Virtual knot technique for curve fitting of rapidly varying data

Curve fitting with piecewise splines for rapidly varying data has been a difficult problem. Often, the curve exhibits unwanted “wiggles” around those data points whose locations change rapidly in comparison to their neighboring data points. Many methods were proposed to solve this problem using non-homogeneous tension spline or fairing process. In this paper, a new approach using the concept of virtual knots is presented. Since the occurrence of the problem is due to the inconsistency between the parametric spans of the knots and the geometric spans of the data points, a number of virtual knots are inserted into the original knot sequence such that the parametric spans are made more consistent with the geometric spans of the data. With this parametric adjustment, a regularization process is used to find the desired curve. Experimental results show that this technique is efficient to adjust the fairness of the desired curve. This technique can be applied to different spline spaces. In this paper, the usages of this technique in linear B-spline and cubic B-spline spaces are demonstrated.