An Algebraic Approach to Offsetting and Blending of Solids

Thomas Sturm ()
Additional contact information
Thomas Sturm: University of Passau, Department of Mathematics and Computer Science

A chapter in Computer Algebra in Scientific Computing, 2000, pp 367-381 from Springer

Abstract: Abstract We propose to broaden the framework of CSG to a representation of solids as boolean combinations of polynomial equations and inequalities describing regular closed semialgebraic sets of points in 3-space. As intermediate results of our operations we admit arbitrary semialgebraic sets. This allows to overcome well-known problems with the computation of blendings via offsets. The operations commonly encountered in solid modelers plus offsetting and constant radius blending can be reduced to quantifier elimination problems, which can be solved by exact symbolic methods. We discuss the general properties of such offsets and blendings for arbitrary regular closed semialgebraic sets in real n-space. Our computational examples demonstrate the capabilities of the REDLOG package for the discussed operations on solids within our framework.

Keywords: Atomic Formula; Boolean Combination; Quantifier Elimination; Cylindrical Algebraic Decomposition; Closed Complement (search for similar items in EconPapers)
Date: 2000
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57201-2_28

Ordering information: This item can be ordered from
http://www.springer.com/9783642572012

DOI: 10.1007/978-3-642-57201-2_28

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().