Oriented projective geometry
On the Folkman-Lawrence topological representation theorem for oriented matroids of rank 3
European Journal of Combinatorics - Special issue on combinatorial geometries
Allocating vertex π-guards in simple polygons via pseudo-triangulations
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A combinatorial approach to planar non-colliding robot arm motion planning
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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
Morphing polyhedra with parallel faces: Counterexamples
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
We study parallel redrawing graphs: graphs embedded on moving point sets in such a way that edges maintain their slopes all throughout the motion. The configuration space of such a graph is of an oriented-projective nature, and its combinatorial structure relates to rigidity theoretic parameters of the graph. For an appropriate parametrization the points move with constant speeds on linear trajectories. A special type of kinetic structure emerges, whose events can be analyzed combinatorially. They correspond to collisions of subsets of points, and are in one-to-one correspondence with contractions of the underlying graph on rigid components. We show how to process them algorithmically via a parallel redrawing sweep. Of particular interest are those planar graphs which maintain non-crossing edges throughout the motion. Our main result is that they are (essentially) pseudo-triangulation mechanisms: pointed pseudo-trian- gulations with a convex hull edge removed. These kinetic graph structures have potential applications in morphing of more complex shapes than just simple polygons.