21,157 research outputs found
Optimal 3D Angular Resolution for Low-Degree Graphs
We show that every graph of maximum degree three can be drawn in three
dimensions with at most two bends per edge, and with 120-degree angles between
any two edge segments meeting at a vertex or a bend. We show that every graph
of maximum degree four can be drawn in three dimensions with at most three
bends per edge, and with 109.5-degree angles, i.e., the angular resolution of
the diamond lattice, between any two edge segments meeting at a vertex or bend.Comment: 18 pages, 10 figures. Extended version of paper to appear in Proc.
18th Int. Symp. Graph Drawing, Konstanz, Germany, 201
Searching Polyhedra by Rotating Half-Planes
The Searchlight Scheduling Problem was first studied in 2D polygons, where
the goal is for point guards in fixed positions to rotate searchlights to catch
an evasive intruder. Here the problem is extended to 3D polyhedra, with the
guards now boundary segments who rotate half-planes of illumination. After
carefully detailing the 3D model, several results are established. The first is
a nearly direct extension of the planar one-way sweep strategy using what we
call exhaustive guards, a generalization that succeeds despite there being no
well-defined notion in 3D of planar "clockwise rotation". Next follow two
results: every polyhedron with r>0 reflex edges can be searched by at most r^2
suitably placed guards, whereas just r guards suffice if the polyhedron is
orthogonal. (Minimizing the number of guards to search a given polyhedron is
easily seen to be NP-hard.) Finally we show that deciding whether a given set
of guards has a successful search schedule is strongly NP-hard, and that
deciding if a given target area is searchable at all is strongly PSPACE-hard,
even for orthogonal polyhedra. A number of peripheral results are proved en
route to these central theorems, and several open problems remain for future
work.Comment: 45 pages, 26 figure
Posing 3D Models from Drawing
Inferring the 3D pose of a character from a drawing is a complex and under-constrained problem. Solving it may help automate various parts of an animation production pipeline such as pre-visualisation. In this paper, a novel way of inferring the 3D pose from a monocular 2D sketch is proposed. The proposed method does not make any external assumptions about the model, allowing it to be used on different types of characters. The inference of the 3D pose is formulated as an optimisation problem and a parallel variation of the Particle Swarm Optimisation algorithm called PARAC-LOAPSO is utilised for searching the minimum. Testing in isolation as well as part of a larger scene, the presented method is evaluated by posing a lamp, a horse and a human character. The results show that this method is robust, highly scalable and is able to be extended to various types of models
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