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Full-Text Articles in Computer Sciences
A Note On Solid Coloring Of Pure Simplicial Complexes, Joseph O'Rourke
A Note On Solid Coloring Of Pure Simplicial Complexes, Joseph O'Rourke
Computer Science: Faculty Publications
We establish a simple generalization of a known result in the plane. The simplices in any pure simplicial complex in Rd may be colored with d+1 colors so that no two simplices that share a (d-1)-facet have the same color. In R2 this says that any planar map all of whose faces are triangles may be 3-colored, and in R3 it says that tetrahedra in a collection may be "solid 4-colored" so that no two glued face-to-face receive the same color.
Flat Zipper-Unfolding Pairs For Platonic Solids, Joseph O'Rourke
Flat Zipper-Unfolding Pairs For Platonic Solids, Joseph O'Rourke
Computer Science: Faculty Publications
We show that four of the five Platonic solids' surfaces may be cut open with a Hamiltonian path along edges and unfolded to a polygonal net each of which can "zipper-refold" to a flat doubly covered parallelogram, forming a rather compact representation of the surface. Thus these regular polyhedra have particular flat "zipper pairs." No such zipper pair exists for a dodecahedron, whose Hamiltonian unfoldings are "zip-rigid." This report is primarily an inventory of the possibilities, and raises more questions than it answers.
On Folding A Polygon To A Polyhedron, Joseph O'Rourke
On Folding A Polygon To A Polyhedron, Joseph O'Rourke
Computer Science: Faculty Publications
We show that the open problem presented in "Geometric Folding Algorithms: Linkages, Origami, Polyhedra" [DO07] is solved by a theorem of Burago and Zalgaller [BZ96] from more than a decade earlier.
On Flat Polyhedra Deriving From Alexandrov's Theorem, Joseph O'Rourke
On Flat Polyhedra Deriving From Alexandrov's Theorem, Joseph O'Rourke
Computer Science: Faculty Publications
We show that there is a straightforward algorithm to determine if the polyhedron guaranteed to exist by Alexandrov's gluing theorem is a degenerate flat polyhedron, and to reconstruct it from the gluing instructions. The algorithm runs in O(n3) time for polygons whose gluings are specified by n labels.
Star Unfolding Convex Polyhedra Via Quasigeodesic Loops, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu
Star Unfolding Convex Polyhedra Via Quasigeodesic Loops, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu
Computer Science: Faculty Publications
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron ℘ to a simple (nonoverlapping) planar polygon: cut along one shortest path from each vertex of ℘ toQ, and cut all but one segment of Q.
The Yao Graph Y6 Is A Spanner, Joseph O'Rourke
The Yao Graph Y6 Is A Spanner, Joseph O'Rourke
Computer Science: Faculty Publications
We prove that Y6 is a spanner. Y6 is the Yao graph on a set of planar points, which has an edge from each point x to a closest point y within each of the six angular cones of 60◦ surrounding x .
Highway Hull Revisited, Greg Aloupis, Jean Cardinal, Sébastien Collette, Ferran Hurtado, Stefan Langerman, Joseph O'Rourke, Belén Palop
Highway Hull Revisited, Greg Aloupis, Jean Cardinal, Sébastien Collette, Ferran Hurtado, Stefan Langerman, Joseph O'Rourke, Belén Palop
Computer Science: Faculty Publications
A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to move from one point to the other, with optional use of H. The highway hull H(S,H) of a point set S is the minimal set containing S as well as the shortest paths between all pairs of points in H(S,H), using the highway time distance. We provide a Θ(nlogn) worst-case …
Morphing Of Triangular Meshes In Shape Space, Stefanie Wuhrer, Prosenjit Bose, Chang Shu, Joseph O'Rourke, Alan Brunton
Morphing Of Triangular Meshes In Shape Space, Stefanie Wuhrer, Prosenjit Bose, Chang Shu, Joseph O'Rourke, Alan Brunton
Computer Science: Faculty Publications
We present a novel approach to morph between two isometric poses of the same non-rigid object given as triangular meshes. We model the morphs as linear interpolations in a suitable shape space S. For triangulated 3D polygons, we prove that interpolating linearly in this shape space corresponds to the most isometric morph in R3 . We then extend this shape space to arbitrary triangulations in 3D using a heuristic approach and show the practical use of the approach using experiments. Furthermore, we discuss a modified shape space that is useful for isometric skeleton morphing. All of the newly presented …