System and method for automatically fitting a B-spline curve to

Details System and method for automatically fitting a B-spline curve to System and method for automatically fitting a B-spline curve to

1994-09-02

1996-10-15

Nguyen, Phu K.

G06F 1500

Patent

active

055662889

ABSTRACT:
A B-spline curve is automatically generated as an approximating curve to a set of data points. A set of four control points are selected at equal intervals along a path defined by a set of data points. A B-spline curve is generated using these control points and the resultant B-spline curve is compared to the path to determine the separation between the B-spline curve and the path. If the separation exceeds a threshold separation, then additional one or more control points are added and the curve generated. The process of adding one or more control points continues until the curve approximates the path along the data points within a specified level of separation. A control point is then removed from the solution and the curve is then regenerated and again compared to the path. If there is no adverse effect resulting from the removal of this control point, the control point is left out of the solution. If, however, removal of the control point adversely impacted the fit of the B-spline curve to the data points, that control point is returned to the solution. This process of checking a control point to determine whether it can be removed from the solution is repeated for the remainder of the control points.

REFERENCES:
patent: 5471573 (1995-11-01), Kaasila
patent: 5500927 (1996-03-01), Sander-Cederlof et al.
Rogers et al., Mathematical Elements For Computer Graphics, McGraw-Hill Book Company, New York, pp. 143-155.
Lozover, et al., "Automatic Construction of a Cubic B-Spline Representation For A General Curve," Computer Graphics, vol. 7, No. 2, 1983, pp. 149-153.

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