Parametric splines in tension

Show full item record

Title: Parametric splines in tension
Author: Gupta, Surendra K.
Abstract: 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.
Record URI: http://hdl.handle.net/1850/10625
Date: 1989

Files in this item

Files Size Format View
SGuptaThesis07-1989.pdf 7.517Mb PDF View/Open

The following license files are associated with this item:

This item appears in the following Collection(s)

Show full item record

Search RIT DML


Advanced Search

Browse