The Stable Evaluation of Multivariate B-Splines.

Abstract

For one variable, the problem of stably evaluating B-splines via their recurrence relations is well understood. For multivariate B-splines, however, the geometry becomes a more complex, and it becomes quite difficult to implement the recurrence relations in such a way that one ends up with a robust evaluation method. This paper gives a general method for the stable evaluation of multivariate B-splines. The problem of evaluation along mesh boundaries is discussed in detail. Several examples are presented to demonstrate the effectiveness of the method for arbitrary B-splines. Originator-supplied keywords include: Simplex spline, Recurrence relation, and Simplex method.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1984
Accession Number
ADA147386

Entities

People

  • T. A. Grandine

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Boundaries
  • Classification
  • Computations
  • Computer Programming
  • Determinants (Mathematics)
  • Equations
  • Geometry
  • Inequalities
  • Linear Programming
  • Linear Systems
  • Mathematics
  • North Carolina
  • Security
  • Simplex Method
  • United States

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Graph Algorithms and Convex Optimization.
  • International Relations and Conflict Resolution