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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 Andrews thesis. www.cise.ufl.edu/ sitharam/drone.pdf www.cise.ufl.edu/ sitharam/dimacs.pdf www.cise.ufl.edu/ sitharam/andrew-thesis.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.ps-Realization in: Euclidean, Projective, Lp, Other metric space?-Realization in: fixed or variable (min possible) dimension-Exact or approximate realization (allow some distortion)-Input is General or Special (regular, symmetric)-Algorithmic or Characterization(construction/existence), or - Extremal/negative constructions - non-realizability, non-embeddability etc.-For fixed dimension and exact realization: generic or non- generic-Defining generic-When 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