In this paper the chordal graph structures of polynomial sets appearing in triangular decomposition in top-down style are studied when the input polynomial set to decompose has a chordal associated graph. In particular, we prove that the associated graph of one specific triangular set computed in any algorithm for triangular decomposition in top-down style is a subgraph of the chordal graph of ...

A triangular grid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional triangular grid. We show that the problem Hamiltonian Cycle is NP-complete for triangular grid graphs, while a hamiltonian cycle in connected, locally connected triangular grid graph can be found in polynomial time. 2000 Mathematics Subject Classification: 05C38 (05C45, 68Q25).

An attractive method for approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces is introduced. The main result is that the arbitrary given order derived vectors of a polynomial triangular surface converge uniformly to those of the approximated rational triangular Bézier surface as the elevated degree tends to infinity. The polynomial triangular surface is con...

This paper puts forward 3D model retrieval method based on normal-angle histogram. The method firstly makes the pretreatment for 3D model, and defines the calculation method of the normal at every vertex of the triangular mesh in 3D model and the included angle among the triangular meshes. Then it classifies the triangular mesh in accordance with the normal at three vertexes of the triangular m...

The hexagonal and the triangular grids are duals of each other. These two grids are the first and second ones in the family of triangular grids (we can call them as oneand two-planes triangular grids). This family comes from the mapping their points to Z3. Their symmetric properties are triangular. The next grid is the three-planes triangular grid, which looks like the mix of them. In this pape...

Mirizzi's syndrome is a rare complication of gallstone disease, that gallbladder lumen can lie alongside the common hepatic duct, resulting in inflammation and resultant bile duct stricture. Most cases are not identified preoperatively. Variations of the cystic duct and its point of union with the common hepatic duct are surgically important. Here, we present an unusual case of type I Mirizzi's...

Triangular B-splines are a new tool for modeling a broad class of objects defined over arbitrary, nonrectangular domains. They provide an elegant and unified representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additi...

Triangular B-splines are a new tool for modeling a broad class of objects deened over arbitrary, non-rectangular domains. They provide an elegant and uniied representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additio...

Background: Patients with cholestatic liver function tests and histological features of primary sclerosing cholangitis (PSC) but a normal cholangiogram are considered to have small duct PSC. The natural history of this condition is unknown. Methods: Thirty three patients with small duct PSC were identified among patients admitted for diagnostic workup of cholestatic liver function tests in one ...

OBJECTIVES We attempted to clarify the mechanism underlying lower bile duct stricture in autoimmune pancreatitis. METHODS Imaging and histologic finding of the bile duct were assessed for 73 patients with autoimmune pancreatitis to clarify whether IgG4-related biliary inflammation or pancreatic head swelling is associated with lower bile duct stricture. RESULTS Lower bile duct stricture was...