The C2 Continuity of Piecewise Cubic Hermite Polynomials with Unequal Intervals.

Abstract : Cubic hermite polynomials are usually C2 continuous. With the introduction of smoothing within the intervals, the second derivatives can be made continuous. This may be applied to the autonomous vehicle problem with unequal laser scanning. In using a laser range finder to measure the range, the direction of these laser rays can be subjected to angular errors. These errors, in the direction of the elevation angle, affect the determination of in-path slopes for navigation of autonomous vehicles. A nonuniform grid may be employed to compute by the spline function method with cubic hermite polynomials. For the purpose of smoothing, it is essential to obtain continuous second derivatives at the gird point from both sides. Keywords: Spline functions; Laser vision systems. (Author)