Abstract. In a;-contact representation of a planar graph G, each ver-tex is represented as an axis-aligned plus shape consisting of two in-tersecting line segments (or equivalently, four axis-aligned line segments that share a common endpoint), and two plus shapes touch if and only

Realizing graphs as interior disjoint intersections (contacts) of geometric objects has been a subject of study for many decades. In such a representation the nodes are geometric objects like disks, segments,

Contact graphs are a special kind of intersection graphs of geometrical objects in which the objects are not allowed to cross but only to touch each other. Contact graphs of simple curves, and line segments as a special case, in the plane are considered. The curve contact representations

planar graph is an intersection graph of segments in the plane. This boosted the study of intersection and contact graphs of restricted classes of curves. In this paper we study planar graphs that are VCPG, i.e. graphs admitting a representation as Vertex Contact graph of Paths on a Grid. In such a

(OBBTrees). At run time, we use hybrid hierarchical representations and exploit frame-to-frame coherence for fast proximity queries. We describe a new overlap test, which is specialized for intersection of a line segment with an oriented bounding box for haptic simulation and takes 42-72 operations

The determination of intersection or contact points between objects in interference is not a simple task. It could be time-consuming in a computer application. Generally, some real time applications use sophisticated algorithms based on hierarchical structure to isolate the segments of contours

. The proposed condition is based on a technique for representing a friction cone as a line segment in a dual plane. This representation allows force-closure test to be formulated as the problem of intersection detection between a line segment and a convex polygon. The resulting geometric condition is presented

that the 4-connected planar graphs constitute a subclass of the intersection graphs of Z-shapes (i.e., a special case of B2-VPG). Additionally, we demonstrate that a B2-VPG representation of a planar graph can be constructed in O(n 3/2) time. We further show that the triangle-free planar graphs are contact

Abstract. Using structural geometric arguments, Whiteley showed that a line drawing is a correct projection of a spherical polyhedron if and only if it has a cross-section compatible with it. We here enlarge the class of drawings to which this test applies, including those of polyhedral disks, possibly with perforations. This extension is helpful, as it makes the test applicable to verify and reconstruct drawings from usual scenes with opaque objects. The presented results rely on geometric constructions, thus offering an alternative approach to line drawing interpretation, complementary to the algebraic-combinatorial treatment given in the classic work by Sugihara.

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