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lec0 - 1 Lectures 1 and 2 1.1 Motivation 1 CAD part and...

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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/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

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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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