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CORR
2011
Springer
148views Education» more  CORR 2011»
12 years 10 months ago
Convex Polyhedra Realizing Given Face Areas
Given n ≥ 4 positive real numbers, we prove in this note that they are the face areas of a convex polyhedron if and only if the largest number is not more than the sum of the ot...
Joseph O'Rourke
VC
1998
106views more  VC 1998»
13 years 3 months ago
Polyhedron realization for shape transformation
Polyhedron realization is the transformation of a polyhedron into a convex polyhedron with an isomorphic vertex neighborhood graph. We present in this paper a novel algorithm for ...
Avner Shapiro, Ayellet Tal
CORR
1999
Springer
89views Education» more  CORR 1999»
13 years 3 months ago
Ununfoldable Polyhedra with Convex Faces
Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper, we study the limits of unfoldability by studying nonconvex polyhedra with the ...
Marshall W. Bern, Erik D. Demaine, David Eppstein,...
CORR
2000
Springer
64views Education» more  CORR 2000»
13 years 3 months ago
On the Development of the Intersection of a Plane with a Polytope
Define a "slice" curve as the intersection of a plane with the surface of a polytope, i.e., a convex polyhedron in three dimensions. We prove that a slice curve develops...
Joseph O'Rourke
DCG
2007
102views more  DCG 2007»
13 years 3 months ago
How to Exhibit Toroidal Maps in Space
Steinitz’s Theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of ...
Dan Archdeacon, C. Paul Bonnington, Joanna A. Elli...
CORR
2007
Springer
100views Education» more  CORR 2007»
13 years 3 months ago
Unfolding Convex Polyhedra via Quasigeodesics
We show that cutting shortest paths from every vertex of a convex polyhedron to a simple closed quasigeodesic, and cutting all but a short segment of the quasigeodesic, unfolds th...
Jin-ichi Itoh, Joseph O'Rourke, Costin Vîlcu
EOR
2008
93views more  EOR 2008»
13 years 3 months ago
Approximate methods for convex minimization problems with series-parallel structure
Consider a problem of minimizing a separable, strictly convex, monotone and differentiable function on a convex polyhedron generated by a system of m linear inequalities. The probl...
Adi Ben-Israel, Genrikh Levin, Yuri Levin, Boris R...
EJC
2010
13 years 3 months ago
On the infinitesimal rigidity of weakly convex polyhedra
The main motivation here is a question: whether any polyhedron which can be subdivided into convex pieces without adding a vertex, and which has the same vertices as a convex poly...
Robert Connelly, Jean-Marc Schlenker
DCG
2010
75views more  DCG 2010»
13 years 3 months ago
Star Unfolding Convex Polyhedra via Quasigeodesic Loops
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 ...
Jin-ichi Itoh, Joseph O'Rourke, Costin Vîlcu
SODA
1992
ACM
140views Algorithms» more  SODA 1992»
13 years 4 months ago
Separation and Approximation of Polyhedral Objects
Given a family of disjoint polygons P1, P2, : : :, Pk in the plane, and an integer parameter m, it is NP-complete to decide if the Pi's can be pairwise separated by a polygon...
Joseph S. B. Mitchell, Subhash Suri