1,624 research outputs found
Bounds on the Complexity of Halfspace Intersections when the Bounded Faces have Small Dimension
We study the combinatorial complexity of D-dimensional polyhedra defined as
the intersection of n halfspaces, with the property that the highest dimension
of any bounded face is much smaller than D. We show that, if d is the maximum
dimension of a bounded face, then the number of vertices of the polyhedron is
O(n^d) and the total number of bounded faces of the polyhedron is O(n^d^2). For
inputs in general position the number of bounded faces is O(n^d). For any fixed
d, we show how to compute the set of all vertices, how to determine the maximum
dimension of a bounded face of the polyhedron, and how to compute the set of
bounded faces in polynomial time, by solving a polynomial number of linear
programs
Agglomerate properties
Modelling of wet granulation requires the rate of agglomerate coalescence to be estimated.
Coalescence is dependent on the frequency of collisions that occur, and the fraction of collisions
which result in coalescence. The collision rate is a function of granulator kinetics and powder
properties, while the coalescence success rate is dependent on factors including the Stokes
number and particle geometry. This work investigates an aspect of the geometry by examining
the distribution of liquid on the surface of agglomerates in the capillary state. Agglomerates
are created by adding particles, one at a time, about a central tetrahedral arrangement of
four primary particles. For a given agglomerate, the wetted fraction of surface area, defined
as the wetness, is evaluated using an approximate fluid surface. Packing density and binder
saturation parameters are incorporated into the model. Given a number of primary particles
and the volume of binder in a particle, the agglomerate wetness is able to be estimated using
computational geometry
Steinitz Theorems for Orthogonal Polyhedra
We define a simple orthogonal polyhedron to be a three-dimensional polyhedron
with the topology of a sphere in which three mutually-perpendicular edges meet
at each vertex. By analogy to Steinitz's theorem characterizing the graphs of
convex polyhedra, we find graph-theoretic characterizations of three classes of
simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric
projection in the plane with only one hidden vertex, xyz polyhedra, in which
each axis-parallel line through a vertex contains exactly one other vertex, and
arbitrary simple orthogonal polyhedra. In particular, the graphs of xyz
polyhedra are exactly the bipartite cubic polyhedral graphs, and every
bipartite cubic polyhedral graph with a 4-connected dual graph is the graph of
a corner polyhedron. Based on our characterizations we find efficient
algorithms for constructing orthogonal polyhedra from their graphs.Comment: 48 pages, 31 figure
Computing largest circles separating two sets of segments
A circle separates two planar sets if it encloses one of the sets and its
open interior disk does not meet the other set. A separating circle is a
largest one if it cannot be locally increased while still separating the two
given sets. An Theta(n log n) optimal algorithm is proposed to find all largest
circles separating two given sets of line segments when line segments are
allowed to meet only at their endpoints. In the general case, when line
segments may intersect times, our algorithm can be adapted to
work in O(n alpha(n) log n) time and O(n \alpha(n)) space, where alpha(n)
represents the extremely slowly growing inverse of the Ackermann function.Comment: 14 pages, 3 figures, abstract presented at 8th Canadian Conference on
Computational Geometry, 199
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