Gregory S. Chirikjian
Professor Mechanical Engineering
(secondary appointment in CS)
Johns Hopkins University
”Closed-Form Primitives for Generating Volume Preserving Deformations”
In this talk, methods for generating closed-form expressions for locally
volume preserving deformations of general volumes in three dimensional space are introduced. These methods have applications
to computer aided geometric design, the mechanics of materials, and
realistic real-time simulation and animation of physical processes.
In mechanics, volume preserving deformations are intimately related
to the conservation of mass. The importance of this fact manifests itself
in design, and in the realistic simulation of many physical systems.
Whereas volume preservation is generally written as a constraint on
equations of motion in continuum mechanics, this talk develops a set
of physically meaningful basic deformations which are intrinsically
volume preserving. By repeated
application of these primitives, an infinite variety of deformations
can be written in closed form. As time permits, we will also discuss
metrics for rating how different two deformations are from one another.
References
Chirikjian, G.S. ``Closed-Form Primitives for Generating
Volume Preserving Deformations." ASME Journal of Mechanical Design}.
117(Sept. 1995): 347-354.
Chirikjian, G.S., Zhou, S., ``Metrics on Motion and
Deformation of Solid Models,''
ASME J. Mechanical Design, Vol. 120, No. 2, June, 1998, pp. 252-261.
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