Abstract
In this paper we propose a new interpolating method for ordered data points by means of a parabolic spline. In this new method, each segment-connecting node is located between two adjoining points. The parabolic spline with this node location can have higher flexibility than conventional one which has no inflexion except on the data points. A parabolic curve of each segment is parametrically expressed by ‘t’. And we can control its shape by changing the t-value when the spline passes through each data point. High curvature points are frequently selected as the feature points of a curve drawing because they have more information about the shape of an original curve as indicated by Attneave and others. In order to interpolate such feature points, a method is presented that maximizes the curvature of the parabolic spline at the data points. The proposed method is compared with cubic splines and circular arcs by applying them to examples of data point sequences and is shown to generate visually natural interpolating curves. It is also pointed out that these curves are similar to handdrawn interpolating curves.
