Pseudospline interpolation for space curves

Thomas, D. H.

doi:10.1090/S0025-5718-1976-0400651-9

Pseudospline interpolation for space curves

Author: D. H. Thomas
Journal: Math. Comp. 30 (1976), 58-67
MSC: Primary 65D10
DOI: https://doi.org/10.1090/S0025-5718-1976-0400651-9
MathSciNet review: 0400651
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Abstract: A method for interpolating a curve through points in space is described. It is the direct analogue of Fowler-Wilson or pseudospline interpolation for plane curves in that local coordinate systems, cubic polynomials of suitable parameters, and mildly nonlinear equations are used to obtain a continuous interpolating curve with continuous tangent and curvature vectors.

J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The theory of splines and their applications, Academic Press, New York-London, 1967. MR 0239327

G. BIRKHOFF, H. BURCHARD & D. THOMAS, Nonlinear Interpolation by Splines, Pseudosplines, and Elastica, GMR-468, General Motors Research Laboratories, Warren, Michigan, February 3, 1965.

M. BORN, Untersuchungen über die Stabilität der elastischen Linie in Ebene und Raum, unter verschiedenen Grenzbedingungen, Inaugural Dissertation, Göttingen, 1906.

A. K. Cline, Scalar- and planar-valued curve fitting using splines under tension, Comm. ACM 17 (1974), 218–220. MR 0343533, DOI https://doi.org/10.1145/360924.360971
James Ferguson, Multivariable curve interpolation, J. Assoc. Comput. Mach. 11 (1964), 221–228. MR 162352, DOI https://doi.org/10.1145/321217.321225

A. R. FORREST, Curves and Surfaces for Computer-Aided Design, Ph.D Thesis, Computer Laboratory, Cambridge University, 1968.

A. H. FOWLER & C. W. WILSON, Cubic Spline, A Curve Fitting Routine, Report Y-1400, Oak Ridge, 1963.

Joseph W. Jerome, Smooth interpolating curves of prescribed length and minimum curvature, Proc. Amer. Math. Soc. 51 (1975), 62–66. MR 380551, DOI https://doi.org/10.1090/S0002-9939-1975-0380551-4
E. H. Lee and G. E. Forsythe, Variational study of nonlinear spline curves, SIAM Rev. 15 (1973), 120–133. MR 331716, DOI https://doi.org/10.1137/1015004

A. E. H. LOVE, A Treatise on the Mathematical Theory of Elasticity, 4th ed., Cambridge Univ. Press, London, 1927.

J. R. MANNING, "Continuity conditions for spline curves," Comput. J., v. 17, 1974, pp. 181-186.

Even Mehlum, Nonlinear splines, Computer aided geometric design (Proc. Conf., Univ. Utah, Salt Lake City, Utah, 1974) Academic Press, New York, 1974, pp. 173–207. With an appendix by W. W. Meyer. MR 0371011
Daniel G. Schweikert, An interpolation curve using a spline in tension, J. Math. and Phys. 45 (1966), 312–317. MR 207174
Dirk J. Struik, Lectures on Classical Differential Geometry, Addison-Wesley Press, Inc., Cambridge, Mass., 1950. MR 0036551

D. H. THOMAS, Pseudospline Interpolation in Space, MA-13 (1966) and GMR-468 (1974), General Motors Research Laboratories, Warren, Michigan.