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Unformatted text preview: Figure 1: ( left ) configuration of Pappuss hexagon theorem; ( middle and right ) configurations consist of embed- ded equilateral triangles 1 Geometric Constraints Problem - algorithm problem 1.1 Input, output and problem statement The input is universe: A set of primitive geometric object ids a set of primitive geometric constrains between objects Desired output could be: 1. Does it have a solution in 2D? 2. Find a realization in 2D 3. Find all realizations in 2D 4. Is the set of realizations finite in 2d? 5. Does the input generically satisfy 1 and 4? Computational Geometry- the study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi diagram for a set of points, triangulation of points in a plane or in space, and other related problems. But for computational geometry, the subsystem size is bounded. For general geometric constraints solving problems, the size is not bounded. For 2D & 3D dimensional geometric constraints solving over R . generic or combinatorial questions questions for which combinatorics alone is insufficient. (algebraic geometry is required) definition of genericity Problem: If a system with only parameterless constraints (tangency, colinearity, coplanarity), how to get the corresponding generic definition? 1.2 Conjecture of point/lines incidence constraint system Here is one conjecture relates to determining dependent constraints combinatorially, when no notion of genericity is present (all constraints are parameterless). It could give hints on what the appropriate notion of genericityis present (all constraints are parameterless)....
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This note was uploaded on 11/09/2011 for the course CIS 6930 taught by Professor Staff during the Fall '08 term at University of Florida.
- Fall '08