โ Scribed by Wolfgang Renz
No coin nor oath required. For personal study only.
A new approach to the problem of smoothing digitized points is presented. The smoothness of the input data is made visible by displaying the first and second differences. Local corrections are performed on the first-and seconddifference curves. The improved original data points are then computed by integration.
The first step in generating smooth geometry in CAD is to develop smooth curves in space passing nearly through a given set of points. The usual approach to this problem is to approximate the given set of points by special functions continuous in at least their second derivatives.
The broad field of CAD methods for approximation, interpolation and smoothing becomes narrower if we consider only the case of digitized point sets having a high accuracy. Final differences between digitized points and smoothed points can be expected to be less than 0.5 rnm. An example may be the outer skin of a car body. Ir this case it is possible first to smooth and then to interpolate the given point set. If the point set is dense, the influence of the interpolation algorithm used is less.
Smoothing by approximation is at a disadvantage because the variety of resulting shapes depends on the family of special functions used.
๐ SIMILAR VOLUMES
The fixed-point smoothing problem of sequentially correlated processes is considered. The filtering technique of such processes is extended to smoothing problems by simultaneously estimating the state and the accumulated contribution of process noise. Suboptimal filtering and smoothing are also disc
Title of program: SPLINESMOOTH smoothing a set of experimental data, measured at a sequence of values of some independent variable. This is done as a first Catalogue number: AAQO step towards interpolating, integrating, differentiating, or otherwise transforming the function represented by the data.