CORR
2011
Springer
13 years 6 months ago
2011
Springer
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...
VC
1998
13 years 11 months ago
1998
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 ...
CORR
1999
Springer
13 years 11 months ago
1999
Springer
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 ...
CORR
2000
Springer
13 years 11 months ago
2000
Springer
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...
DCG
2007
13 years 11 months ago
2007
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 ...
CORR
2007
Springer
13 years 11 months ago
2007
Springer
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...
EOR
2008
13 years 11 months ago
2008
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...
EJC
2010
13 years 11 months ago
2010
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...
DCG
2010
13 years 11 months ago
2010
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 ...
SODA
1992
ACM
14 years 18 days ago
1992
ACM
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...