khảo
I. Applegart, P.D. Kaklis and S. Wahl, Benchmark Tests on the Generation of Fair Shapes Subject to Constraints(B.G. Teubner, Stuttgart, 2000).
S. Asaturyan, P. Costantini and C. Manni, G 2shape preserving parametric planar curve interpolation, in: Creating Fair and Shape-Preserving Curves and Surfaces, eds. H. Nowacki and P.D. Kaklis (B.G. Teubner, Stuttgart, 1998) pp. 89-98.
S. Asaturyan, P. Costantini and C. Manni, Local shape-preserving interpolation by space curves, IMA J. Numer. Anal. (2001), to appear.
J.M. Carnicer, T.N.T. Goodman and J.M. Pena, A generalization of the variation diminishing property, Adv. Comput. Math. 3 (1995) 375-394.
P. Costantini, Shape-preserving interpolation with variable degree polynomial splines, in: Advanced Course on FAIRSHAPE, eds. J. Hoschek and P.D. Kaklis (B.G. Teubner, Stuttgart, 1996) pp. 87-114.
P. Costantini, Variable degree polynomial splines, in: Curves and Surfaces in Geometric Design, eds. P.-J. Laurent, A. Le Méhauté and L.L. Schumaker (Vanderbilt University Press, 1996) pp. 85-94.
P. Costantini, Curve and surface construction using variable degree polynomial splines, Comput. Aided Geom. Design 17 (2000) 419-446.
G. Farin, Curves and Surfaces for Computer Aided Geometric Design(Academic Press, New York, 1993).
T.N.T. Goodman, Two ways to construct a smooth piecewise rational curve, J. Approx. Theory 72 (1993) 69-86.
T.N.T. Goodman, Total positivity and the shape of curves, in: Total Positivity and its Applications, eds. M. Gasca and C.A. Micchelli (Kluwer, Dordrecht, 1996) pp. 157-186.
T.N.T. Goodman and B.H. Ong, Shape preserving interpolation by space curves, Comput. Aided Geom. Design 15 (1997) 1-17.
T.N.T. Goodman and B.H. Ong, Shape preserving interpolation by curves in three dimensions, in: Advanced Course on FAIRSHAPE, eds. J. Hoschek and P. Kaklis (B.G. Teubner, Stuttgart, 1996) pp. 40-46.
T.N.T. Goodman and B.H. Ong, Shape preserving interpolation by G 2curves in three dimensions, in: Curves and Surfaces with Applications in CAGD, eds. A. Le Méhauté, C. Rabut and L.L. Schumaker (Vanderbilt University Press, 1997) pp. 151-158.
T.N.T. Goodman, B.H. Ong and M.L. Sampoli, Automatic interpolation by fair, shape preserving, G2 space curves, Comput. Aided Design 30 (1998) 813-822.
J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design(A.K. Peters, Wellesley, MA, 1993).
P.D. Kaklis and D.G. Pandelis, Convexity preserving polynomial splines of non-uniform degree, IMA J. Numer. Anal. 10 (1990) 223-234.
P.D. Kaklis and M.T. Karavelas, Shape preserving interpolation in ℝ3, IMA J. Numer. Anal. 17 (1997) 373-419.
P.D. Kaklis and M.T. Karavelas, Spatial shape-preserving interpolation using v-splines, Numer. Algorithms 23 (2000) 217-250.