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Unformatted text preview: 1. Lectures 1 and 2 1.1. Motivation 1. CAD part and assembly design, Teaching Geometry and automated theorem proving, Robotics, Graphics Animation References for CAD applications. www.solidworks.com www.dcubed.com www.cise.ufl.edu/ ∼ sitharam  FRONTIER opensource software Formalization. • What are geometric constraint satisfaction problems? • Roughly what are the questions:Realizability  Genericity;Generic classification: rigidity (wellconstrainedness)/ under constrainedness/ overconstrainedness;Finer classification of generic realization space structure;Finding generic realizations;Finer classification of nongeneric realization space structure; My surveys and Andrew’s thesis. www.cise.ufl.edu/ ∼ sitharam/drone.pdf www.cise.ufl.edu/ ∼ sitharam/dimacs.pdf www.cise.ufl.edu/ ∼ sitharam/andrewthesis.pdf • Overall framework for GCS questions:What is the input constraint system: Complete or partial graph/metric space (usually) or a matroid, coxeter matroid? www.math.umn.edu/ ∼ reiner/Papers/rigidity.psRealization in: Euclidean, Projective, Lp, Other metric space?Realization in: fixed or variable (min possible) dimensionExact or approximate realization (allow some distortion)Input is General or Special (regular, symmetric)Algorithmic or Characterization(construction/existence), or  Extremal/negative constructions  nonrealizability, nonembeddability etc.For fixed dimension and exact realization: generic or non genericDefining genericWhen are combinatorial characterizations possible? What does 1 2 ”combinatorial” mean?Inverse problem: Given desired realizations, find ”easiest” in put  partial constraint system Grad class (first few) lecture notes taken by students....
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 Fall '08
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