Solving Interval Constraints by Linearization in Computer-Aided Design

Solving Interval Constraints by Linearization in Computer-Aided Design Current parametric CAD systems require geometric parameters to have fixed values. Specifying fixed parameter values implicitly adds rigid constraints on the geometry, which have the potential to introduce conflicts during the design process. This paper presents a soft constraint representation scheme based on nominal interval. Interval geometric parameters capture inexactness of conceptual and embodiment design, uncertainty in detail design, as well as boundary information for design optimization. To accommodate under-constrained and over-constrained design problems, a double-loop Gauss-Seidel method is developed to solve linear constraints. A symbolic preconditioning procedure transforms nonlinear equations to separable form. Inequalities are also transformed and integrated with equalities. Nonlinear constraints can be bounded by piecewise linear enclosures and solved by linear methods iteratively. A sensitivity analysis method that differentiates active and inactive constraints is presented for design refinement. Reliable Computing Springer Journals

Solving Interval Constraints by Linearization in Computer-Aided Design

Loading next page...
Springer Netherlands
Copyright © 2007 by Springer Science + Business Media B.V.
Mathematics; Numeric Computing; Mathematical Modeling and Industrial Mathematics; Approximations and Expansions; Computational Mathematics and Numerical Analysis
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial