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Error Function in Spline Curve Fitting

IP.com Disclosure Number: IPCOM000106850D
Original Publication Date: 1993-Dec-01
Included in the Prior Art Database: 2005-Mar-21
Document File: 2 page(s) / 37K

Publishing Venue

IBM

Related People

Thornton, AT: AUTHOR

Abstract

Disclosed is a speed-efficient calculation of the goodness of fit between two parametised curves.

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 81% of the total text.

Error Function in Spline Curve Fitting

      Disclosed is a speed-efficient calculation of the goodness of
fit between two parametised curves.

      When a curve is produced that passes through a subset of
vertices, it is often necessary to assess the quality of the
curve-fit to the total set of vertices.  A measure of the error is
needed to quantify the distance between each vertex on the polyline
and the corresponding point on the spline curve with the same
parametric value.  Wherever this exceeds a given percentage of the
chord length of the polyline selected by the user to find a balance
between the quality of the fit, against time and data size
requirements, the curve fit is deemed to be in need of improvement.
As the parameterisations of the polyline and spline are equivalent,
this approach is quicker and more accurate than finding the minimum
distance between each vertex and the spline curve.  Assuming that the
error bound is exceeded in some parts of the curve, it indicates both
the vertices and the parameter values where improvement is required,
for use in the next stage of correcting process.

      The technique has the advantage of easy and computationally
efficient measure of the error function, and when used with recursive
adaptive binary subdivision approach [*]  gives a fast, high quality
fit of the curve with a reasonable amount of data reduction.  It is a
useful technique for fitting a curve in a highly interactive
environment, such as CA...