Results 1 
6 of
6
On the existence of a perfect matching for 4regular graphs derived from quadrilateral meshes. SCI Institute
, 2006
"... In 1891, Peterson [Pet91] proved that every 3regular bridgeless graph has a perfect matching. It is wellknown that the dual of a triangular mesh on a compact manifolds is a 3regular graph. M. Gopi and D. Eppstein [GE04] use Petersons theorem to solve the problem of constructing strips of triangle ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
In 1891, Peterson [Pet91] proved that every 3regular bridgeless graph has a perfect matching. It is wellknown that the dual of a triangular mesh on a compact manifolds is a 3regular graph. M. Gopi and D. Eppstein [GE04] use Petersons theorem to solve the problem of constructing strips of triangles from triangular meshes on a compact manifold. P. DiazGutierrez and M. Gopi [DG04] elaborate on the creation of strips of quadrilaterals when a perfect matching exists. In this paper, it is shown that the dual of a quadrilateral mesh on a 2dimensional compact manifold with an even number of quadrilaterals (which is a 4regular graph) also has a perfect matching. In general, however, not all 4regular graphs have a perfect matching. Indeed, a counterexample is given that is planar. 1
A Novel PageBased Data Structure for Interactive Walkthroughs
"... Given a data layout of a large walkthrough scene, we present a novel and simple spatial hierarchy on the diskpages of the layout that has notable advantages over a conventional spatial hierarchy on the scene geometry. Assume that each diskpage consists of a set of triangles whose bounding boxes ar ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Given a data layout of a large walkthrough scene, we present a novel and simple spatial hierarchy on the diskpages of the layout that has notable advantages over a conventional spatial hierarchy on the scene geometry. Assume that each diskpage consists of a set of triangles whose bounding boxes are computed. A spatial hierarchy of the walkthrough space is constructed, not with the given scene, but with the bounding boxes of diskpages. The leaf nodes of the spatialhierarchy refer directly to the page numbers of the pages of the bounding box it contains. We call this hierarchy on the pages as the diskpage hierarchy. We also propose a selfcontained diskpage format that would suit this data structure well. Further, we present a new cacheoblivious graphbased data layout algorithm called the 2factor layout that would preserve the proximity and orientation properties of the primitives in the layout. Walkthrough experiments have been conducted on a city scene consisting of over 110M triangles. Our system renders this scene on a laptop within a one pixel projection error at over 20 fps with simple texture substitution based simplification of distant objects, and with no explicit data/cache management.
An Algorithm for Computing Simple kFactors
"... A kfactor of graph G is defined as a kregular spanning subgraph of G. For instance, a 2factor of G is a set of cycles that span G. 2factors have multiple applications in Graph Theory, Computer Graphics, and Computational Geometry [5, 4, 6, 11]. We define a simple 2factor as a 2factor without d ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
A kfactor of graph G is defined as a kregular spanning subgraph of G. For instance, a 2factor of G is a set of cycles that span G. 2factors have multiple applications in Graph Theory, Computer Graphics, and Computational Geometry [5, 4, 6, 11]. We define a simple 2factor as a 2factor without degenerate cycles. In general, simple kfactors are defined as kregular spanning subgraphs where no edge is used more than once. We propose a new algorithm for computing simple kfactors for all values of k ≥ 2. 1
A Novel PageBased Data Structure for Interactive Walkthroughs
"... Given a data layout of a large walkthrough scene, we present a novel and simple spatial hierarchy on the diskpages of the layout that has notable advantages over a conventional spatial hierarchy on the scene geometry. Assume that each diskpage consists of a set of triangles whose bounding boxes ar ..."
Abstract
 Add to MetaCart
Given a data layout of a large walkthrough scene, we present a novel and simple spatial hierarchy on the diskpages of the layout that has notable advantages over a conventional spatial hierarchy on the scene geometry. Assume that each diskpage consists of a set of triangles whose bounding boxes are computed. A spatial hierarchy of the walkthrough space is constructed, not with the given scene, but with the bounding boxes of diskpages. The leaf nodes of the spatialhierarchy refer directly to the page numbers of the pages of the bounding box it contains. We call this hierarchy on the pages as the diskpage hierarchy. We also propose a selfcontained diskpage format that would suit this data structure well. Further, we present a new cacheoblivious graphbased data layout algorithm called the 2factor layout that would preserve the proximity and orientation properties of the primitives in the layout. Walkthrough experiments have been conducted on a city scene consisting of over 110M triangles. Our system renders this scene on a laptop within a one pixel projection error at over 20 fps with simple texture substitution based simplification of distant objects, and with no explicit data/cache management.
An Algorithm for Computing Simple kFactors
"... A kfactor of graph G is defined as a kregular spanning subgraph of G. For instance, a 2factor of G is a set of cycles that span G. 2factors have multiple applications in Graph Theory, Computer Graphics, and Computational Geometry [5, 4, 6, 14]. We define a simple 2factor as a 2factor without d ..."
Abstract
 Add to MetaCart
(Show Context)
A kfactor of graph G is defined as a kregular spanning subgraph of G. For instance, a 2factor of G is a set of cycles that span G. 2factors have multiple applications in Graph Theory, Computer Graphics, and Computational Geometry [5, 4, 6, 14]. We define a simple 2factor as a 2factor without degenerate cycles. In general, simple kfactors are defined as kregular spanning subgraphs where no edge is used more than once. We propose a new algorithm for computing simple kfactors for all values of k ≥ 2. Key words: graph algorithms, graph factors, kfactors, simple kfactors, 2factors 1.