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On Balanced;-Contact Representations

by Stephane Durocher, Debajyoti Mondaly
"... 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 if their correspo ..."
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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

Tetrahedron Contact Graphs

by Md. Jawaherul, Alam Muriel, Dulieu Justin, Iwerks Joseph O’rourke
"... 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, ..."
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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,

The Maximal Clique and Colourability of Curve Contact Graphs

by Petr Hlineny
"... 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 are stud ..."
Abstract - Cited by 3 (3 self) - Add to MetaCart
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

Vertex Contact Graphs of Paths on a Grid

by Nieke Aerts, Stefan Felsner
"... Contact and intersection representations of graphs and particularly of planar graphs have been studied for decades. The by now best known result in the area may be the Koebe-Andreev-Thurston circle packing theorem. A more recent highlight in the area is a result of Chalopin and Gonçalves: every pla ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
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

Fast and Accurate Collision Detection for Haptic Interaction Using a Three Degree-of-Freedom Force-Feedback Device

by A. Gregory, M. C. Lin, S. Gottschalk, R. Taylor , 2000
"... We present a fast and accurate collision detection algorithm for haptic interaction with polygonal models. Given a model, we pre-compute a hybrid hierarchical representation, consisting of uniform grids (represented using a hash table) and trees of tight-fitting oriented bounding box trees (OBBTrees ..."
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(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

Oriented bounding boxes using multiresolution contours for fast interference detection of arbitrary geometry objects

by Luis A. Rivera Escriba, L. A. Rivera, Vania Vieira Estrela, Luiz Velho, V. V. Estrela, Paulo C. Carvalho, Vania V. Estrela - JOURNAL OF WSCG 2004 , 2004
"... 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 of o ..."
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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

Geometric Reformulation of 3-Fingered Force-Closure Condition

by Attawith Sudsang, Thanathorn Phoka
"... Abstract — This paper addresses the problem of testing whether three contact points form a 3-fingered force-closure grasp in two dimensions. In particular, assuming frictional point contacts, we present a new necessary and sufficient condition for three fingers to form a force-closure grasp. The pro ..."
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. 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

Planar graphs as VPG-graphs

by Steven Chaplick, Torsten Ueckerdt , 2013
"... A graph is Bk-VPG when it has an intersection representation by paths in a rectangular grid with at most k bends (turns). It is known that all planar graphs are B3-VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are B2-VPG. We also show that th ..."
Abstract - Cited by 5 (3 self) - Add to MetaCart
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

c ○ 2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands. Geometric Methods for Shape Recovery from Line Drawings of Polyhedra

by Lluís Ros, Federico Thomas
"... 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, possi ..."
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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.

Wireless Sensor Networking in Challenging Environments

by Mo Sha, Raj Jain, Jonathan Turner, Guoliang Xing, Mo Sha , 2014
"... This Dissertation is brought to you for free and open access by Washington University Open Scholarship. It has been accepted for inclusion in All Theses and Dissertations (ETDs) by an authorized administrator of Washington University Open Scholarship. For more information, please contact ..."
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This Dissertation is brought to you for free and open access by Washington University Open Scholarship. It has been accepted for inclusion in All Theses and Dissertations (ETDs) by an authorized administrator of Washington University Open Scholarship. For more information, please contact
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