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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**[1]**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****[2]**G. BIRKHOFF, H. BURCHARD & D. THOMAS,*Nonlinear Interpolation by Splines, Pseudosplines, and Elastica*, GMR-468, General Motors Research Laboratories, Warren, Michigan, February 3, 1965.**[3]**M. BORN,*Untersuchungen über die Stabilität der elastischen Linie in Ebene und Raum, unter verschiedenen Grenzbedingungen*, Inaugural Dissertation, Göttingen, 1906.**[4]**A. K. Cline,*Scalar- and planar-valued curve fitting using splines under tension*, Comm. ACM**17**(1974), 218–220. MR**0343533**, https://doi.org/10.1145/360924.360971**[5]**James Ferguson,*Multivariable curve interpolation*, J. Assoc. Comput. Mach.**11**(1964), 221–228. MR**0162352**, https://doi.org/10.1145/321217.321225**[6]**A. R. FORREST,*Curves and Surfaces for Computer-Aided Design*, Ph.D Thesis, Computer Laboratory, Cambridge University, 1968.**[7]**A. H. FOWLER & C. W. WILSON,*Cubic Spline, A Curve Fitting Routine*, Report Y-1400, Oak Ridge, 1963.**[8]**Joseph W. Jerome,*Smooth interpolating curves of prescribed length and minimum curvature*, Proc. Amer. Math. Soc.**51**(1975), 62–66. MR**0380551**, https://doi.org/10.1090/S0002-9939-1975-0380551-4**[9]**E. H. Lee and G. E. Forsythe,*Variational study of nonlinear spline curves*, SIAM Rev.**15**(1973), 120–133. MR**0331716**, https://doi.org/10.1137/1015004**[10]**A. E. H. LOVE,*A Treatise on the Mathematical Theory of Elasticity*, 4th ed., Cambridge Univ. Press, London, 1927.**[11]**J. R. MANNING, "Continuity conditions for spline curves,"*Comput. J.*, v. 17, 1974, pp. 181-186.**[12]**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****[13]**Daniel G. Schweikert,*An interpolation curve using a spline in tension*, J. Math. and Phys.**45**(1966), 312–317. MR**0207174****[14]**Dirk J. Struik,*Lectures on Classical Differential Geometry*, Addison-Wesley Press, Inc., Cambridge, Mass., 1950. MR**0036551****[15]**D. H. THOMAS,*Pseudospline Interpolation in Space*, MA-13 (1966) and GMR-468 (1974), General Motors Research Laboratories, Warren, Michigan.

Retrieve articles in *Mathematics of Computation*
with MSC:
65D10

Retrieve articles in all journals with MSC: 65D10

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1976-0400651-9

Keywords:
Interpolation,
curve fitting,
linearized cubic spline,
Fowler-Wilson spline,
pseudospline,
elastica,
nonlinear spline

Article copyright:
© Copyright 1976
American Mathematical Society