21,157 research outputs found

    Optimal 3D Angular Resolution for Low-Degree Graphs

    Full text link
    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

    Full text link
    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

    Get PDF
    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
    • 

    corecore