Abstract/Details

Geometric constraint systems with applications in CAD and biology


2008 2008

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Abstract (summary)

Motivated by applications in Computer Aided Design (CAD) and biology, we investigate geometric constraint systems, composed of atomic elements with constraints between them. A well-studied model in rigidity theory is the bar-and-joint structure, where the atomic elements are universal joints connected by fixed-length bar constraints. We propose several new models involving constraints arising in CAD and biology and provide the theoretical foundation for each. In particular, we present a model addressing the pairwise constraints among points, lines and planes found in constraint-based CAD software, such as in the assembly environment of the widely-used SolidWorks CAD application.

As a result, we identify and generalize combinatorial properties that appear as necessary conditions for generic rigidity of these new constraint systems; in some cases, the conditions are also sufficient, thus providing a complete characterization. We study sparsity for graphs, arising from known rigidity results and present extensions of this concept to graded, mixed and nested sparsity. For these sparsity properties, we present algorithms that solve the fundamental questions of Decision, Extraction and Components, based on the efficient and elegant pebble games first developed for planar bar-and-joint rigidity.

Indexing (details)


Subject
Computer science
Classification
0984: Computer science
Identifier / keyword
Applied sciences, Bar-and-joint structure, Computer-aided design, Geometric constraint systems, Graph theory, Rigidity theory
Title
Geometric constraint systems with applications in CAD and biology
Author
Lee, Audrey
Number of pages
172
Publication year
2008
Degree date
2008
School code
0118
Source
DAI-B 69/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549822240
Advisor
Streinu, Ileana
Committee member
Barrington, David; Haller, Kirk; Mettu, Ramgopal; Wang, Rui
University/institution
University of Massachusetts Amherst
Department
Computer Science
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3329957
ProQuest document ID
304567855
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304567855
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