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 | 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 & J. E. WALSH,*The Theory of Splines and Their Applications*, Academic Press, New York and London, 1967. MR**39**#684. MR**0239327 (39:684)****[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. Assoc. Comput. Mach.*, v. 17, 1974, pp. 218-223. MR**0343533 (49:8274)****[5]**J. FERGUSON, "Multivariable curve interpolation,"*J. Assoc. Comput. Mach.*, v. 11, 1964, pp. 221-228. MR**28**#5551. MR**0162352 (28:5551)****[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]**J. W. JEROME, "Smooth interpolating curves of prescribed length and minimum curvature,"*Proc. Amer. Math. Soc.*, v. 51, 1974, pp. 62-66. MR**0380551 (52:1451)****[9]**E. H. LEE & G. E. FORSYTHE, "Variational study of nonlinear spline curves,"*SIAM Rev.*, v. 15, 1973, pp. 120-133. MR**48**#10048. MR**0331716 (48:10048)****[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]**E. MEHLAM, "Nonlinear splines," in*Proceedings of the Conference on Computer-Aided Design*, University of Utah, 1974. (To appear.) MR**0371011 (51:7234)****[13]**D. G. SCHWEIKERT, "An interpolation curve using a spline in tension,"*J. Math. and Phys.*, v. 45, 1966, pp. 312-317. MR**34**#6990. MR**0207174 (34:6990)****[14]**D. J. STRUIK,*Lectures on Classical Differential Geometry*, Addison-Wesley, Reading, Mass., 1950. MR**12**, 127. MR**0036551 (12:127f)****[15]**D. H. THOMAS,*Pseudospline Interpolation in Space*, MA-13 (1966) and GMR-468 (1974), General Motors Research Laboratories, Warren, Michigan.

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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