Multivariate Scattered Data Derivative Generation by Functional Minimization,
Abstract
Many multivariate interpolation schemes require as data values of derivatives that are not available in a practical application, and that therefore have to be generated suitably. A specific approach to this problem is described that is modeled after univariate spline interpolation. Derivative values are defined by the requirement that a certain functional be minimized over a suitable space subject to interpolation of given positional data. In principle, the technique can be applied in arbitrarily many variables. The theory is described in general, and particular applications are given in one and two variables. A major tool in the implementation of the technique is the Bezier-Bernstein form of a multivariate polynomial. The technique yields visually pleasing surfaces and is therefore suitable for design applications. It is less suitable for the approximation of derivatives of a given function. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1984
- Accession Number
- ADA144663
Entities
People
- P. Alfeld
Organizations
- University of Wisconsin–Madison