Numerical Algorithms

, Volume 5, Issue 11, pp 549–555 | Cite as

C1 surface interpolation with constraints

  • Emanuele Galligani
Geometric Modelling

Abstract

Givenn pairwise distinct and arbitrarily spaced pointsPi in a domainD of thex−y plane andn real numbersfi, consider the problem of computing a bivariate functionf(x, y) of classC1 inD whose values inPi are exactlyfi,i=1,…,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQl inD.

In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.

The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.

Keywords

Bivariate interpolation quadratic programming method of multipliers parallel computation 

AMS subject classification

65D05 65K05 

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Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • Emanuele Galligani
    • 1
  1. 1.Department of MathematicsUniversity of ModenaItaly

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