Parabolic Interpolation

Cubic splines is a powerful and convenient tool, but they are not perfect: it is necessary to take into account the influence of the direction and magnitude of tangent vectors to cover all the points of the curve to its image. The calculation of the cubic spline requires treatment of a large matrix, which depends on all elements of the spline, i.e., the changing of any segment affects to all other segments. Effect decreases with distance from the point of disturbance, but it cannot be completely ignored. The parabolic interpolation solves most of these problems due to the fact that it only is continuous, i.e. at the joints between segments retained only the first derivative continuity and a parabolic interpolation does not require much calculation.

The idea is a linear interpolation (equating derivatives) overlapping parts of two parabolas. Parabola defined by four consecutive points: first by the first three points, the second by the last three. The intersection lies between the second and third points. Despite the fact that the parabolas are flat curves, the linear interpolation is the cubic space curve, as shown in Fig. 3.4.

Fig.3.4. Parabolic Interpolation

Поиск по сайту: