A sum of squares theorem for visibility
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Visualization of an algorithm for convexifying a simple planar polygon with rigid motions
CCSC '01 Proceedings of the sixth annual CCSC northeastern conference on The journal of computing in small colleges
Computational geometry column 43
ACM SIGACT News
Pseudotriangulations, polytopes, and how to expand linkages
Proceedings of the eighteenth annual symposium on Computational geometry
Allocating vertex π-guards in simple polygons via pseudo-triangulations
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Folding and Unfolding Linkages, Paper, and Polyhedra
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Chain Reconfiguration. The INs and Outs, Ups and Downs of Moving Polygons and Polygonal Linkages
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Flat-State Connectivity of Linkages under Dihedral Motions
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Tight degree bounds for pseudo-triangulations of points
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
An algorithmic study of manufacturing paperclips and other folded structures
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Spatial embedding of pseudo-triangulations
Proceedings of the nineteenth annual symposium on Computational geometry
Planar minimally rigid graphs and pseudo-triangulations
Proceedings of the nineteenth annual symposium on Computational geometry
Proceedings of the nineteenth annual symposium on Computational geometry
Kinetic collision detection between two simple polygons
Computational Geometry: Theory and Applications
Transforming pseudo-triangulations
Information Processing Letters
An energy-driven approach to linkage unfolding
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
The polytope of non-crossing graphs on a planar point set
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Convexity minimizes pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry CCCG02
Certifying and constructing minimally rigid graphs in the plane
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Pointed and colored binary encompassing trees
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Enumerating pseudo-triangulations in the plane
Computational Geometry: Theory and Applications
Planar minimally rigid graphs and pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
The Erdős-Nagy theorem and its ramifications
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Locked and unlocked chains of planar shapes
Proceedings of the twenty-second annual symposium on Computational geometry
Proceedings of the twenty-second annual symposium on Computational geometry
Pre-triangulations and liftable complexes
Proceedings of the twenty-second annual symposium on Computational geometry
Minimum weight pseudo-triangulations
Computational Geometry: Theory and Applications
Matching edges and faces in polygonal partitions
Computational Geometry: Theory and Applications
On the number of pseudo-triangulations of certain point sets
Journal of Combinatorial Theory Series A
Efficient algorithms for the d-dimensional rigidity matroid of sparse graphs
Computational Geometry: Theory and Applications
Decomposing a simple polygon into pseudo-triangles and convex polygons
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
On Unfolding 3D Lattice Polygons and 2D Orthogonal Trees
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Flattening single-vertex origami: the non-expansive case
Proceedings of the twenty-fifth annual symposium on Computational geometry
Enumerating pseudo-triangulations in the plane
Computational Geometry: Theory and Applications
Planar minimally rigid graphs and pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
The Erdős--Nagy theorem and its ramifications
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
On constrained minimum pseudotriangulations
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Transforming pseudo-triangulations
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
The stochastic walk algorithms for point location in pseudo-triangulations
Advances in Engineering Software
Construction of pseudo-triangulation by incremental insertion
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Algorithms for the d-dimensional rigidity matroid of sparse graphs
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Single-Vertex origami and spherical expansive motions
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Parallel-redrawing mechanisms, pseudo-triangulations and kinetic planar graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
On straightening low-diameter unit trees
GD'05 Proceedings of the 13th international conference on Graph Drawing
On unfolding lattice polygons/trees and diameter-4 trees
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Decompositions, partitions, and coverings with convex polygons and pseudo-triangles
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Minimum weight pseudo-triangulations
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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We propose a combinatorial approach to plan noncolliding motions for a polygonal bar-and-joint framework. Our approach yields very efficient deterministic algorithms for a category of robot arm motion planning problems with many degrees of freedom, where the known general roadmap techniques would give exponential complexity. It is based on a novel class of one-degree-of-freedom mechanisms induced by pseudo triangulations of planar point sets, for which we provide several equivalent characterization and exhibit rich combinatorial and rigidity theoretic properties. The main application is an efficient algorithm for the Carpenter's rule problem: convexify a simple bar-and-joint planar polygonal linkage using only non self-intersecting planar motions. A step in the convexification motion consists in moving a pseudo-triangulation-based mechanism along its unique trajectory in configuration space until two adjacent edges align. At that point, a local alteration restores the pseudo triangulation. The motion continues for O(n/sup 2/) steps until all the points are in convex position.