A brief review of curve fitting terminology is presented, and the cubic spline interpolation scheme is outlined. Parametric and non-parametric curve fitting techniques are compared. The technique to fit parametric cubic splines is derived using the Euler- Lagrange formulation. Previous work on splines in tension is identified. Employing the notion of splines in tension, a method is proposed to fit a parametric curve to a set of (n + 1) points in ^-dimension space satisfying a specified set of boundary conditions. The curve fitted will not have any inflection points within any span and will be invariant with respect to coordinate translation and rotation. Using Euler-Lagrange formulation, a system of linear equations in terms of the unknown second derivatives at knots is developed. Three kinds of boundary conditions are investigated. Software is developed in VAX Fortran to fit both parametric splines in tension and parametric cubic splines. Applications where splines in tension may find use are identified. Some examples of such applications are presented and comparison to cubic spline made. Splines in tension offer a better alternative than Fourier transform in describing boundary of shape in digital image processing application. Possible extensions to the numerical scheme developed and related investigations by other workers in this field are also listed.

Library of Congress Subject Headings

Curve fitting--Data processing; Spline theory--Data processing; Computer graphics

Publication Date


Document Type


Department, Program, or Center

Computer Science (GCCIS)


Johnson, Guy

Advisor/Committee Member

Anderson, Peter

Advisor/Committee Member

Lutz, Peter


Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: QA297.6 .G866 1989


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